Search Results for Bologna
Biographies
- Eustachio Manfredi (1674-1739)
- Born: 20 September 1674 in Bologna, Papal States (now Italy)
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- Died: 15 February 1739 in Bologna, Papal States (now Italy)
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- Eustachio Manfredi's father, Alfonso Manfredi, was a lawyer in Bologna.
- Alfonso, who came originally from Lugo, which is about 40 km east of Bologna, married Anna Maria Fiorini on 23 October 1670, and they had four sons and two daughters.
- They produced literary works aimed at the educated middle-class inhabitants of Bologna.
- After attending school at the Jesuit Convent of St Lucia, Eustachio studied at the Jesuit College in Bologna.
- By 1694 the group had expanded to include philosophers, mathematicians and anatomists not only from Bologna but also from surrounding towns.
- They had to find a larger place to meet and they met from that time on at the home of Jacopo Sandri, a professor of anatomy and medicine at Bologna University.
- In 1699 Manfredi was appointed as a public lecturer in mathematics at the University of Bologna.
- In particular his father had been forced to leave Bologna and the responsibility for the whole family had fallen on Manfredi.
- However, he was supported by Giovanni Giuseppe, the Marquis Orsi (1652-1733), a Senator of Bologna who was described by a contemporary as "one of the most knowledgeable men in Italy".
- From around 1700 Manfredi was also supported by Count Luigi Ferdinando Marsili (1658-1730), a soldier and naturalist who was engaged in military campaigns but, nevertheless, wished to create an academy in Bologna similar to the Royal Society in London and the Academy of Sciences in Paris.
- In 1704, while continuing to hold his lectureship in mathematics at the University of Bologna, he became head of the Collegio Montalto in Bologna (later San Luigi College), which was a college for the education of Jesuit priests.
- Giovanni Cassini, who had been professor in Bologna for many years, was by this time head of the Paris Observatory but kept in close contact with developments in Bologna.
- Following the building of the new Bologna Observatory, Manfredi carried out observations to calculate its precise latitude and longitude.
- These gave results consistent with others which had been made earlier in different parts of Bologna.
- The problem was that the Reno, a tributary of the river Po, was causing devastating floods between Bologna and Ferrara.
- Manfredi represented Bologna in the discussions which were set up between experts from the States of Mantua and of Venice in attempts to solve this problem.
- We have explained above how Manfredi founded the Accademia degli Inquieti, that became the Academy of Sciences of the Institute of Bologna in 1714.
- These include: Observations of the solar eclipse witnessed at Bologna on 14 September 1727 (read 16 January 1728); Observations of the moon, Venus and Saturn made at Bologna (read 16 January 1728); Observations of the eclipses of Jupiter's satellites (read 16 January 1728); Astronomical passage of a Lumen Boreale observed near Bologna March 14 1727 (read 16 May 1728); Observations of the lumen borealis seen at Bologna on 14 March 1727 (read 16 May 1728); Concerning Newton's work on optics (read 31 October 1728); Observations of lunar eclipse on 28 July 1729 (read 22 January 1729); Concerning Mr Bradley's theory about fixed stars (29 January 1729); Observations of a solar eclipse witnessed at Bologna (read 29 October 1730); Observations of the solar eclipse on 3 May 1734 (read 23 October 1735); Account of the conjunction of Mercury with the Sun observed at the Astronomical Observatory of the Institute of Bologna on 11 November 1736 drawn up by Eustachio Manfredi (read 13 January 1737).
- Manfredi died in Bologna and was buried in the family tomb in the church of Santa Maria Maddalena, in Via Zamboni formerly called San Donato Road.
- Ettore Bortolotti (1866-1947)
- Born: 6 March 1866 in Bologna, Kingdom of Sardinia (now Italy)
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- Died: 17 February 1947 in Bologna, Italy
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- Ettore Bortolotti studied under Pincherle in Bologna, graduating in 1889.
- In 1886-87 the first course on Galois theory to be given in Italy was put on at Bologna.
- The notes which Bortolotti took of that course have survived and are discussed in [',' L Martini, The first lectures in Italy on Galois theory : Bologna, 1886-1887, Historia Math.
- He became an assistant there and worked at Bologna until 1891.
- Bortolotti was Dean of the Faculty at Modena in 1913-19, then he was appointed professor of geometry at the University of Bologna where he remained for the rest of his life, retiring in 1936.
- He was an extremely patriotic man; in particular he loved Bologna and it must have been a real joy to him to be able to spend the final part of his career in the University of Bologna where he had begun his studies.
- First, to put his historical work in context it is useful to see the opinion of Panza in [',' M Panza, Ettore Bortolotti, historian of mathematics (Italian), Italian mathematics between the two world wars (Bologna, 1987), 293-305.','7] and also that of Dieudonne in his review of [',' M Panza, Ettore Bortolotti, historian of mathematics (Italian), Italian mathematics between the two world wars (Bologna, 1987), 293-305.','7]:-
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- But the author of the paper [',' M Panza, Ettore Bortolotti, historian of mathematics (Italian), Italian mathematics between the two world wars (Bologna, 1987), 293-305.','7] stresses how lopsided and unconvincing were many opinions of Bortolotti on the history of mathematics.
- They stemmed from his powerful nationalist feelings, which led him (long before fascism) to attribute in every case priority and leadership to Italian mathematicians (and more particularly to those who worked in Bologna), with a corresponding downgrading of the work of their contemporaries.
- The author of [',' M Panza, Ettore Bortolotti, historian of mathematics (Italian), Italian mathematics between the two world wars (Bologna, 1987), 293-305.','7] discusses several examples of this unfortunate tendency, usually supported by unjustified interpretations by Bortolotti of the papers he considered.
- Paolo Bonasoni was a professor at the University of Bologna during the late sixteenth century.
- His book Algebra geometrica Ⓣ, written around 1575, was unpublished and unknown until 1924 when it was discovered in the University of Bologna archives by Bortolotti.
- Salvatore Pincherle (1853-1936)
- Died: 10 July 1936 in Bologna, Italy
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- Maurizio studied medicine and was appointed Professor in the Pediatric Clinic at the University of Bologna in 1929.
- Graziano and Edvige had a daughter, Emma Senigaglia (1909-1991), who became a mathematician, studying for her doctorate at Bologna advised by Giuseppe Vitali.
- It was a post he only held for a few months for he was offered a similar chair at the University of Bologna.
- At Bologna, Pincherle became a colleague of Luigi Donati (1846-1932), who was appointed to Bologna in 1877, and Cesare Arzela who had been appointed to the chair of Infinitesimal Calculus in 1880.
- All three of these mathematicians were graduates of the Scuola Normale Superiore of Pisa and they quickly improved the department at Bologna which had somewhat lost its vigour [',' U Amaldi, Della Vita e delle Opere di Salvatore Pincherle, in Salvatore Pincherle, Opere Scelte, a cura della Unione Matematica Italiana 1 (Edizione Cremonese, Rome, 1954), 3-16.','9]:-
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- 153 (2003), 331-342.','18] (see also [',' F Mainardi and G Pagnini, The Role of Salvatore Pincherle in the Development of Fractional Calculus, in S Coen (ed.), Mathematicians in Bologna (Springer, Basel, 2012), 373-382.','17]) Francesco Mainardi and Gianni Pagnini discuss another very significant contribution by Pincherle:-
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- Universita di Bologna e Redatte per uso Degli Studenti Ⓣ.
- Universita di Bologna e Redatte per uso Degli Studenti by S Pincherle, Amer.
- He participated in the management of the teacher's college at Bologna and wrote a number of school level textbooks.
- The Unione Matematica Italiana (Italian Mathematical Union) was established in Bologna by Pincherle on 7 December 1922.
- He invited the Congress to Bologna for the 1928 Congress but it was decided to delay a decision on whether to accept.
- Bologna was accepted for the 1928 International Congress of Mathematicians with Pincherle as president.
- Basically he achieved this by having the invitation to the 1928 Congress coming from the University of Bologna and inviting mathematicians directly.
- The Bologna Congress stands as Pincherle's personal 'tour de force'.
- Pincherle was awarded the Sacchetti prize by the city of Bologna when he was appointed to the chair there in 1928.
- He was elected to the National Academy of Sciences of Italy (the "Academy of Forty"), the Reale Accademia delle Scienze of the Institute of Bologna, the Reale Accademia delle Scienze of the Institute of Turin, the Reale Istituto Lombardo di Scienze e Lettere, the Reale Istituto Veneto, the Accademia Pontaniana of Naples, the Royal Society of Edinburgh, the Bavarian Academy of Sciences, the Academy of Science of Coimbra, the Helvetic Society of Sciences, and made an honorary member of the Moscow Mathematical Society and the Calcutta Mathematical Society.
- He was frequently dean of the Faculty of Sciences at Bologna and president of the Academy of Sciences of Bologna.
- Finally, we note that in 1925 the "Manifesto of Fascist Intellectuals", establishing the political and cultural foundations of Fascism, was published in Bologna.
- Gabriele Manfredi (1681-1761)
- Born: 25 March 1681 in Bologna, Papal States (now Italy)
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- Died: 5 October 1761 in Bologna, Papal States (now Italy)
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- Gabriele Manfredi's father, Alfonso Manfredi, was a lawyer in Bologna.
- Alfonso, who came originally from Lugo, which is about 40 km east of Bologna, married Anna Maria Fiorini and they had four sons and two daughters.
- They produced literary works aimed at the educated middle-class inhabitants of Bologna.
- Gabriele Manfredi also studied with Guglielmini but, after his brother Eustachio turned to astronomy and Guglielmini left Bologna to move to Padua in 1699, Gabriele carried on studying mathematics on his own.
- Bianchini was a historian, antiquarian and astronomer who, at this time, had been commissioned by Pope Clement XI to construct a sundial and meridian line in Santa Maria degli Angeli in Rome, modelled on one that Giovanni Cassini had designed for the Basilica of San Petronio in Bologna.
- In the spring of 1706, Manfredi left Rome and returned to Bologna where he published his most famous work, De constructione aequationum differentialium primi gradus Ⓣ (Bologna 1707), the first monograph in the world dedicated to the study of differential equations [',' L Pepe, Gabriele Manfredi, in Dizionario Biografico degli Italiani 68 (2007).','4]:-
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- Manfredi became a chancellor in the Senate of Bologna in 1708, and continued to hold a position in the Senate until his retirement in 1752.
- He also taught mathematics at the University of Bologna, where he was appointed as a professor in 1720.
- Between 1727 and 1761, Manfredi had fifteen memoirs read to the Bologna Institute of the Accademia delle scienze.
- The problem that he faced was that the river Reno, a tributary of the river Po, was causing devastating floods between Bologna and Ferrara.
- Eustachio had represented Bologna in the discussions between experts from the States of Mantua and of Venice in attempts to solve this problem.
- He died in Bologna and was buried in the family tomb in the church of Santa Maria Maddalena, in Via Zamboni formerly called San Donato Road.
- Laura Bassi (1711-1778)
- Born: 31 October 1711 in Bologna, Papal States (now Italy)
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- Died: 20 February 1778 in Bologna, Papal States (now Italy)
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- Tacconi was very impressed with the abilities of his pupil and through him she began to gain a reputation among the circle of scholars in Bologna.
- He had been born in Bologna and awarded a doctorate in theology and law by the University of Rome.
- He was elevated to cardinal in 1728, and in 1731 he returned to Bologna where he was elevated to archbishop by Pope Clement XII.
- Lambertini became Bassi's patron and, to show off his protege, set up a debate between her and four professors from Bologna on 17 April 1732.
- The debate was held in the grand Palazzo Pubblico in Bologna and Bassi defended forty-nine philosophical theses.
- Her success led to the award of a doctorate in philosophy in May 1732 and, following this, an appointment as Reader in Philosophy allowed her to lecture at the University of Bologna.
- In 1738 Bassi married Giovanni Giuseppe Veratti, a lecturer in science at the University of Bologna.
- The marriage was considered wrong by many in Bologna who felt, in the same spirit as fellows in Colleges at the University of Cambridge could not marry and continue to hold their fellowships, Bassi should not be allowed to marry and continue to hold a lecturing position.
- In 1739 she requested that the University of Bologna increase her teaching duties but, despite support from Lambertini and Flamino Scarselli, the secretary to the Bolognese ambassador at the papal court, all she was granted was funds for equipment to conduct physics experiments in her home.
- Of 28 papers by Bassi which are held in the Bologna Academy of Sciences in Bologna, thirteen are on physics, eleven are on hydraulics, two are on mathematics, one is on mechanics, one is on technology, and one is on chemistry.
- Although many of her papers remain in manuscript, having never been published, one of her papers on mechanics De problemate quodam mechanico Ⓣ and one on hydraulics De problemate quodam hydrometrico Ⓣ were published in the Commentaries of the Bologna Institute in 1757.
- The greatest honour given to Bassi was in 1776 when she was appointed to the Chair of Experimental Physics at Bologna.
- Scipione del Ferro (1465-1526)
- Born: 6 February 1465 in Bologna (now Italy)
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- Died: 5 November 1526 in Bologna, Papal States (now Italy)
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- Of Scipione del Ferro's education little is known but it is probable that it was at the University of Bologna which was founded in the 11th century and so was a long established and famous university four hundred years before del Ferro was born.
- We know that del Ferro was appointed as a lecturer in arithmetic and geometry at the University of Bologna in 1496 and that he retained this post for the rest of his life.
- Hannibal Nave took over del Ferro's lecturing duties at the University of Bologna in 1526 and also his name since he adopted the name of dalla Nave alias dal Ferro.
- Nave still had the notebook in 1543, for in that year Cardan and Ferrari travelled to Bologna to see him and his father-in-law's notebook for Ferrari records this in his writings.
- There has been much conjecture as to whether del Ferro came to work on the solution to cubic equations as a result of a visit which Pacioli made to Bologna.
- Pacioli taught at the University of Bologna during 1501-02 and discussed mathematical problems with del Ferro at that time.
- Some time after Pacioli's visit to Bologna, del Ferro solved one of the two cases of this classic problem (but as we mention below, he may have solved both cases).
- Four years ago when Cardano was going to Florence and I accompanied him, we saw at Bologna Hannibal della Nave, a clever and humane man who showed us a little book in the hand of Scipione del Ferro, his father-in-law, written a long time ago, in which that discovery [solution of cubic equations] was elegantly and learnedly presented.
- Scipione Ferro of Bologna, almost thirty years ago, discovered the solution of the cube and things equal to a number [which in today's notation is the case x3 + mx = n], a really beautiful and admirable accomplishment.
- Pompeo Bolognetti, who lectured at the University of Bologna on mathematics from 1554 to 1568, also had access to the original solution by del Ferro as well as the solution as given by Cardan in Ars Magna which had been published by then.
- Around 1925, Bortolotti (see [',' E Bortolotti, La Storia della Matematica nella Universita di Bologna (Bologna, 1974).','2]) examined sixteenth century manuscripts reproducing work by Bolognetti, Cardan and Bombelli.
- Francesco Grimaldi (1618-1663)
- Born: 2 April 1618 in Bologna, Papal States (now Italy)
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- Died: 28 December 1663 in Bologna, Papal States (now Italy)
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- His father, Paride Grimaldi, was a silk merchant of noble birth who had moved to Bologna in 1589.
- He married in Bologna, but the couple were childless when his wife died.
- However, he was in Parma for less than a year before he was transferred to Bologna to complete his first year of study of philosophy.
- His second year studying philosophy,1636-37, was spent at Ferrara before he returned to Bologna to finish the three year course in session 1637-38.
- Having completed the three year philosophy course, he taught rhetoric and humanities in the College of Santa Lucia at Bologna for four years from 1638 to 1642.
- Grimaldi was taught by Giovanni Battista Riccioli in Parma in 1635 and both had moved to Bologna at the same time in 1636.
- However, it was when Grimaldi returned to Bologna and was teaching there in 1640 that he began assisting Riccioli with experiments.
- Grimaldi and Riccioli's astronomical observations had been made in an observatory set up at the College of Santa Lucia in Bologna.
- Another project on which Grimaldi worked was a survey, using triangulation, to determine a meridian line for Bologna.
- Again he collaborated on this with Riccioli but, in addition, he was assisted by Ovidio Montalbini (1601-1672), a professor at Bologna University and the custodian of its science museum, and Giovanni Domenico Cassini, who had been appointed as professor of mathematics at the University of Bologna in 1650 following the death of Bonaventura Cavalieri.
- Giuseppe Vitali (1875-1932)
- Died: 29 February 1932 in Bologna, Italy
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- After graduating from the Dante Alighieri High School, Vitali studied for two years at the University of Bologna, beginning in the autumn of 1895.
- His main teachers at Bologna were Cesare Arzela, who had held the chair of Higher Analysis, and Federigo Enriques who taught at Bologna on a temporary basis from 1894, but held the chair of projective and descriptive geometry from 1896.
- Maria Teresa Borgato writes [',' M T Borgato, Giuseppe Vitali: Real and Complex Analysis and Differential Geometry, in Mathematicians in Bologna 1861-1960 (Springer, New York, 2012), 31-55.','4]:-
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- Vitali, however, kept in contact with his mentors, and Arzela in particular remained a constant point of reference for him, through exchange of letters and also meetings above all during the holiday periods (Vitali returned to Bologna during his teaching years in Voghera, and Arzela, in his turn, spent long periods in Santo Stefano Magra in Liguria).
- He always maintained a friendship with Enriques, who had followed his transfer from the University of Bologna to the Scuola Normale Superiore of Pisa, but his lifelong friend was Guido Fubini, who had been a fellow student in Pisa.
- Vitali published a remarkable volume of mathematics over these years and was an invited speaker at the International Congress of Mathematicians held in Bologna in September 1928, giving the lecture Rapporti inattesi su alcuni rami della matematica Ⓣ.
- In 1930 Vitali moved to the chair of mathematics at the University of Bologna.
- Here is an extract from his inaugural lecture at Bologna, given on 4 December 1930 (see [',' C S Roero and M Guillemot, Tullio Viola and his Maestri in Bologna: Giuseppe Vitali, Leonida Tonelli and Beppo Levi, in Mathematicians in Bologna 1861-1960 (Springer, New York, 2012), 383-413.','10]):-
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- Viola writes about his teacher, fifty years after Vitali died (see [',' T Viola, Ricordo di Giuseppe Vitali a 50 anni dalla sua scomparsa, in Atti del Convegno La Storia delle Matematiche in Italia, Cagliari 1982 (Monograf, Bologna, 1984), 535-544.','14]):-
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- Maria Teresa Borgato gives this summary of his contributions [',' M T Borgato, Giuseppe Vitali: Real and Complex Analysis and Differential Geometry, in Mathematicians in Bologna 1861-1960 (Springer, New York, 2012), 31-55.','4]:-
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- Viola recalled the moment when he was in Paris and he heard of Vitali's death (see [',' T Viola, Ricordo di Giuseppe Vitali a 50 anni dalla sua scomparsa, in Atti del Convegno La Storia delle Matematiche in Italia, Cagliari 1982 (Monograf, Bologna, 1984), 535-544.','14]):-
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- I heard people whispering "Vitali est mort!" A few days later I received the painful confirmation directly from Bologna: the Maestro had fallen, struck down suddenly while walking arm in arm with his colleague Ettore Bortolotti, under the porticos of that learned city in which I had spent the most beautiful years of the university studies, and in which were laid, and lie still, the remains of those who gave me life.
- Vitali was honoured with election to the Academy of Sciences of Turin in 1928, to the Accademia Nazionale dei Lincei in 1930, and to the Academy of Bologna in 1931.
- Bonaventura Cavalieri (1598-1647)
- Died: 30 November 1647 in Bologna, Papal States (now Italy)
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- In 1619 Cavalieri applied for the chair of mathematics in Bologna, which had become vacant following the death of Giovanni Antonio Magini, but was not successful since he was considered too young for a position of this seniority.
- In 1629 Cavalieri was appointed to the chair of mathematics at Bologna.
- in 1629, wrote to Cesare Marsili, a gentleman of Bologna and member of the Accademia dei Lincei, who had been commissioned to find a new lecturer in mathematics.
- In his letter, Galileo said of Cavalieri, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry." In support of his application to the Bologna position, Cavalieri sent Marsili his geometry manuscript and a small treatise on conic sections and their applications in optics.
- The chair of mathematics at Bologna was not the only position he received for he was also appointed prior of the Jesuati convent in Bologna attached to the Church of Santa Maria della Mascarella.
- He published eleven books during his eighteen years in Bologna.
- However, his health deteriorated around the time of his appointment to Bologna, and he suffered from problems with his legs which persisted throughout the rest of his life.
- In fact Cavalieri's appointment to Bologna had, in the first instance, been for a 3-year trial period but, as we explain below, it was extended.
- Cavalieri's geometry manuscript which had been a factor in his appointment to Bologna, although completed in December 1627, was not published until 1635.
- We mentioned above that his appointment to Bologna had been initially for a 3-year period.
- He studied with Cavalieri at Bologna at a time when Cavalieri was quite old and suffering from arthritis.
- Returning to Bologna, life became increasingly difficult for Cavalieri.
- He had the chance to leave Bologna when he was offered the chair of mathematics at Pisa, but he turned it down.
- Cardinal Federico Borromeo offered him a position at the Biblioteca Ambrosiana in Milan, but again Cavalieri chose to remain in Bologna.
- He was buried in the church of Santa Maria della Mascarella in Bologna.
- Pietro Cataldi (1548-1626)
- Born: 15 April 1548 in Bologna, Papal States (now Italy)
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- Died: 11 February 1626 in Bologna, Papal States (now Italy)
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- Pietro Cataldi's father was Paolo Cataldi who, like his son, was born in Bologna.
- Pietro was educated in Bologna although he does not seem to have attended the university there; rather he began teaching mathematics at the age of seventeen.
- He remained there until 1584 and then returned to Bologna where he was awarded a doctorate in philosophy and in medicine.
- He taught mathematics and astronomy at the Studio di Bologna for almost forty years until his death.
- This work was dedicated to the Senate of Bologna, but it is believed that he published it at his own expense.
- Among his other works were Transformatione geometrica (1611), dedicated to the Grand Duke Cosimo II, and a book which studied problems of the range of artillery which included tables on the rising of the sun and the time of midday for Bologna (1613).
- Bologna, 1612] claims a place as beginning with the quadrature of Pellegrino Borello of Reggio, who will have the circle to be exactly 3 diameters and 69/484 of a diameter.
- Cataldi tried, without success, to set up an academy of mathematics in Bologna.
- Giovanni Magini (1555-1617)
- Died: 11 February 1617 in Bologna, Papal States (now Italy)
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- Magini completed his education at the University of Bologna, receiving a doctorate in philosophy in 1579.
- Egnatio Danti held the chair of mathematics at the University of Bologna and, following his death in October 1586, a competition was announced to fill the chair.
- Two quadrants exit, one with the inscription "Giovanni Antonio Magini of Padua designed this in Bologna in the year 1592", the other is dated 1595 and inscribed "Giovanni Antonio Magini Professor of Mathematics in the University of Bologna had this made".
- The chair of mathematics at Bologna saw Magini receive a salary of 1000 lire which was doubled to 2000 lire in 1597.
- He had triumphed over Galileo in the competition for the chair at Bologna but he also strongly opposed Galileo's views [',' A van Helden, Telescopes and Authority from Galileo to Cassini, Osiris 9 (1994), 8-29.','11]:-
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- During the Easter holidays of 1610, Galileo stopped in Bologna on his way from Padua to Florence to stay at the house of his colleague Giovanni Antonio Magini ..
- Many in Bologna, including Magini, were sceptical of Galileo's discoveries, and therefore an opportunity presented itself for a demonstration.
- On 15 March 1595 Magini published a map of the Bologna region and wrote in the dedication (see for example [',' T Ashby, Review: L’ ’Italia’ di Giovanni Magini e la Cartografia dell’ Italia nei secoli xvi.
- Inasmuch as I desire to publish a complete atlas of Italy, showing, besides the provinces, the territories of each city, I have decided to publish first this map of the territory of Bologna ..
- [The Bologna map] was soon followed by other maps, and in two years he had the greater part of the maps of North Italy already engraved, and some of them published.
- They were apparently sold separately and are extremely rare in this state; for, being unable to obtain material for his maps of Southern Italy, he started correcting and revising what he had already done, publishing a new map of the territory of Bologna in two sheets in 1599.
- The printing at last began in Bologna at the end of 1616; but Magini's death delayed the appearance of the work until 1620, when his son Fabio, who was not fifteen when his father died, finally brought it out.
- Finally, let us note that one of the main sources of biographical information about Magini is his correspondence with leading scientists which was edited and published by Antonio Favaro in 1886 (see [',' A Favaro, Carteggio inedito di Ticone Brahe, Giovanni Keplero e di altri celebri astronomi e matematici dei secoli XVI e XVII con Giovanni Antonio Magini (Bologna, 1886).','3]).
- Pietro Mengoli (1626-1686)
- Born: 1626 in Bologna, Papal States (now Italy)
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- Died: 1686 in Bologna, Papal States (now Italy)
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- Pietro Mengoli was taught mathematics by Cavalieri at the University of Bologna before he himself taught at Bologna from 1648.
- While he taught he studied for a doctorate in philosophy which was awarded by the University of Bologna in 1650.
- Continuing to study while he held chairs of mathematics, three years later he obtained a second doctorate in civil and canon law from Bologna.
- After Cavalieri died in November 1647, Mengoli had been appointed to his chair at the University of Bologna.
- Mengoli held a number of chairs at the University of Bologna where he taught all his life.
- In addition to these chairs he was also a priest in the parish of Santa Maria Maddelena in Bologna from 1660.
- Mengoli used infinite series to good effect in Novae quadraturae arithmeticae, seu de additione fractionum Ⓣ published in Bologna in 1650, developing ideas which had first been investigated by Cataldi.
- Cesare Arzelà (1847-1912)
- During this year [',' L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.','6]:-
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- Arzela only taught at Palermo for two years for, having entered a competition for a professorship at the University of Bologna, he was appointed as professor of Infinitesimal Calculus in 1880.
- In 1884 he became a full professor at Bologna when he was appointed to the Chair of Higher Analysis.
- Salvatore Pincherle was appointed as a professor at the University of Bologna in 1881 so the department was greatly strengthened by these appointments and it was only due to them that Bologna could award degrees in mathematics [',' L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.','6]:-
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- During the 1870s, students at Bologna could not obtain a degree in mathematics because of the lack of professors capable of teaching the high-level courses of the last two years of the curriculum.
- This change resulted from the addition of excellent professors to the faculty with the express objective of bringing Bologna's mathematics teaching up to international standards.
- The two new professors undertook research in analysis, Arzela concentrating on the theory of functions of a real variable while Pincherle concentrated on analytic functions using the approach by Weierstrass [',' L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.','6]:-
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- The interesting papers [',' L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.','6] and [',' L Martini, An episode in the evolution of a mathematical community: the case of Cesare Arzela at Bologna, in Mathematics unbound: the evolution of an international mathematical research community, 1800-1945, Charlottesville, VA, 1999 (Amer.
- Soc., Providence, RI, 2002), 165-178.','7] by Laura Martini, discuss a course on Galois theory given by Arzela at the University of Bologna in session 1886-87.
- The book by Netto clearly had clearly made the biggest impression on Arzela who [',' L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.','6]:-
.
- Since details of Ruffini's proofs were not widely known or available when Arzela gave his course, Martini is led to conclude [',' L Martini, An episode in the evolution of a mathematical community: the case of Cesare Arzela at Bologna, in Mathematics unbound: the evolution of an international mathematical research community, 1800-1945, Charlottesville, VA, 1999 (Amer.
- It is possible that Arzela had read Ruffini's first proof which, after all, had been published privately in Bologna and which was well-known to several of Ruffini's Italian contemporaries in mathematics.
- We mentioned above Arzela's school text which he wrote in 1880 but this is not the only school or undergraduate text he wrote [',' L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.','6]:-
.
- He also wrote 'Complementi di algebra elementare' Ⓣ (1896) and (with G Ingrami) 'Aritmetica razionale' Ⓣ (1894) for the secondary school audience in addition to the university-level text, 'Lezioni di calcolo infinitesimale' Ⓣ (1901-06), which encompasses the lectures on infinitesimal calculus given at the University of Bologna beginning in the academic year 1880-1881.
- We have mentioned that Salvatore Pincherle was a colleague of Arzela's at the University of Bologna but we should also mention that Federigo Enriques became a colleague in 1896.
- Among the students that Arzela taught at Bologna who became leading mathematicians, in addition to Bortolotti who we mentioned above, we should add the names of Leonida Tonelli and Giuseppe Vitali.
- Lodovico Ferrari (1522-1565)
- Born: 2 February 1522 in Bologna, Papal States (now Italy)
.
- Died: 5 October 1565 in Bologna, Papal States (now Italy)
.
- Lodovico Ferrari's grandfather, Bartholomew Ferrari, was forced to leave his home town of Milan and settled in Bologna.
- Despairing of ever publishing their ground breaking work, Cardan and Ferrari travelled to Bologna to call upon their mathematical colleague, Annibale della Nave, who had been appointed there on the death of Scipione del Ferro.
- He moved back to his home town of Bologna where he lived with his widowed sister Maddalena, and was called to a professorship of mathematics at the University of Bologna in 1565 but, sadly, Ferrari died later that year.
- Giovanni Battista Riccioli (1598-1671)
- Died: 25 June 1671 in Bologna (now Italy)
.
- He only spent one more year in Parma before being sent to Bologna in 1636 where he taught for the rest of his career.
- During this year in Parma, Riccioli taught Francesco Maria Grimaldi and after the two moved to Bologna in 1636 they did much work together.
- In order to make accurate astronomical observations Riccioli, with Grimaldi's assistance, set up an observatory at the College of Santa Lucia in Bologna which [',' A Dinis, Giovanni Battista Riccioli and the science of his time, in Mordechai Feingold (ed.), Jesuit science and the republic of letters (Transform.
- Another project on which Riccioli was assisted by Grimaldi was a survey, using triangulation, undertaken to determine a meridian line for Bologna.
- In addition to Grimaldi, he was also assisted by Ovidio Montalbini (1601-1672), a professor at Bologna University and the custodian of its science museum, and Giovanni Domenico Cassini, who had been appointed as professor of mathematics at the University of Bologna in 1650 following the death of Bonaventura Cavalieri.
- However, Riccioli went ahead and published the papal infallibility book with an altered permission to print, thus angering the Dominican inquisitor at Bologna.
- Throughout his life, Riccioli corresponded with many leading scientists, for example: Johannes Hevelius, the Polish astronomer living in Danzig, now Gdańsk; Christiaan Huygens; Giovanni Domenico Cassini, who had learnt much from Riccioli while in Bologna; and Athanasius Kircher, the German Jesuit priest and scholar who lived in Rome from 1634 onwards and acted in a similar way to Mersenne in corresponding with a wide range of scholars.
- Enrico Bompiani (1889-1975)
- This is not surprising if one considers the description of Gerbaldi by Renato Calapso, the son of Gerbaldi's assistant Pasquale Calapso [',' C Ciliberto and E S Del Colombo, Enrico Bompiani: The Years in Bologna, in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, Basel, 2012), 143-177.','7]:-
.
- Before he had made a final decision on accepting the School of Architecture chair, he was offered a chair of projective and descriptive geometry at Bologna which had become vacant since Federigo Enriques had just left Bologna to take up a chair in La Sapienza University of Rome.
- The Faculty of Science at Bologna had agreed to appoint him at a meeting on 23 October 1923 when they made the following assessment (see for example [',' Enrico Bompiani (Italian), Accad.
- This position looked very attractive, not least since Enriques had gone from Bologna to Rome, so it seemed the right stepping stone for Bompiani in his quest for a chair at the University of Rome.
- However, shortly after accepting the Bologna chair, his life was complicated by the University of Milan making him a financially tempting offer of a chair there.
- Bompiani took this advice and, after his appointment in 1923, spent the next three years in Bologna.
- In 1923-24 Bompiani taught Riemannian geometry and absolute differential calculus at Bologna and, in the following year, first order differential equations.
- Bompiani's appointment to Bologna was to an extraordinary chair and he had the right to seek an ordinary professorship after three years.
- Enrico Bompiani, ordinary professor of Projective and Descriptive Geometry at the University of Bologna, developed over the last fifteen years, with a strong commitment and strenuous work, a coherent research project on various topics of metric and projective differential geometry, following the viewpoint of Monge, the founder of descriptive geometry.
- Bompiani's value is universally well known, his teaching ability makes clear why our faculty decided to propose him for the vacant chair of Descriptive Geometry, which is a part of the discipline taught by him in Bologna.
- He was also elected a member of: the Academy of Sciences of the Institute of Bologna; the Academy of Romania; the Lombard Institute of Sciences, Letters and Arts; the Academy of Sciences of Turin; the Society of Sciences of Liege; the Austrian Academy of Sciences; and the Royal Belgium Academy of Science.
- He was awarded an honorary degree from the universities of Groningen (1964), Bologna (1966) and Jassy (1970).
- Gianfranco Cimmino (1908-1989)
- Died: 30 May 1989 in Bologna, Italy
.
- These four assistants are referred to as "Mauro Picone's four musketeers" by Scorza Dragoni in his obituary of Miranda [',' M Benzi, Gianfranco Cimmino’s contributions to numerical mathematics, Seminario di Analisi Matematica, Dipartimento di Matematica, dell’Universita di Bologna, Ciclo di Conferenze in Ricordo di Gianfranco Cimmino, Marzo-Maggio 2004 (Tecnoprint, Bologna, 2005), 87-109.','4]:-
.
- However, he did not remain long at Cagliari for, in November 1939, he moved to Bologna when appointed to the chair of Mathematical Analysis at the University.
- From 1965 to 1972 he was Dean of the Faculty of Mathematical, Physical and Natural Sciences of the University of Bologna.
- However, as Michele Benzi points out in [',' M Benzi, Gianfranco Cimmino’s contributions to numerical mathematics, Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, USA (5 January 2004).','3] (and [',' M Benzi, Gianfranco Cimmino’s contributions to numerical mathematics, Seminario di Analisi Matematica, Dipartimento di Matematica, dell’Universita di Bologna, Ciclo di Conferenze in Ricordo di Gianfranco Cimmino, Marzo-Maggio 2004 (Tecnoprint, Bologna, 2005), 87-109.','4]), it was his work on numerical analysis, particularly the 1938 paper we mentioned above, that:-
.
- He was awarded the Gualtiero Sacchetti prize from the city of Bologna in 1964-65 [Gualtiero Sacchetti (1836-1917) was an engineer and Senator of the Kingdom of Italy].
- He was elected a member of the Academy of Sciences of the Institute of Bologna, of the National Academy of Lincei (in 1969), of the National Academy of Sciences, Arts and Literature of Modena, and of the National Society of Sciences, Arts and Literature of Naples.
- Alfonso Del Re (1859-1921)
- This was won by Domenico Montesano, who had previously held a chair in Bologna, with 45/50 points.
- When Domenico Montesano won the competition for the chair at Naples in 1893, he moved from the University of Bologna leaving vacant the extraordinary professorship in descriptive and projective geometry there.
- What followed was a drawn out battle for the position which is now known as the "Bologna Affair." Given the results of the two earlier competitions, Del Re and Pieri were considered the leading candidates.
- The faculty at Bologna, encouraged by Pincherle, decided that they wished to appoint Pieri without a competition.
- The minister of education, however, did not approve Pieri's appointment, telling the Faculty at Bologna that they had to hold a competition and make a temporary appointment while this was taking place.
- With no competition announced, Del Re made a request to the minister of education that he be transferred from the University of Modena to Bologna for family reasons.
- Since by this time Del Re held a full chair in Modena and was requesting a move to an extraordinary position at Bologna, this seemed a strong request.
- The Faculty at Bologna repeatedly requested the minister to hold a competition but no competition was held.
- Enriques, keen to remain at Bologna, asked Castelnuovo to intervene and make sure the minister did not agree to Del Re's request.
- With no competition taking place, the Faculty at Bologna reappointed Enriques for another temporary year in January 1895.
- The Faculty at Bologna now split with Arzela favouring Del Re's transfer with Pincherle and others opposed.
- Del Re was arguing that he needed to relocate his family to Bologna.
- The "Bologna Affair" ended in 1896 when the minister resigned after a crisis following the Battle of Adwa, and a new minister was appointed who immediately opened a competition.
- Rafael Bombelli (1526-1572)
- Born: January 1526 in Bologna, Papal States (now Italy)
.
- The Bentivoglio family ruled over Bologna from 1443.
- Sante Bentivoglio was "signore" (meaning lord) of Bologna from 1443 and he was succeeded by Giovanni II Bentivoglio who improved the city of Bologna, in particular developing its waterways.
- The Mazzoli family were supporters of the Bentivoglio family but their fortunes changed when Pope Julius II took control of Bologna in 1506, driving the Bentivoglio family into exile.
- Antonio Mazzoli was able to return to live in Bologna.
- Scipione del Ferro, the first to solve the cubic equation was the professor at Bologna, Bombelli's home town, but del Ferro died the year that Bombelli was born.
- In 1923, however, Bombelli's manuscript was discovered in a library in Bologna by Bortolotti.
- Lamberto Cesari (1910-1990)
- Born: 23 September 1910 in Bologna, Italy
.
- His important discoveries during this period are discussed in [',' D Graffi, On the contributions of Lamberto Cesari to applied mathematics, in Nonlinear analysis and optimization, Bologna, 1982, Lecture Notes in Math.
- The Cesaris left Pisa in 1942 when Lamberto was appointed to the University of Bologna.
- Again during these war years spent in Bologna they carried out humanitarian work.
- He was appointed as Professor of Mathematical Analysis at the University of Bologna in 1947 after winning a competition for the chair.
- Cesari received many honours including election to the Accademia dei Lincei in Rome and the Academies of Bologna, of Modena and of Milan.
- The University of Texas organised a conference in his honour in 1980 and, two years later, the University of Bologna organised an international conference in his honour.
- Giovanni Cassini (1625-1712)
- In 1644 the Marquis Cornelio Malvasia, who was a senator from Bologna with a great interest in astrology, invited Cassini to Bologna.
- In 1650, Cassini became professor of mathematics and astronomy at the University of Bologna, filling the chair which had been vacant since the death of Cavalieri at the end of November 1647.
- This appointment came about through the support of the Marquis Malvasia whose important position in Bologna gave him considerable influence in naming Cavalieri's successor.
- One of Cassini's predecessor's as professor of mathematics and astronomy at Bologna had been Egnatio Danti who had been appointed in 1576.
- Danti had built a gnomon at the Church of San Petronio in Bologna, one of the largest Christian churches ever built.
- The church of San Petronio had mostly been built between 1445 and 1525, but work continued on extending it and not long before Cassini arrived in Bologna further building work had made Danti's gnomon unusable [',' R Taton, Biography in Dictionary of Scientific Biography (New York 1970-1990).
- He was an expert in hydraulics and engineering and as such was consulted regarding the dispute of 1657 between Bologna and Ferrara on the course of the River Reno.
- However, Cassini preferred to keep his post as professor of mathematics and astronomy at Bologna where he taught when not undertaking Papal duties.
- The senate of Bologna and Pope Clement IX agreed to the trip which they believed would be a short one of at most two years.
- He took his eighteen year old son Jacques Cassini with him and they made numerous geodesic observations, as well as returning to Bologna where they repaired the gnomon at the Church of San Petronio in Bologna which Cassini had designed nearly thirty years before.
- Federigo Enriques (1871-1946)
- An extraordinary professorship (called professor straordinario) in descriptive and projective geometry became vacant at the University of Bologna when Domenico Montesano left Bologna to take up a chair at Naples in 1893.
- In either case, Enriques would be a stronger candidate than he would be that year for straordinario at Bologna.
- Volterra replied that Arzela had written to him from Bologna referring to a possible incaricato position; and Volterra suggested that Enriques go to Bologna to talk with Pincherle and Arzela.
- The Bologna faculty agreed to appoint Pieri without a competition and it appeared that it would be a formality that the minister of education would take the advice of the Faculty of Bologna and confirm Pieri's appointment.
- The new minister of education did not approve Pieri's appointment, telling the Faculty at Bologna that they had to hold a competition and make a temporary appointment while this was taking place.
- The competition for the permanent Bologna post did not take place until October 1896; Enriques was appointed to the chair of descriptive and projective geometry with Pieri coming a close second.
- During that time he organised the fourth international congress of philosophy in Bologna in 1911.
- He remained at Bologna until 1922 when he was called to Rome to teach complementary mathematics, a new course designed for high school mathematics teachers.
- As a teacher, Enriques loved nothing better than to engage in his own leisurely peripatetic conversations with students, in the public gardens in Bologna or under its arcades after class.
- Mario Pieri (1860-1913)
- In 1876 Mario entered the Royal Technical Institute in Bologna.
- His elder brother Silvio was undertaking postgraduate work at the University of Bologna on literature and philology at this time and Mario lived with his brother who took on the role of being his guardian and mentor.
- A decision was taken that he would spend one year at the University of Bologna so he could continue to live with Silvio (who had one more year of study there).
- He entered the University of Bologna in 1880, having had the fees waived, taking the courses on 'Projective geometry' and 'Design for projective geometry' with Pietro Boschi.
- His talents for mathematics were quickly spotted by Salvatore Pincherle, who took up the chair of mathematics at Bologna in 1881, when he examined Pieri in June of that year.
- The chair at Bologna was left vacant when Montesano left to take up the chair at Naples.
- I knew already the outcome, rather flattering to you, of the competitions at Naples and Turin, and would be quite happy if, having had you as student in Bologna, it should be possible to have you as colleague.
- Pincherle hoped that he could appoint Pieri without holding a competition and, on 18 November 1893, Augusto Righi contacted Pieri with the news that the Faculty at Bologna had approved his appointment.
- It appeared that it was a formality that the minister of education took the advice of the Faculty of Bologna and would confirm Pieri's appointment but the government became embroiled in a scandal and the minister of education resigned.
- The new minister of education did not approve Pieri's appointment, telling the Faculty at Bologna that they had to hold a competition and make a temporary appointment while this was taking place.
- The competition for the permanent Bologna post did not take place until October 1896; Enriques was appointed with Pieri coming a close second.
- Vincenzo Riccati (1707-1775)
- From the age of ten he studied at the Jesuit College of San Francesco Saverio in Bologna, being taught mathematics and philosophy there by Luigi Marchenti, a former pupil of Pierre Varignon at Paris.
- He returned to Bologna in 1739 where he taught mathematics, replacing his former teacher Luigi Marchenti.
- He moved to Bologna in 1766 and published some important mathematical works.
- Leopoldo Marco Antonio Caldani (1725-1813) studied under Riccati in Bologna but went on to take a medical degree in 1750.
- Five years later he became professor of practical medicine at Bologna.
- His brother, Petronio Maria Caldani (1735-1808), also studied with Riccati and went on to become professor of mathematics at Bologna.
- Riccati was skilled in hydraulic engineering and carried out flood control projects which saved the regions round Venice and Bologna from flooding [',' A Natucci, Biography in Dictionary of Scientific Biography (New York 1970-1990).','1]:-
.
- As we have noted, Riccati taught at Jesuit Colleges in Bologna but as the years went by the Jesuit Order came under attack from opponents within the Catholic Church.
- All the Jesuit schools and colleges in Bologna were closed following the papal brief of 21 July 1773 and all the religious staff given notice to leave the city.
- Riccati left Bologna and went to Treviso to live with his two brothers Giordano and Montino who were living in the house which had belonged to their father Jacopo Riccati.
- In 1773, shortly after he moved to Treviso, Vincenzo Riccati was offered the chair of mathematics at the University of Bologna and, around the same time, he was also offered the chair of mathematics at Pisa.
- Gregorio Ricci-Curbastro (1853-1925)
- Died: 6 August 1925 in Bologna, Italy
.
- This time he went, not to Rome but to the University of Bologna.
- He first systematically presented the important ideas in 1888 in a paper written for the 800th anniversary of the University of Bologna.
- He also was a member of the Accademia dei Lincei from 1899, the Accademia di Padua from 1905, the Academy of Sciences of Turin from 1918, the Societa dei Quaranta from 1921, the Reale Accademia di Bologna from 1922 and the Accademia Pontifica from 1925.
- Leonida Tonelli (1885-1946)
- He completed his schooling in Pesaro, where he undertook technical studies, and then entered the University of Bologna in 1902 at the age of seventeen.
- His lecturers at Bologna included Salvatore Pincherle, who taught him analysis, Federigo Enriques, who taught him projective and descriptive geometry, and Cesare Arzela who taught function theory.
- Tonelli caught a serious infection while on an excursion to the mountains south of Bologna and this meant that he could not study for some considerable time.
- Cesare Arzela (1847-1912), who had studied in Pisa with Ulisse Dini and Enrico Betti, was Tonelli's thesis advisor at Bologna.
- After the award of his doctorate, Tonelli was appointed as Salvatore Pincherle's assistant at Bologna to work in algebra and analytic geometry.
- He had taken up again the duties of his chair at Parma in 1918 but in the spring of 1922 he was called to the Chair of Higher Analysis at the University of Bologna.
- Four years later, he was a plenary speaker at the International Congress of Mathematicians held in Bologna in September 1928, giving the lecture Il contributo italiano alla teoria delle funzioni di variabili reali Ⓣ.
- As well as producing deep research, Tonelli was also involved in teaching Analysis courses at the University of Ferrara up to 1927, and later, at Bologna, he taught mathematics course for students of Chemistry and the Life Sciences.
- Giulio Vivanti (1859-1949)
- At this stage in his education, Vivanti decided that he wanted to study engineering and he entered the Polytechnic of Turin to study that subject, He was awarded his civil engineering degree in 1881 but the mathematics he had studied as part of this degree convinced him that mathematics was the subject for him and he entered the University of Bologna where he was taught by Cesare Arzela and Salvatore Pincherle.
- He was awarded his laurea in mathematics from Bologna on 30 June 1883.
- He then began teaching at the University of Bologna, in particular teaching courses on algebraic number theory.
- Vivanti obtained his 'libera docenza' (similar to the habilitation in that it is the 'right to teach') in infinitesimal calculus at the University of Bologna on 13 May 1892.
- Vivanti introduced the note having arisen from the course he was teaching on this topic (see, for example [',' S Coen, Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012).','1]):-
.
- Dr Giulio Vivanti, a graduate with a laurea in mathematics from Bologna in 1883, obtained a 'libera docenza' teaching position in infinitesimal calculus, which was then transferred to Pavia.
- Nor should the lithographed courses on analytic geometry, calculus and other parts of mathematics, held in Bologna, Pavia, and Messina, and which together have their merits, be kept in silence.
- Salvatore Coen writes [',' S Coen, Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012).','1]:-
.
- Giuseppe Biancani (1566-1624)
- Born: 8 March 1566 in Bologna, Papal States (now Italy)
.
- He also taught at the University of Parma; Paul Grendler in [',' P F Grendler, The Universities Of The Italian Renaissance (JHU Press, 2004).','1] lists the professors teaching at the university in session 1617-18 which includes 'Giuseppe Biancani of Bologna' lecturing in the afternoon on mathematics as part of "Arts and Theology".
- Giuseppe Biancani's treatise, 'De mathematicarum natura disertatio' (Bologna, 1615) ..
- Egnatio Danti (1536-1586)
- He built other instruments, namely ones to indicate the wind direction both while in Florence, and later also in Bologna, and also made a surveying instrument called the radio latino.
- After leaving Tuscany, as Francis required, Danti moved to Bologna in 1575.
- In the following year the Senate of Bologna appointed him Professor of Mathematics at the university.
- From 1577 Danti accepted a commission from Ghisilieri, the Governor of his native city of Perugia, to map the area around Perugia but this only took him away from Bologna for short periods and during this period he continued with his duties at the University of Bologna.
- While he lived in Bologna, Danti continued his interest in astronomical instruments and he built a gnomon at the cathedral.
- The next work by Danti we mention is Usus et tractatio gnomonis magni, quem Bononiae ipse in Divi Petroni templo conferit anno domini 1576 which was published in Bologna but contains no date of publication.
- It was probably published around 1577 or 1578 and it contains a description of the gnomon he designed and used on Santa Petronio in Bologna in 1576.
- Ugo Amaldi (1875-1957)
- He served as a magistrate in several different cities over the following years, mostly in Pavia before ending his career as Attorney General in Bologna.
- After graduating from the high school in 1894, Amaldi entered the University of Bologna in 1894 where he was taught by Cesare Arzela, who held the chair of Infinitesimal Calculus, and Salvatore Pincherle who held the chair of Algebraic Analysis and Analytic Geometry.
- In 1902 he became an assistant lecturer in Complementary Algebra and Analytical Geometry at the University of Bologna.
- He produced important results on infinite dimensional Lie groups acting on 3-dimensional space as Enrico Rogora explains in [',' E Rogora, Development of the theory of Lie Groups in Bologna (1884-1900), in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012), 415-426.','7]:-
.
- Enrico Rogora tries to explain why this happened [',' E Rogora, Development of the theory of Lie Groups in Bologna (1884-1900), in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012), 415-426.','7]:-
.
- Maria Agnesi (1718-1799)
- Some accounts of Maria Agnesi describe her father as being a professor of mathematics at Bologna.
- Agnesi was fortunate, however, in her bid to learn mathematics for a monk, Ramiro Rampinelli, a mathematician who had been a professor at both Rome and Bologna, arrived in Milan and became a frequent visitor to the Agnesi house.
- Pope Benedict XIV wrote to Agnesi saying that he had studied mathematics when he was young and could see that her work would bring credit to Italy and to the Academy of Bologna.
- Soon after this he appointed Agnesi to the position of honorary reader at the University of Bologna.
- Then Agnesi was approached by the president of the Academy of Bologna and three other professors of the Academy and invited to accept the chair of mathematics at the University of Bologna.
- She had already devoted herself to a holy, retired life; while her name remained on the rolls of the university for forty-five years, she never went to Bologna.
- Beppo Levi (1875-1961)
- Gentile organised the first Congress of Fascist Institutions of Culture in Bologna in March 1925 and this led to the 'manifesto Gentile' in April which sought the support of intellectuals for Fascism.
- In 1928 he left Parma and transferred to the chair of the theory of functions at the University of Bologna.
- At Bologna, Levi had a heavy teaching and administrative load, yet he continued to undertake research with the same passions as he had done throughout his life.
- In many ways things went well for Levi at Bologna: his daughter Laura (the author of [',' L Levi, Beppo Levi: Italia y Argentina en la vida de un matematico (Libros del Zorzal, 2000).','1]) began doctoral studies in physics there, he had an excellent relationship with Salvatore Pincherle who was retired but still active, and he was elected to the Reale Accademia dei Lincei in 1935.
- Perhaps because of this, he was able to carry out his duties in Bologna with little political interference for several years.
- This resulted in Levi being dismissed from his position in Bologna in 1938.
- Levi had been offered the chance of returning to his chair in Bologna after World War II ended, but he had chosen to remain in Argentina.
- Nicolaus Copernicus (1473-1543)
- So that he might have the necessary qualifications Copernicus decided to go to the University of Bologna to take a degree in canon law.
- In the autumn of 1496 he travelled to Italy, entering the University of Bologna on 19 October 1496, to start three years of study.
- As a native German speaker he joined the "German Nation of Bologna University".
- On 20 October 1497, while in Bologna, Copernicus received official notification of his appointment as a canon and of the comfortable income he would receive without having to return to carry out any duties.
- At Bologna University Copernicus studied Greek, mathematics and astronomy in addition to his official course of canon law.
- He had not completed his degree in canon law at Bologna so he requested his uncle that he be allowed to return to Italy both to take a law degree and to study medicine.
- In the spring of 1503 he decided formally to obtain his doctorate in Canon Law, but he did not return to Bologna but rather took the degree at the University of Ferrara.
- Eugenio Bertini (1846-1933)
- Eugenio was born in Forli which is about 60 km southeast of Bologna and just a little further northeast of Florence.
- He went to the University of Bologna in 1863, supported by a scholarship from Forli, with the intention of studying engineering.
- The University of Bologna was founded in the 11th century and was at the time Bertini entered it (and of course still is today), one of the most famous and oldest universities in Europe.
- The city of Bologna and the surrounding area had been controlled by the Austrians from 1849 until it became part of the Kingdom of Italy in 1860.
- Cremona was an ardent Italian nationalist who, after fighting against the Austrians to help achieve an independent Italy, had been appointed as a professor at Bologna three years before Bertini entered the university.
- Bertini returned to his studies at Bologna but was advised by Cremona to transfer to the University of Pisa where he obtained a degree in mathematics in 1867 in the school of Betti and Dini.
- Beniamino Segre (1903-1977)
- By 1931 when he was appointed to the Chair of Geometry at the University of Bologna he already had 40 publications in algebraic geometry, differential geometry, topology and differential equations.
- Article 4 of the Royal Decree Law of 5 September 1938 was titled 'Measures for the defence of race in fascist schools' and, after Segre had been identified as Jewish by the University of Bologna, he was expelled from the University on 16 October 1938.
- In 1946 he returned to Bologna succeeding Francesco Severi in Rome in 1950.
- He was elected to numerous academies including: the Academy of Sciences of the Institute of Bologna; the Academy of Sciences of Turin; the Academy of Sciences, Letters and Arts of Palermo; the National Academy of Sciences, Letters and Arts Modena; the Ligurian Academy of Sciences and Letters; the Istituto Lombardo Accademia di Scienze e Lettere; the Accademia Petrarca di Lettere Arti e Scienze di Arezzo; the Academie des Sciences de l'Institut de France; the Academie des sciences, inscriptions et belles-lettres de Toulouse; the Societe Royale des Sciences de Liege; the Academie Royale de Belgique; and the Academia Nacional de Ciencias de Buenos Aires.
- He received medals such as the gold Medal of the Accademia dei XL, the Medaglia ai Benemeriti della cultura e dell'arte, the Grand Prix of the City of Bologna, the "Golden Pen Award" of the President of the Council of Ministers, the order of Cavaliere Gran Croce OMRI, and Chevalier de la Legion d'Honneur.
- He was awarded honorary degrees by the universities of Sussex, Bologna, and Bratislava.
- Stephano degli Angeli (1623-1697)
- His health, however, was poor and he was given medical advice to transfer to Bologna, which is about 50 km south west, in 1645.
- It might seem strange medical advice to move to another town only 50 km away, but in fact Ferrara is situated on marshland whereas Bologna is situated at a height of 55 metres above sea level at the foot of the Apennine mountains.
- It was a good move in terms of Angeli's health, and also a good move for mathematics since in Bologna he came under the influence of Cavalieri.
- Cavalieri was teaching at the University of Bologna, one of the oldest and most famous universities in Europe, dating from the 11th century.
- After leaving Bologna, Angeli continued his contacts with Cavalieri by correspondence, and was entrusted to publish Cavalieri's final work, Exercitationes geometricae sex Ⓣ, since by 1647 Cavalieri's health had deteriorated to such an extent that he was unable to carry out the work himself.
- After Cavalieri's death, later in 1647, Angeli was offered his chair of mathematics at the University of Bologna but he was still too modest about his own mathematical achievements to accept the position.
- Gianfrancesco Malfatti (1731-1807)
- He began his education at the Jesuit College in Verona before continuing his studies at Bologna.
- He studied under Laura Bassi, Vincenzo Riccati, Francesco Maria Zanotti (1692-1777) and Gabriele Manfredi at the College of San Francesco Saverio in Bologna.
- Leaving Bologna, in 1754 Malfatti went to Ferrara where he was appointed as curator of the extensive library of the Marquis Cristiano Bevilacqua which had officially opened in the previous year.
- Dirk Struik, describing the papers in [',' L Pepe, L Biasini, L Capra and M Fiorentini (eds.), Gianfrancesco Malfatti nella cultura del suo tempo, Proceedings of the Conference on Gianfrancesco Malfatti 23-24 October 1981, Ferrara (Bologna, 1982).','5], writes that Malfatti:-
.
- There are several papers in [',' L Pepe, L Biasini, L Capra and M Fiorentini (eds.), Gianfrancesco Malfatti nella cultura del suo tempo, Proceedings of the Conference on Gianfrancesco Malfatti 23-24 October 1981, Ferrara (Bologna, 1982).','5] which describe Malfatti's work.
- In December 1796 Napoleon Bonaparte created the Cispadane Republic by merging of the duchies of Reggio and Modena and the legate states of Bologna and Ferrara.
- Alessandro Padoa (1868-1937)
- Then in March of that year he moved again, this time to the University of Bologna.
- He lectured at congresses in Paris (1900, 1935), Rome (1908), Cambridge (1912), Livorno, Parma, Padua, Bologna (1911, 1928) and Florence (1937).
- M Padoa - previously my distinguished student and now my colleague and my friend - has given to this subject, since 1898, a series of well-attended conferences in the Universities of Brussels, Pavia, Rome, Padua, Cagliari and Geneva, and has presented highly regarded papers to the Congresses of philosophy and mathematics in Paris, Livorno, Parma, Padua and Bologna.
- Finally we note that Padoa married Elisabetta Padoa (born at Bologna on 30 August 1870), the daughter of Felice Padoa and Ginevra Vivanti: they had three children, Baldo (born at Turin on 13 December 1893), Gino (born at Pinerolo on 8 February 1898) and Giovanna (born at Bologna on 14 October 1901).
- Gaetano Scorza (1876-1939)
- After eight years as professor of algebra at Bologna from 1966, he returned to Padua where he worked until he retired.
- Bologna, Bologna, 2010), 167-180.','13].
- Bologna, Bologna, 2010), 149-165.','14].
- Luigi Cremona (1830-1903)
- With events moving quickly towards a unified Italy under Victor Emmanuel II as King, Cremona was appointed by Royal decree as an ordinary professor at the University of Bologna on 10 June 1860.
- Cremona was to remain in Bologna until October 1867.
- In Cremona's Complete Works there appear 45 articles which he published while at Bologna.
- Also while at Bologna Cremona developed the theory of birational transformations, later known as Cremona transformations, and wrote a series of papers on twisted cubic surfaces.
- Greitzer, writing in [',' S L Greitzer, Biography in Dictionary of Scientific Biography (New York 1970-1990).','1], describes the importance of Cremona transformations which he introduced in his Bologna period:-
.
- Roberto Marcolongo (1862-1943)
- In fact Marcolongo established a lengthy and fruitful collaboration with Cesare Burali-Forti and they were jokingly baptised by their colleagues as the "vector binomial." Their Elementi di calcolo vettoriale con numerose applicazioni alla geometria, alla meccanica e alla fisica matematica Ⓣ (Bologna 1909, French translation, Paris 1910, 2nd ed., Bologna 1921, 3rd ed., Milan 1925) presented the fundamentals and notation of a so-called minimum system and gave applications to the mechanics of continuous geometry and differential geometry on a surface.
- A second edition of the first volume of this work, entitled Trasformazioni lineari Ⓣ (Bologna 1929), was published in a encyclopaedia of vector analysis written in collaboration with Pietro Burgatti and Tommaso Boggio, two other members of the so-called school of Italian vectorists.
- Already in Elementi di calcolo vettoriale con numerose applicazioni alla geometria, alla meccanica ed alla fisica matematica Ⓣ, published by Zanichelli in Bologna in 1909, the mathematics was accompanied by in-depth notes on the history of the vector calculus; later he specialised in the history of mechanics, with particular attention to the Italian author, Galileo Galilei and, above all, to the drawings and manuscripts of Leonardo da Vinci.
- Among his monographs in this field: Il problema dei tre corpi da Newton (1686) al nostri giorni Ⓣ (Pisa 1915, other editions Naples 1915, Milan 1918, Bologna 1919), and Leonardo da Vinci, artista-scienziato Ⓣ (Ulrico Hoepli, Milan, 1939; 2nd ed., Ulrico Hoepli, Milan, 1943) which is the synthesis of many previous works.
- Jacopo Riccati (1676-1754)
- Among his reading material was the scientific journals of the day, in particular the Commentari dell' Accademia delle Scienze di Bologna, the Acta Eruditorum Lipsiae, and the Proceedings of the Imperial Academy of Sciences based in St Petersburg.
- These include: Giovanni Rizzetti (1675-1751), famed as a critic of Newton's theory of light; Gabriele Manfredi, professor of mathematics and chancellor of the University of Bologna, and the brother of eminent mathematician and astronomer Eustachio Manfredi; Giovanni Poleni, who was a professor at the University of Padua; Antonio Vallisneri (1661-1730), who held the chairs of Practical Medicine and Theoretical Medicine at the University of Padua and was an editor of the Giornale de' Letterati d'Italia; Ramiro Rampinelli, a mathematician who was a professor at Rome and at Bologna; and Bernardino Zendrini (1679-1747), a scientist working for the Republic of Venice.
- Of these scientist, it was Manfredi who had the greatest influence on Riccati's approach to mathematics, particularly through his book De constructione aequationum differentialium primi gradus Ⓣ, printed in Bologna in 1707.
- Girolamo Cardano (1501-1576)
- Four years ago when Cardano was going to Florence and I accompanied him, we saw at Bologna Hannibal Della Nave, a clever and humane man who showed us a little book in the hand of Scipione del Ferro, his father-in-law, written a long time ago, in which that discovery was elegantly and learnedly presented.
- Realising he had to move, Cardan applied for a professorship of medicine at Bologna and was appointed to the post.
- Cardan's time in Bologna was full of controversy.
- Cardan sadly reported Aldo to the authorities, and Aldo was banished from Bologna.
- Gabriel Koenigs (1858-1931)
- Bologna and Stockholm emerged as the only competitors.
- Pincherle, as President of the International Mathematical Union, felt he could not press for Bologna but Koenigs went as far as to say that if Stockholm were chosen the unfavourable exchange rate would stop France and many other countries attending.
- Bieberbach asked all Germans to boycott Bologna but Hilbert argued that they should attend.
- He accordingly wrote to all Union members advising them not to take part in the Bologna Congress.
- Eugenio Beltrami (1835-1900)
- He was appointed to the University of Bologna in 1862 as a visiting professor of algebra and analytic geometry.
- After two years in Bologna, Beltrami accepted the chair of geodesy at the University of Pisa, which he held from 1864 to 1866.
- In 1866 he returned to Bologna where he was appointed professor of rational mechanics.
- Oscar Chisini (1889-1967)
- The young Oscar received a classical education, first in Ravenna and then in Bologna.
- Later, enrolled as an engineering student at the University of Bologna, Oscar Chisini met Federigo Enriques in a meeting that was to change his life.
- The four volumes of this monograph, started in 1915 and finished in 1934, were conceived in what Chisini called a peripatetic way, that is walking under the porches of Bologna with Enriques possibly stopping to write on the flooring with the tip of his umbrella.
- Domenico Montesano (1863-1930)
- By 1888 Montesano had 13 publications and was in a strong position when he entered the competition for the chair of descriptive and projective geometry at the University of Bologna.
- Let us note that filling the chair of descriptive and projective geometry at the University of Bologna, which Montesano vacated in 1893 when he went to Naples, remained unfilled until 1896 when a competition was held.
- An involution mapped on the general cubic variety of S4 is probably an example; two series of such were given at the Bologna Congress of 1928 ..
- Frederico Commandino (1506-1575)
- Two years later, in 1565, Cardinal Farnese became Bishop of Bologna and Commandino followed his patron to Bologna.
- These two works were published in Bologna but Commandino did not spend long in that city since Cardinal Farnese died on 28 October 1565, after which Commandino returned to Urbino.
- Alessandro Faedo (1913-2001)
- The authors of [',' A Guerraggio and P Nastasi, Leonida Tonelli: A Biography, in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer, Berlin, 2012), 289-316.','9] explain how this came about:-
.
- This did, however, provide Faedo with an excellent opportunity and he was appointed as Tonelli's assistant [',' A Guerraggio and P Nastasi, Leonida Tonelli: A Biography, in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer, Berlin, 2012), 289-316.','9]:-
.
- Faedo attended the Second Congress of the Italian Mathematical Union in Bologna in April 1940.
- Giovanni Alfonso Borelli (1608-1679)
- Leaving Florence, Borelli went on to Bologna where he had useful discussions with the professor of mathematics, Bonaventura Cavalieri.
- Bonaventura Cavalieri died in Bologna at the end of November 1647 and [',' T B Settle, Biography in Dictionary of Scientific Biography (New York 1970-1990).','1]:-
.
- After he arrived in Pisa he met Marcello Malpighi (1628-1694) who was appointed to Bologna in 1656.
- Friedrich Hartogs (1874-1943)
- Daniele Struppa writes in [',' D Struppa, The first eighty years of Hartogs’ theorem, in Geometry Seminars, 1987-1988, Bologna, 1987-1988 (Univ.
- Bologna, Bologna, 1988), 127-209.','4]:-
.
- Paolo Frisi (1728-1784)
- Now in 1751 he requested that he be transferred to the seminary in Bologna since he knew many of the scientists there and felt that would further his scientific studies.
- In 1764 the city senate of Bologna appointed him an honorary university mathematics professor.
- Streets named after Frisi include: the Via Paolo Frisi, Milan; the Via Paolo Frisi, Melegnano; the Via Paolo Frisi, Lissone; the Via Paolo Frisi, Pavia; the Via Paolo Frisi, Rome; and the Via Paolo Frisi, Bologna.
- Bruno de Finetti (1906-1985)
- In particular, the International Congress of Mathematicians held in Bologna in 1928 gave him the opportunity to meet many important mathematicians, including F P Cantelli, G Castelnuovo, M Frechet, A Khinchin, Paul Levy, J Neyman, R A Fisher and G Polya.
- I and II (Bologna, 2006)','3], under the auspices of the Italian Mathematical Union and the Associazione per la Matematica Applicata alle Scienze Economiche e Sociali, on the occasion of the centenary of Bruno de Finetti's birth.
- Luca Pacioli (1445-1517)
- Pacioli, like Leonardo, had a spell away from Florence when he taught at the University of Bologna during 1501-02.
- Certainly Pacioli discussed this topic in the Summa and some time after Pacioli's visit to Bologna, del Ferro solved one of the two cases of this classic problem.
- Gustave Dumas (1872-1955)
- Representing the University of Lausanne, he attended the 1920 ICM in Strasbourg, the 1928 ICM in Bologna, and the 1932 ICM in Zurich.
- He gave a talk in Bologna, entitled Sur les singularites des surfaces Ⓣ, in section II-B (geometry).
- Vito Volterra (1860-1940)
- The name Volterra comes from the Tuscan town of Volterra where one of Vito's ancestor moved in the 15th century, having originally come from Bologna.
- Let us note that he was again invited as a plenary speaker at the 1928 International Congress of Mathematicians in Bologna where he gave the lecture La teoria dei funzionali applicata ai fenomeni ereditari Ⓣ.
- Corrado Gini (1884-1965)
- Gini studied in the Faculty of Law at the University of Bologna.
- It is likely that he first became interested in this topic while he was studying at the University of Bologna when he may have read papers published in 1895 and 1897 by Vilfredo Pareto on the topic.
- Gheorghe Vrnceanu (1900-1979)
- In 1928 at the International Congress of Mathematics in Bologna, the notion of a non-holonomic space which he had discovered was studied by Schouten and Cartan.
- He was awarded honorary degrees from Bologna University (1967) and Iasi University (1970).
- Anders Celsius (1701-1744)
- In late 1733 he travelled to Bologna, where he assisted Eustachio Manfredi with his observations.
- After Bologna he travelled to Rome where again he made observations.
- Virgil Snyder (1869-1950)
- He was the National Research Council and International Mathematical Union delegate at the International Congress of Mathematicians in Toronto in 1924, in Bologna in 1928 and in Zurich in 1932.
- He was also the United States Government delegate to the International Congress of Mathematicians in Bologna in 1928 and in Oslo in 1936.
- Olive Clio Hazlett (1890-1974)
- The resulting papers were published in Bulletin of the American Mathematical Society, Transactions of the American Mathematical Society, Annals of Mathematics, Journal of Mathematics, and Journal de Mathematiques Pures et Appliquees as well as in Proceedings of the International Mathematical Congress (Toronto, 1924) and Atti del Congresso Internazionale dei Matematici (Bologna, 1928).
- The International Congress of Mathematicians in Bologna which Hazlett mentions at the end of this quote was one to which she presented a paper Integers as Matrices.
- Annibale Comessatti (1886-1945)
- He also taught geometry courses at the University of Bologna during the years 1937-39.
- It was led by his famous pupil Ugo Morin and his wife and relatives were present as well as Angelo Tonolo, representing the Italian Mathematical Union, and Beniamino Segre, representing the Rector of the University of Bologna.
- Johann Castillon (1704-1791)
- He received further honours from foreign academies, being appointed a member of the Bologna Academy in 1768, the Mannheim Academy in 1777, the Padua Academy in 1784, and the Prague Academy in 1785.
- Coscienza Storica e Cultura Politico Nell’Illuminismo Berlinese (Il Mulino, Bologna, 1989), 57.','10]:-
.
- Carlo Bonferroni (1892-1960)
- In the middle of his stay at Bari, he attended the International Congress of Mathematicians which was held in Bologna in 1928.
- The inequality P0 ≥ 1 - S1 had been noted by George Boole, and Francesco Paolo Cantelli had highlighted Boole's inequality in a talk he gave at the International Congress of Mathematicians in Bologna in September 1928.
- Max Abraham (1875-1922)
- During this time Abraham and Einstein disagreed strongly about the theory of relativity in a correspondence discussed in [',' C Cattani and M De Maria, Max Abraham and the reception of relativity in Italy: his 1912 and 1914 controversies with Einstein, Einstein and the history of general relativity (Boston, MA, 1989), 160-174.','3] and [',' M De Maria, The first reactions to general relativity in Italy: the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.','4].
- Einstein also argued about relativity in a correspondence with Levi-Civita and Abraham played a role in this argument too, see for example [',' M De Maria, The first reactions to general relativity in Italy: the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.','4].
- Grigore Moisil (1906-1973)
- Moisil was elected to the Romanian Academy of Sciences in 1948, the Academy of Sciences in Bologna and to the International Institute of Philosophy.
- Vincenzo Viviani (1622-1703)
- However, things did not go as planned for although Viviani wrote his Life of Galileo it did not appear in the edition of Galileo's Collected Works published by Manolessi in Bologna 1655-56.
- Jakob Hermann (1678-1733)
- In 1708 Hermann was elected to the Academy at Bologna and, 1733, to the Academie Royale des Sciences in Paris.
- George Birkhoff (1884-1944)
- He was elected to the National Academy of Sciences, the American Philosophical Society, the American Academy of Arts and Sciences, the Academie des Sciences in Paris, the Pontifical Academy of Sciences, the Circolo Matematico di Palermo, the Royal Danish Academy of Sciences and Letters, the Gottingen Academy, the Royal Institute of Bologna, the Edinburgh Mathematical Society, the London Mathematical Society, and the National Academy of Sciences of Lima, Peru.
- Emmy Noether (1882-1935)
- Further recognition of her outstanding mathematical contributions came with invitations to address the International Congress of Mathematicians at Bologna in September 1928 and again at Zurich in September 1932.
- Leone Battista Alberti (1404-1472)
- Leone Battista attended a school in Padua then, from 1421, he attended the University of Bologna where he studied law but did not enjoy this topic.
- Giovanni Ricci (1904-1973)
- Sull'irrazionalita del rapporto della circonferenza al diametro Ⓣ (1942) was the published version of a lecture he gave at the Second Italian Mathematical Congress in Bologna in 1940.
- Albrecht Dürer (1471-1528)
- He visited Bologna to meet with Pacioli whom he considered held the mathematical secrets of art.
- Donald Pack (1920-2016)
- For example, he was a Guest Professor at the Technische Universitat in Berlin in 1967, at Bologna University in 1980 and, in the same year, at the Politecnico Milano.
- Mischa Cotlar (1913-2007)
- Beppo Levi was Jewish and dismissed from his position in Bologna, Italy, after Mussolini brought in the Manifesto of Race in July 1938.
- Tullio Levi-Civita (1873-1941)
- In [',' L Dell’Aglio and G Israel, The themes of stability and qualitative analysis in the works of Levi-Civita and Volterra (Italian), Italian mathematics between the two world wars (Pitagora, Bologna, 1987), 125-141.','18] the authors argue that Levi-Civita was interested in the theory of stability and qualitative analysis of ordinary differential equations for three reasons: his interest in geometry and geometric models; his interest in classical mechanics and celestial mechanics, in particular, the three-body problem; and his interest in stability of movement in the domain of analytic mechanics.
- Evangelista Torricelli (1608-1647)
- Another pupil of Castelli, Bonaventura Cavalieri, held the chair of mathematics at Bologna.
- Julio Rey Pastor (1888-1962)
- The same year Rey Pastor presented a summary of his ideas in his paper given to the International Congress of Mathematicians at Bologna, which he attended with a large group of his Argentinean students.
- Luigi Berzolari (1863-1949)
- He was also elected to the Academy of Sciences of Turin, the Academy of Science of the Institute of Bologna and the Academy Pontaniana of Naples.
- Edward Waring (1736-1798)
- He was awarded other honours, however, such as election to the Royal Society of Gottingen and the Royal Society of Bologna.
- Galileo Galilei (1564-1642)
- Despite making a very favourable impression on Clavius, Galileo failed to gain an appointment to teach mathematics at the University of Bologna.
- Christian Juel (1855-1935)
- Juel attended the International Congress of Mathematicians held in Bologna in September 1928.
- Tartaglia (1500-1557)
- Cardan and Ferrari travelled to Bologna in 1543 and learnt from della Nave that it had been del Ferro, not Tartaglia, who had been the first to solve the cubic equation.
- Clifford Ambrose Truesdell III (1919-2000)
- He was elected to the Accademia Nazionale di Scienze, Lettere ed Arti, Modena (1960), the Academie Internationale d'Histoire des Sciences, Paris (1961), the Istituto Lombardo Accademia di Scienze e Lettere (1968), the Istituto Veneto di Scienze, Lettere ed Arti (1969), the Accademia delle Scienze dell'Istituto di Bologna (1971), the Accademia Nazionale dei Lincei Rome (1972), the Academie Internationale de Philosophie des Sciences, Bruxelles (1974), the Accademia delle Scienze, Torino (1978), the Academia Brasileira de Ciencias (1981), the Polish Society for Theoretical and Applied Mechanics (1985), the Regia societas scientiarum Upsaliensis (1987), and the American Academy of Arts and Sciences (1991).
- Henri Lebesgue (1875-1941)
- He was elected to the Academy of Sciences on 29 May 1922, to the Royal Society, the Royal Academy of Science and Letters of Belgium (6 June 1931), the Academy of Bologna, the Accademia dei Lincei, the Royal Danish Academy of Sciences, the Romanian Academy of Sciences, and the Krakow Academy of Science and Letters.
- Jean Beaugrand (about 1590-1640)
- He visited Cavalieri in Bologna, Castelli in Rome, and Galileo in his home at Arcetri near Florence.
- Regiomontanus (1436-1476)
- This passage in the "Epitome", which was printed in Venice, attracted the attention of Copernicus, then a student at the University of Bologna.
- Nicolaus(I) Bernoulli (1687-1759)
- For example he was elected a member of the Berlin Academy in 1713, a Fellow of the Royal Society of London in 1714, and a member of the Academy of Bologna in 1724.
- Albertus (about 1200-1280)
- After joining the Dominican Order, he studied and taught at Padua, Bologna, Cologne and other German convents in Hildesheim, Freiburg, Ratisbon, Strasbourg, and Cologne.
- Jacques Cassini (1677-1756)
- The following year he travelled with his father in Italy and they made numerous geodesic observations, as well as visiting Bologna where they repaired the gnomon at the Church of San Petronio which Cassini's father had designed nearly thirty years before.
- Fabio Conforto (1909-1954)
- He attended the Congress of the Italian Mathematical Union held in Bologna in April 1937 and gave the talk Sulle righe razionali del quinto ordine Ⓣ in Section II (Geometry) which was published in the proceedings of the Congress.
- Arthur Cayley (1821-1895)
- He received honorary degrees from the universities of Cambridge, Oxford, Edinburgh, Dublin, Gottingen, Heidelberg, Leyden and Bologna.
- Emil Weyr (1848-1894)
- In April 1871 Emil Weyr set off on a sightseeing tour of Italy, visiting Padua, Bologna, Pisa, Florence, Rome, and Naples.
- Alexis Clairaut (1713-1765)
- He had been elected to the Royal Society of London, the Academy of Berlin, the Academy of St Petersburg and the Academies of Bologna and Uppsala.
- Mikhail Krawtchouk (1892-1942)
- Four years later he attended the International Mathematical Congress in Bologna.
- John Charles Fields (1863-1932)
- He was vice-president of the next International Congress of Mathematicians at Bologna in 1928 (at which the excluded nations were readmitted).
- Guido Grandi (1671-1742)
- Guido's family had a number notable people in it, perhaps the most significant being Lorenzo, a maternal uncle, who was a physician and professor of Greek at the University of Bologna, and the 17th century writer Domenico Legati.
- Benedetto Castelli (1578-1643)
- At this time he was appointed to take care of the waterways of Ferrara and Bologna.
- Francesco Tricomi (1897-1978)
- Francesco Tricomi studied first at the University of Bologna, then at the University of Naples.
- Nicolas-Louis de Lacaille (1713-1762)
- He was elected a member of the Science Academies of St Petersburg, Berlin, Stockholm, London, Gottingen and Bologna.
- Nina Bari (1901-1961)
- After attending the Polish Mathematical Congress in Lvov, she also attended the International Congress of Mathematicians in Bologna in 1928 at which she gave the invited lecture Sur la structure analytique d'une fonction continue arbitraire Ⓣ.
- Yurii Alekseevich Mitropolskii (1917-2008)
- Mitropolskii was elected to the Academy of Sciences of the Ukraine in 1961, to the Bologna Academy of Sciences (1971), and to the Academy of Sciences of the USSR in 1984.
- Pietro Abbati Marescotti (1768-1842)
- Napoleon's troops occupied Modena which, in 1796, became part of the Cisalpine Republic consisting of Lombardy, Emilia, Modena and Bologna.
- Alfredo Capelli (1855-1910)
- In Palermo, the situation finally began to change in 1878 with the arrival of Cesare Arzela (1847-1912), who held the chair of algebra for two years, and of Capelli, who replaced Arzela when the latter moved to Bologna.
- Alexander Animalu (1938-)
- While still at the Cavendish Laboratory in Cambridge, he had been given leave of absence to visit Bologna in Italy where he worked with F Bonsignori and V Bortolani and wrote two joint papers with them (see below).
- Georg Peurbach (1423-1461)
- He lectured in Germany, France and Italy on astronomy and after giving lectures in Bologna and Padua he was offered appointments in these universities but turned them down.
- Giuseppe Veronese (1854-1917)
- Freguglia, in [',' P Freguglia, The foundations of higher-dimensional geometry according to Giuseppe Veronese (Italian), in Geometry Seminars, 1996-1997 (Bologna, 1998), 253-277.','5], describes Veronese's study of geometry in higher dimensions.
- Joseph Pérès (1890-1962)
- This work is discussed in [',' A Guerraggio, The ’Theorie generale des fonctionnelles’ of V Volterra and J Peres (Italian), in Italian mathematics between the two world wars, Milan-Gargnano, 1986 (Bologna, 1987), 187-207.','9] where the author points out that the book belongs to an older tradition, being based on ideas introduced by Volterra himself from 1887 onwards.
- Felice Casorati (1835-1890)
- He was elected to the Gottingen Academy of Sciences (Konigliche Gesellschaft der Wissenschaften) in 1877, the Turin Mathematical Society (by then the Turin Academy of Sciences) in 1880, the Bologna Academy of Sciences in 1885, and the Berlin Academy of Sciences in 1886.
- Francesco Severi (1879-1961)
- From Turin, Severi and his wife moved to Bologna where he became an assistant to Federigo Enriques in 1902.
- Charles Bossut (1730-1814)
- The academies of Lyons and Toulouse awarded him prizes, and he was elected to the St Petersburg Academy of Sciences as well as the academies at Turin and Bologna.
- Daniel Bernoulli (1700-1782)
- He was elected to most of the leading scientific societies of his day including those in Bologna, St Petersburg, Berlin, Paris, London, Bern, Turin, Zurich and Mannheim.
- Pietro Paoli (1759-1839)
- Paoli received many honours including election to the academies of Bologna, Naples, and Mantua, and to the Mathematical Circle of Palermo.
- Derrick Norman Lehmer (1867-1938)
- The history of factor tables really begins in the seventeenth century, starting perhaps with a table by Cataldi (Bologna, 1603), which gave all of the factors of all the numbers up to 750 ..
- Duilio Gigli (1878-1933)
- This was published by N Zanichelli in Bologna in 1912 and comprised of 147 pages.
- Nikolaos Hatzidakis (1872-1942)
- He also attended the International Congress of Mathematicians in 1920 in Strasbourg, where he gave the lecture Sur quelques formules de geometrie cinematique Ⓣ, and the 1928 International Congress of Mathematicians in Bologna where he gave the lecture Due proposte per l'insegnamento medio Ⓣ.
- Samuel Haughton (1821-1897)
- Haughton received many honours including election to the Royal Irish Academy (1845), election to the Royal Society of London (1858), and honorary degrees from the University of Oxford in 1868, the University of Cambridge in 1880, the University of Edinburgh in 1884, and the University of Bologna in 1888.
- Georgii Vasilovich Pfeiffer (1872-1946)
- He participated in the International Congress of Mathematicians in Rome (in April 1908), Bologna (in September 1928), and Zurich (in September 1932).
- Max Dehn (1878-1952)
- In 1932 Dehn wrote the essay Das Mathematische im Menschen Ⓣ which he published in Scientia, an Italian journal produced in Bologna by Federigo Enriques [',' B Bergman, M Epple and R Ungar, Transcending tradition.
- Gottfried Köthe (1905-1989)
- While on this visit to Gottingen, Kothe attended the International Congress of Mathematicians held in Bologna in September 1928 as did Emmy Noether.
- Panagiotis Zervos (1878-1952)
- The second of these four papers was the published version of the talk she gave in the 'Matematiche elementari, Questioni didattiche, Logica matematica' Section of the International Congress of Mathematicians in Bologna in September 1928.
- Gino Loria (1862-1954)
- In 1928 the International Commission on Mathematical Instruction meeting in Bologna asked Loria to prepare a report for the International Congress of Mathematicians to take place in Zurich in 1932.
- Gösta Mittag-Leffler (1846-1927)
- He was awarded honorary degrees from the universities of Oxford, Cambridge, Aberdeen, St Andrews, Bologna and Christiania (now Oslo).
- James Bradley (1693-1762)
- With his work on, and announcement of, nutation, he began to receive international recognition; 1746 saw him become a member of the Royal Academy of Berlin; in July 1748 he was made a foreign associate of the Academie Royale des Sciences in Paris; in 1750, he became a corresponding member of the Imperial Academy of Sciences in St Petersburg, becoming a full member in 1754; in 1757 was when he was elected to become a member of the Academy of Sciences of Bologna Institute.
- John Couch Adams (1819-1892)
- He did, however, accept honorary degrees from Oxford, Dublin, Edinburgh, and Bologna.
- Georges Darmois (1888-1960)
- At the International Congress of Mathematicians held at Bologna in September 1928, one of the plenary talks was given by Emile Borel who gave the address Le calcul des probabilites et les sciences exactes.
- Salvatore Cherubino (1885-1970)
- He was invited to give the talk Sui polinomi definiti o semidefiniti Ⓣ at the International Congress of Mathematicians at Bologna in 1928 and he published a paper of the same title in the Proceedings of the Congress.
- George Allman (1824-1904)
- Queen's College Galway sent him as their delegate to the University of Bologna in 1888 to take part in their octo-centenary.
- Gian-Carlo Rota (1932-1999)
- He held four honorary degrees from the University of Strasbourg (1984), the University L'Aquila (1990), the University of Bologna (1996), and Brooklyn Polytechnical University (1997).
- Michael Scot (1175-1235)
- His very meticulous description in Latin concerning the medical case of "Mary of Bologna" dismissed as a "calcified fibroid tumor", was realized in the 1970s to be the description of a very rare case of miscarriage or "spontaneous abortion", not followed by immediate expulsion, of twin embryos, dead at different dates and calcified.
- Vladimir Arnold (1937-2010)
- In addition to these honours, Arnold has been awarded honorary degrees from the University P and M Curie, Paris (1979), Warwick University, Coventry (1988), Utrecht University, Netherlands (1991), University of Bologna, Italy (1991), University Complutense, Madrid (1994), and the University of Toronto, Canada (1997).
- Gaetano Fichera (1922-1996)
- He was elected to the National Academy of Sciences of Italy (the "Academy of Forty"), the Academy of Sciences of Turin, the Academy of Palermo, the Academy of Bologna, the Lombardo Institute, the Peloritana Academy, the Zelantea Academy, the Academy of Modena, the Gioenia Academy, the German Academy of Sciences Leopoldina, the Royal Society of Edinburgh, the Academia Europaea, the Russian Academy of Sciences, and the Georgian Academy of Sciences.
- João Delgado (1553-1612)
- The debate arose from the writings of Alessandro Piccolomini (1508-1578) who was born in Sienna, studied in Padua, Bologna and Rome, and taught in Sienna and Rome.
- Matteo Bottasso (1878-1918)
- Arriving back in Italy Bottasso was appointed as an assistant professor of projective geometry at the University of Bologna.
- Enzo Martinelli (1911-1999)
- He attended the Second Congress of the Italian Mathematical Union in Bologna from 4 to 6 April 1940 where he delivered the lecture Intorno alla teoria delle funzioni biarmoniche e delle funzioni analitiche di due variabili complesse Ⓣ.
- Guido Ascoli (1887-1957)
- This Commission began to function on 17 April 1955 when the first official meeting was held in Bologna with Ascoli as president and he continued to serve as president until the meeting in Turin on 24 April 1957.
- Nikolai Nikolaevich Bogolyubov (1909-1992)
- One of his papers was awarded in 1930 a prize by the Bologna Academy of Sciences (the A Merlani prize).
- Ehrenfried Walter von Tschirnhaus (1651-1708)
- He then travelled to Turin, Milan, Venice, Bologna and Rome.
- Lothar Collatz (1910-1990)
- Collatz received many honours for his contributions including election to the German Academy of Scientists Leopoldina, the academy at Bologna and that at Modena.
- Albert Tucker (1905-1995)
- DeLury suggested Paris, Gottingen or Bologna as the best places, with Cambridge as the best option if he felt he had to have teaching in English.
- James Alexander (1888-1971)
- During this period abroad, Alexander studied at Paris and Bologna.
- Paolo Ruffini (1765-1822)
- Napoleon set up the Cisalpine Republic consisting of Lombardy, Emilia, Modena and Bologna.
- Louis Mordell (1888-1972)
- As well as the honours from the Royal Society and the London Mathematical Society which we mentioned above, Mordell also received honorary degrees from several universities (Glasgow, Mount Allison and Waterloo) and was elected a member of the Academies of Oslo, Uppsala and Bologna.
- Johann Bernoulli (1667-1748)
- He was elected a fellow of the academies of Paris, Berlin, London, St Petersburg and Bologna.
- Pafnuty Chebyshev (1821-1894)
- He was elected a Corresponding Member of the Societe Royale des Sciences of Liege in 1856, of the Societe Philomathique, also in 1856, of the Berlin Academy of Sciences in 1871, the Bologna Academy in 1873, the Royal Society of London in 1877, the Italian Royal Academy in 1880, and the Swedish Academy of Sciences in 1893.
- Francisco José Duarte (1883-1972)
- He participated in International Congresses of Mathematicians in Bologna (1928), Zurich (1932), and Boston (1950); Congresses of the Geodesic Union and International Geophysics in Madrid (1924), Prague (1928), Lisbon (1932), and Brussels (1951); International Congresses for the peaceful use of the atomic energy in Geneva (1955, 1958); and in the Assembly on the World Map in London (1928).
- Maurice Fréchet (1878-1973)
- He was invited to address the International Congress of Mathematicians in Bologna in 1928 and in Oslo in 1932.
- Luis Antonio Santaló (1911-2001)
- The head of this new Mathematical Institute was the 64 year old Beppo Levi who had been dismissed from his chair of the theory of functions at the University of Bologna due to Mussolini's July 1938 anti-Semitic Manifesto of Race which removed Italian citizenship from Jews and banned them from jobs in education.
History Topics
- Quadratic etc equations
- Scipione dal Ferro (1465-1526) held the Chair of Arithmetic and Geometry at the University of Bologna and certainly must have met Pacioli who lectured at Bologna in 1501-2.
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- Soon rumours started to circulate in Bologna that the cubic equation had been solved.
Go directly to this paragraph
- References for Set theory
- I Grattan-Guinness (ed.), Selected essays on the history of set theory and logics (1906-1918) by Philip E B Jourdain (Bologna, 1991).
- References for General relativity
- M De Maria, The first reactions to general relativity in Italy : the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- References for Bourbaki 1
- C Houzel, The influence of Bourbaki (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 241-246.
- References for Mathematical games
- References for Bourbaki 2
- C Houzel, The influence of Bourbaki (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 241-246.
- Longitude1
- With offers of large amounts of money Cassini came to Paris on 4 April 1669, although the Senate of Bologna, the Pope and Cassini himself believed it to be only for a short visit.
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- U of St Andrews History
- Prior to this bishops in St Andrews had provided funds to send their students to the universities of Bologna, Paris and Oxford but the political situation at the time made it increasingly difficult to continue this practice.
- References for Infinity
- Bologna 10 (1988/89), 117-134.
Societies etc
- Italian Academy of Sciences
- A mathematician, physicist, and astronomer, he was professor of mathematics at the University of Bologna.
- He was secretary of the Academy of Sciences in Bologna.
- A physicist who made contributions to chemistry, he worked at Bologna and Pisa where he taught logic, then physics.
- An astronomer and engineer, he was director of the Observatory in Bologna.
- He observed the 1761 transit of Venus in Bologna and made many observations of the moon, the sun and the planets.
- An anatomist and physiologist, he was professor of practical medicine at the University of Bologna and then professor of theoretical medicine at the University of Padua.
- International Mathematical Union
- Pincherle invited all mathematicians to the International Congress of Mathematicians to be held in 1928 in Bologna, Italy.
- The argument had little effect on the Bologna Congress which was attended by mathematicians from a wide range of countries and was a great success.
- References for Italian
- Slovenian Academy of Sciences
- Following the example of the Accademia dell'Arcadia in Rome, dei Gelati in Bologna and other learned Italian societies, the chronicler, historian and lawyer Janez Gregor Dolničar (Thalnitscher) (1655-1719) and the cathedral provost, Janez Krstnik Prešeren (1656-1704) became leaders of Ljubljana's intellectual elite, founding a similar society in 1693 called 'Academia Operosorum Labacensium' (The Workers' Academy of Ljubljana).
- Italian Mathematical Union
- In 1924 Pincherle was elected President of the International Mathematical Union and Italian Mathematical Union organised the International Congress of Mathematicians in Bologna in 1928.
Honours
- Galway Group Theory.html
- Marta Morigi (Bologna) On groups with restricted centralizers of w-values
.
- International Congress Speaker
References
- References for Beppo Levi
- An attempt at replacing the axiom of choice (1918-1923) (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 99-105.
- S Coen, Beppo Levi: una biografia, in Beppo Levi, Opere I: 1897-1906 (Unione Matematica Italiana, Bologna, 1999), 13-54.
- S Coen, Elenco completo delle opere di Beppo Levi, in Beppo Levi, Opere I: 1897-1906 (Unione Matematica Italiana, Bologna, 1999), 85-122.
- S Coen, Beppo Levi: la vita, in Salvatore Coen, Seminari di geometria, Universita di Bologna, Italia, 1991-1993 (Department of Mathematics, Universita degli Studi di Bologna, Bologna, 1994), 193-232.
- S Coen, Geometry and complex variables in the work of Beppo Levi, in Geometry and complex variables, Bologna, 1988/1990 (Dekker, New York, 1991), 111-139.
- L., in Beppo Levi, Opere I: 1897-1906 (Unione Matematica Italiana, Bologna, 1999), 67-76.
- S Spagnolo, 1906: un anno di grazia per Beppo Levi, in Beppo Levi, Opere I: 1897-1906 (Unione Matematica Italiana, Bologna, 1999), 67-81.
- References for Enrico Bompiani
- S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, Basel, 2012)
.
- (4) 12 (3) (Supplement) (1975), (Bologna, 1975), i-xxxvi; 1-490.
- Bologna Cl.
- C Ciliberto and E S Del Colombo, Enrico Bompiani: The Years in Bologna, in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, Basel, 2012), 143-177.
- Sessions on Topology and Geometry of Manifolds (Italian) (Bologna, 1990) (Univ.
- Bologna, Bologna, 1992), 145-155.
- B Segre, Enrico Bompiani (1889-1975), in E Bompiani Opere scelte, (Unione Matematica Italiana, Bologna, 1978), 1-17.
- References for Salvatore Pincherle
- U Bottazzini, Va' pensiero: Immagini della matematica nell'Italia dell'ottocento (Societa Editrice Il Mulino, Bologna, 1994).
- S Coen (ed.), Mathematicians in Bologna (Springer, Basel, 2012).
- U Bottazzini, Pincherle's Early Contributions to Complex Analysis, in S Coen (ed.), Mathematicians in Bologna (Springer, Basel, 2012), 57-72.
- S Francesconi, The teaching of mathematics at the University of Bologna from 1860 to 1940 (Italian), in Geometry and complex variables, Bologna 1988-90 (Dekker, New York, 1991), 415-474.
- F Mainardi and G Pagnini, The Role of Salvatore Pincherle in the Development of Fractional Calculus, in S Coen (ed.), Mathematicians in Bologna (Springer, Basel, 2012), 373-382.
- Universita di Bologna e Redatte per uso Degli Studenti by S Pincherle, Amer.
- I Sabadini and D C Struppa, Difference Equations in Spaces of Regular Functions: a tribute to Salvatore Pincherle, in S Coen (ed.), Mathematicians in Bologna (Springer, Basel, 2012), 427-438.
- References for Giuseppe Vitali
- M T Borgato, Giuseppe Vitali: Real and Complex Analysis and Differential Geometry, in Mathematicians in Bologna 1861-1960 (Springer, New York, 2012), 31-55.
- M T Borgato and A V Ferreira, Giuseppe Vitali: mathematical research and academic activity after 1918 (Italian), Italian mathematics between the two world wars (Pitagora, Bologna, 1987), 43-58.
- L Pepe, Una biografia di Giuseppe Vitali, in L Pepe (ed.), G Vitali, Opere sull'analisi reale e complessa, carteggio (Cremonese, Bologna, 1984), 1-24.
- C S Roero and M Guillemot, Tullio Viola and his Maestri in Bologna: Giuseppe Vitali, Leonida Tonelli and Beppo Levi, in Mathematicians in Bologna 1861-1960 (Springer, New York, 2012), 383-413.
- A Vaz Ferreira, Giuseppe Vitali and the mathematical research at Bologna, Geometry and complex variables, Lecture Notes in Pure and Appl.
- T Viola, Ricordo di Giuseppe Vitali a 50 anni dalla sua scomparsa, in Atti del Convegno La Storia delle Matematiche in Italia, Cagliari 1982 (Monograf, Bologna, 1984), 535-544.
- References for Federigo Enriques
- G Castelnuovo, Commemorazione di Federigo Enriques, Federigo Enriques : Memorie scelte di geometria (Bologna, 1956-66).
- R Simili (ed.), Federigo Enriques : filosofo e scienziato (Bologna, 1989).
- P Gario, Enriques and the European mathematical communities from the late nineteenth to the early twentieth century (Italian), in Geometry Seminars, 1996-1997 (Italian) (Bologna) (Univ.
- Bologna, Bologna, 1998), 279-306.
- S Di Sieno and M Galuzzi, Mathematics and the history of mathematics in the works of Federigo Enriques (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 161-168.
- References for Tullio Levi-Civita
- 1893-1900, Pubblicate a cura dell'Accademia Nazionale dei Lincei (Nicola Zanichelli Editore, Bologna, 1954).
- 1901-1907, Pubblicate a cura dell'Accademia Nazionale dei Lincei (Nicola Zanichelli Editore, Bologna, 1956).
- 1908-1916, Pubblicate a cura dell'Accademia Nazionale dei Lincei (Nicola Zanichelli Editore, Bologna, 1957).
- 1917-1928, Pubblicate a cura dell'Accademia Nazionale dei Lincei (Nicola Zanichelli Editore, Bologna, 1960).
- 1929-1937, Pubblicate a cura dell'Accademia Nazionale dei Lincei (Nicola Zanichelli Editore, Bologna, 1970).
- L Dell'Aglio and G Israel, The themes of stability and qualitative analysis in the works of Levi-Civita and Volterra (Italian), Italian mathematics between the two world wars (Pitagora, Bologna, 1987), 125-141.
- References for Giovanni Vailati
- L Ronchetti (ed.), L'Archivio Giovanni Vailati (Cisalpino, Bologna, 1998).
- A Santucci, Il pragmatismo in Italia (Il Mulino, Bologna, 1963).
- F Arzarello, The Peano school and the debate on the didactics of mathematics (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 25-41.
- G Lolli, Le forme della logica: Giovanni Vailati, in Le ragioni fisiche e le dimostrazioni matematiche (Bologna, 1985), 107-132.
- References for Gaetano Scorza
- Bologna, Bologna, 2010), 167-180.
- Bologna, Bologna, 2010), 149-165.
- References for Cesare Arzelà
- S Francesconi, The teaching of mathematics at the University of Bologna from 1860 to 1940 (Italian), in Geometry and complex variables, Bologna, 1988/1990 (Dekker, New York, 1991), 415-474.
- L Martini, The First Lectures in Italy on Galois Theory: Bologna, 1886-1887, Historia Mathematica 26 (1999), 201-223.
- L Martini, An episode in the evolution of a mathematical community: the case of Cesare Arzela at Bologna, in Mathematics unbound: the evolution of an international mathematical research community, 1800-1945, Charlottesville, VA, 1999 (Amer.
- References for Rafael Bombelli
- S A Jayawardene, Unpublished Documents Relating to Rafael Bombelli in the Archives of Bologna, Isis 54 (1963), 391-395.
- S A Jayawardene, Documenti inediti negli archivi di Bologna intorno a Raffaele Bombelli e la sua famiglia, Atti Accad.
- Bologna Cl.
- References for Francesco Grimaldi
- R Savelli, Grimaldi e la rifrazione (Bologna, 1951).
- G Tabarroni, P F M Grimaldi Bolognese iniziatore della ottica-fisica (Bologna, 1964)
.
- G Tabarroni, Nel terzo contenario della morte de F M Grimaldi (Bologna, 1964).
- References for Scipione del Ferro
- E Bortolotti, La Storia della Matematica nella Universita di Bologna (Bologna, 1974).
- L Frati, Scipione dal Ferro, Studi e memorie per la storia dell'Universita di Bologna 2 (1911), 193-205.
- References for Friedrich Hartogs
- D Struppa, The first eighty years of Hartogs' theorem, in Geometry Seminars, 1987-1988, Bologna, 1987-1988 (Univ.
- Bologna, Bologna, 1988), 127-209.
- References for Ugo Amaldi
- S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012).
- E Rogora, Development of the theory of Lie Groups in Bologna (1884-1900), in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012), 415-426.
- References for Ettore Bortolotti
- L Martini, The first lectures in Italy on Galois theory : Bologna, 1886-1887, Historia Math.
- M Panza, Ettore Bortolotti, historian of mathematics (Italian), Italian mathematics between the two world wars (Bologna, 1987), 293-305.
- B Segre, Ettore Bortolotti - commemorazione, Rendicont dell'Accademia della scienze dell'Istituto di Bologna 52 (1949), 47-86.
- References for Gianfrancesco Malfatti
- L Pepe, L Biasini, L Capra and M Fiorentini (eds.), Gianfrancesco Malfatti nella cultura del suo tempo, Proceedings of the Conference on Gianfrancesco Malfatti 23-24 October 1981, Ferrara (Bologna, 1982).
- E Giusti, Problemi e metodi di analisi matematica nell'opera di Gianfrancesco Malfatti, in L Pepe, L Biasini, L Capra and M Fiorentini (eds.), Gianfrancesco Malfatti nella cultura del suo tempo, Proceedings of the Conference on Gianfrancesco Malfatti 23-24 October 1981, Ferrara (Bologna, 1982), 37-56.
- References for Guido Grandi
- References for Gianfranco Cimmino
- M Benzi, Gianfranco Cimmino's contributions to numerical mathematics, Seminario di Analisi Matematica, Dipartimento di Matematica, dell'Universita di Bologna, Ciclo di Conferenze in Ricordo di Gianfranco Cimmino, Marzo-Maggio 2004 (Tecnoprint, Bologna, 2005), 87-109.
- References for Georges Darmois
- F de Finetti, Some links between Bruno De Finetti and the University of Bologna, in Bruno de Finetti, Radical Probabilist Bologna 26-28 October 2006.
- References for Eustachio Manfredi
- P Dore, Origine e funzione dell'Istituto e della Accademia delle scienze di Bologna, L'archiginnasio 35 (1940), 201; 206.
- La presenza femminile dal XVIII al XX secolo (Bologna 1988), 39-67.
- References for Paolo Ruffini
- References for Mauro Picone
- L Amerio, Mauro Picone and the 'Istituto per le Applicazioni del Calcolo' (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 15-23.
- Bologna Cl.
- References for Bonaventura Cavalieri
- A Favaro, Bonaventura Cavalieri nello studio di Bologna (Fava e Garagnani, Bologna, 1855).
- References for Denis Papin
- C S Maffioli, Guglielmini vs Papin (1691-1697), Science in Bologna at the end of the XVIIth century through a debate on hydraulics, Janus 71 (1-4) (1984), 63-105.
- References for Evangelista Torricelli
- References for Nicolas Bourbaki
- C Houzel, The influence of Bourbaki (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 241-246.
- References for Daniel Bernoulli
- References for Tartaglia
- References for Antonio Mario Lorgna
- W Tega (ed.), Anatomie accademiche II (Societa Editrice Il Mulino, Bologna, 1987).
- References for Maria Agnesi
- J H Sampson, Maria Gaetana Agnesi (Italian), Geometry Seminars, 1988-1991 (Bologna, 1991), 145-167.
- References for Lamberto Cesari
- D Graffi, On the contributions of Lamberto Cesari to applied mathematics, in Nonlinear analysis and optimization, Bologna, 1982, Lecture Notes in Math.
- References for Renato Caccioppoli
- G Scorza Dragoni, Remembering Renato Caccioppoli (Italian), Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Bologna, 1987), 387-392.
- References for Johann Castillon
- Coscienza Storica e Cultura Politico Nell'Illuminismo Berlinese (Il Mulino, Bologna, 1989), 57.
- References for Hermann von Helmholtz
- R Tazzioli, The Riemann-Helmholtz-Lie problem : 'hypotheses', 'facts' and 'transformation groups' (Italian), in Geometry Seminars, 1991-1993 (Italian) (Bologna, 1994), 249-270.
- References for Enrico Betti
- V Volterra, Enrico Betti, Saggi scientifici (Bologna, 1920), 37; 40-41; 46-50; 52-54.
- References for René Eugène Gateaux
- Intersezioni (Il Mulino, Bologna, 2005).
- References for Michael Scot
- C Burnett, Michael Scot and the Transmission of Scientific Culture from Toledo to Bologna via the Court of Frederick II Hohenstaufen, Micrologus: Natura, scienze e societa medievali, Le scienze alla corte di Federico II (Nature, Sciences and Medieval Societies, Sciences at the Court of Frederick II) 2 (1994) 101-126.
- References for Giuseppe Veronese
- P Freguglia, The foundations of higher-dimensional geometry according to Giuseppe Veronese (Italian), in Geometry Seminars, 1996-1997 (Bologna, 1998), 253-277.
- References for Albert Einstein
- M De Maria, The first reactions to general relativity in Italy : the polemics between Max Abraham and Albert Einstein (Italian), in Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- References for Philip Jourdain
- I Grattan-Guinness (ed.), Philip E B Jourdain : Selected essays on the history of set theory and logics (1906-1918) (Bologna, 1991).
- References for Bruno de Finetti
- I and II (Bologna, 2006)
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- References for Giulio Vivanti
- S Coen, Mathematicians in Bologna 1861-1960 (Springer Science & Business Media, 2012).
- References for Hermann Minkowski
- 1992-1993 Seminars, Siena/Bologna/Pavia (CNR, Rome, 1994), 189-214.
- References for Cesare Burali-Forti
- P Freguglia, Cesare Burali-Forti e gli studi sul calcolo geometri, in La matematica italiana tra le due guerre mondiali, Milano-Gargnano del Garda, 8-11 ottobre 1986 (Pitagora, Bologna, 1986), 173-180.
- References for Giovanni Magini
- A Favaro, Carteggio inedito di Ticone Brahe, Giovanni Keplero e di altri celebri astronomi e matematici dei secoli XVI e XVII con Giovanni Antonio Magini (Bologna, 1886).
- References for Max Abraham
- M De Maria, The first reactions to general relativity in Italy: the polemics between Max Abraham and Albert Einstein (Italian), Italian mathematics between the two world wars (Bologna, 1987), 143-159.
- References for Élie Cartan
- A Trautman, Comments on the paper by Elie Cartan: 'On a generalization of the notion of Riemann curvature and spaces with torsion', in Cosmology and gravitation, Bologna, 1979 (Plenum, New York-London, 1980), 493-496.
- References for Alessandro Faedo
- A Guerraggio and P Nastasi, Leonida Tonelli: A Biography, in S Coen (ed.), Mathematicians in Bologna 1861-1960 (Springer, Berlin, 2012), 289-316.
- References for Gabriele Manfredi
- delle scienze dell'Istituto di Bologna, cl.
- References for René Descartes
- Ital., 14, CLUEB, Bologna, 2011), 47-60.
- References for Vito Volterra
- L Dell'Aglio and G Israel, The themes of stability and qualitative analysis in the works of Levi-Civita and Volterra (Italian), Italian mathematics between the two world wars (Bologna, 1987), 125-141.
- References for Francesco Cantelli
- E Regazzini, Theory and calculus of probabilities, in Italian mathematics between the two world wars, Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 339-386.
- References for Luigi Fantappiè
- D C Struppa, Luigi Fantappie and the theory of analytic functionals (Italian), in Italian mathematics between the two world wars (Italian), Milan/Gargnano, 1986 (Pitagora, Bologna, 1987), 393-429.
- References for Galileo Galilei
- Bologna (N.S.) 46 (1942), 92-117.
- References for Luigi Berzolari
- Bologna 57 (1952-1953), 27-41.
- References for Joseph Pérès
- A Guerraggio, The 'Theorie generale des fonctionnelles' of V Volterra and J Peres (Italian), in Italian mathematics between the two world wars, Milan-Gargnano, 1986 (Bologna, 1987), 187-207.
- References for Israil Gelfand
- S G Gindikin, Israel Gelfand, in Geometry and physics (Bologna, 1991), ix-xii.
- References for Pietro Cataldi
- G Fantuzzi, P A Cataldi, in Notizie degli scrittori bolognese 3 (Bologna, 1781- 94), 152-157.
Additional material
- Sansone publications
- Giovanni Sansone, Nuove formule risolutive delle congruenze cubiche, Atti Congresso Bologna 2 (1930), 13-16.
- II: Giovanni Sansone, Sviluppi in serie di funzioni ortogonali (N Zanichelli, Bologna, 1936).
- Bologna (4) 16 (1937), 39-48.
- Bologna (4) 20 (1941), 105-135.
- II (Nicola Zanichelli, Bologna, 1941).
- Monografie di Matematica Applicata (Nicola Zanichelli, Bologna, 1943).
- Monografie di Matematica Applicata (Nicola Zanichelli, Bologna, 1946).
- 1 (2nd edition) (Nicola Zanichelli, Bologna, 1948).
- 2 (2nd edition) (Nicola Zanichelli, Bologna, 1949).
- Aggregati, analisi delle funzioni, integrazione, derivazione (3rd edition) (Nicola Zanichelli, Bologna, 1951).
- (Nicola Zanichelli Editore, Bologna, 1952).
- Giovanni Sansone and Roberto Conti, Curve caratteristiche di sistemi omogenei, in Scritti matematici in onore di Filippo Sibirani (Cesare Zuffi, Bologna, 1957), 243-260.
- Giovanni Sansone, Equazioni differenziali nel campo reale (Part 2) (Terza edizione Zanichelli, Bologna, 1963).
- di Bologna, 1972), Boll.
- Marcolongo publications
- Cesare Burali-Forti and Roberto Marcolongo, Elementi di calcolo vettoriale con numerose applicazioni alla geometria, alla meccanica ed alla fisica matematica (Zanichelli, Bologna, 1909).
- Cesare Burali-Forti and Roberto Marcolongo, Elementi di calcolo vettoriale con numerose applicazioni alla geometria, alla meccanica e alla fisica matematica (2° edizione) (N Zanichelli, Bologna, 1921).
- I: Trasformazioni lineari (2nd ed.) (Zanichelli, Bologna, 1929).
- Roberto Marcolongo, Leonardo da Vinci nella storia della matematica e della meccanica, Atti Congresso Bologna 1 (1929), 275-293.
- Roberto Marcolongo, Il calcolo vettoriale nell'insegnamento secondario, Atti Congresso Bologna 3 (1930), 415-419.
- Roberto Marcolongo, Sullo stato attuale della pubblicazione italiana dei manoscritti di Leonardo da Vinci ed in particolare su quella del Codice Arundel, Atti Congresso Bologna 6 (1932), 427-430.
- Roberto Marcolongo, La misura del tempo II, Scientia, Bologna 61 (1937), 82-92.
- Roberto Marcolongo, La misura del tempo I, Scientia, Bologna 61 (1937), 16-23.
- Roberto Marcolongo, Nel trecentenario dei "discorsi sopra due nuove scienze" di Galileo Galilei, Franzosische Ubersetzung: Scientia, Bologna, Suppl.
- Roberto Marcolongo, Nel trecentenario dei "discorsi sopra due nuove scienze" di Galileo Galilei, Scientia, Bologna 65 (1939), 143-150.
- Bompiani publications
- delle Scienze di Bologna (8) 2 (1924-25), 61-65.
- Enrico Bompiani, Il principio di continuita e l'immaginario in geometria, in F Enriques (ed.), Questioni riguardanti le matematiche elementari (Zanichelli, Bologna,1925), 271-308.
- delle Scienze di Bologna (8) 3 (1925-26), 35-38.
- II (Zanichelli, Bologna (1926), 671-727.
- delle Scienze di Bologna (8) 4 (1926-27), 15-19.
- Enrico Bompiani, Moderni indirizzi di geometria differenziale, Atti del I Congresso U.M.I., Zanichelli, Bologna (1937), 88-108.
- Enrico Bompiani, Un procedimento di integrazione approssimata, Atti del I Congresso U.M.I., Zanichelli, Bologna (1937), 161-167.
- Enrico Bompiani, Sulle curve appartenenti a complessi di rette, Atti del I Congresso U.M.I., Zanichelli, Bologna (1937), 292-295.
- Enrico Bompiani, Statica grafica e geometria proiettivo-differenziale, Atti del I Congresso U.M.I., Zanichelli, Bologna (1937), 296-299.
- Borali-Forti publications
- C Burali-Forti, Elementi sulla teorica delle funzioni circolari ed applicazioni alla trigonometria piana e sferica (Zanichelli, Bologna, 1888).
- C Burali-Forti and R Marcolongo, Elementi di calcolo vettoriale con numerose applicazioni alla geometria, alla meccanica e alla fisica-matematica (Zanichelli, Bologna, 1909).
- C Burali-Forti and R Marcolongo, Elementi di calcolo vettoriale con numerose applicazioni alla geometria alla meccanica e alla fisica matematica (2nd ed.) (Zanichelli, Bologna, 1921).
- C Burali-Forti and R Marcolongo, Analisi vettoriale generale e applicazioni Vol I: Trasformazioni lineari (2nd ed.) (Zanichelli, Bologna, 1929).
- C Burali-Forti, P Burgatti and T Boggio, Analisi vettoriale generale e applicazioni Vol II: Geometria differenziale (Zanichelli, Bologna, 1930).
- Halsted Beltrami
- Thus he who for lack of a degree had seen himself disbarred from the secondary schools and from the corps of military engineers, was, on the basis of his publications in the Annali di Matematica, named (18 October 1862) "Professore straordinario" in the University of Bologna.
- From Pisa he returned to Bologna in September, 1866, as professor of rational mechanics.
- "Bologna, 9 June, 1868.
- "Bologna, 23 July, 1868.
- Publications of Gino Fano
- G Fano, Trasformazioni di contatto birazionali del piano, Atti Congresso Bologna 4 (1928), 35-42.
- Bologna 1928 (Zanichelli, Bologna, 1928), 115-121.
- G Fano, Geometria non euclidea (Introduzione geometrica alla teoria della relativita) (Zaniclielli, Bologna, 1935).
- Enriques' reviews
- The able work, 'Problemi della Scienza', from the pen of F Enriques, Professor of Geometry in the University of Bologna, well deserved an English translation.
- Among mathematicians Enriques, who is professor of projective and descriptive geometry in the University of Bologna, has long been favourably known for his contributions to geometry, especially for his admirable treatise on "Projective Geometry" and for his penetrating essays on "The Foundations of Geometry." In the work before us the distinguished geometrician addresses a far wider circle of students and thinkers: not only mathematicians, but psychologists, logicians, philosophers, astronomers, mechanicians, physicists, chemists, biologists and others.
- This is the first volume of a series "Per la Storia e la Filosofia delle Matematiche," published under the auspices of the Istituto Nazionale per la Storia delle Scienze Fisiche e Matematiche, and edited by Professor Enriques of the University of Bologna.
- Brusotti publications
- Bologna 4 (1931), 139-145.
- Luigi Brusotti, Luigi Cremona (nel cinquantenario della morte), in Celebrazioni di L Cremona (Bologna, 1954), 19-34.
- in onore di F Sibirani (Zuffi, Bologna, 1957), 33-39.
- Rudio's talk
- At the age of 23 he went to Italy, in order to prepare for the post as Canon in Frauenburg, which his uncle, the future Bishop of Ermland intended for him, by studying theology and medicine in Bologna.
- Among the most famous teachers at the University of Bologna at the time was the astronomer Domenico Maria di Novara.
- Surely we can look for the origins of the bold ideas to which we owe our modern worldview in the stimulating scientific exchange that Copernicus experienced in Bologna and later on in Rome, Padua and Ferrara.
- Publications of Alessandro Padoa
- A Padoa, Questioni fisolofiche a cura della Societa Filosofica Italiana, Chiantore-Formiggini (Bologna, 1908).
- Enriques, Pt.1: Critica dei principi; Pt.2: I problemi classici della geometria e le equazioni algebriche; Pt.3: Numeri primi e analisi indeterminata - Massimi e minimi, Zanichelli 4 (Bologna, 1924-1927).
- Zervos publications
- 8th International Congress of Mathematicians Bologna 1928 3 (1930), 37-40.
- 8th International Congress of Mathematicians Bologna 1928 4 (1931), 409-412.
- Gigli publications
- Duilio Gigli, Dei numeri complessi a due e piu unita, in Questioni riguardanti le matematiche elementari (N Zanichelli, Bologna, 1912), 1-146.
- La funzione esponenziale e I logaritmi (N Zanichelli, Bologna, 1931).
- Napierian logarithms explained by Pietro Mengoli
- The Italian mathematician, Pietro Mengoli, the last disciple of Bonaventura Cavalieri in Bologna, has not yet received the just appreciation he merits.
- The Geometria Speciosa of Pietro Mengoli, published in 1659 in Bologna, contains an elementary, purely arithmetical, and rigorous theory of Napierian logarithms.
- Viola on Amaldi
- Born in Verona on 18 April 1875, he completed his university studies in Bologna, where he was a pupil of Federigo Enriques, of Cesare Arzela and, above all, of Salvatore Pincherle, who guided him in his first research in Mathematical Analysis.
- Between his first publications emerged the treatise, that took time, entitled: Le operazioni distributive e le loro applicazioni all'Analisi (Bologna, 1901) (Distributive operations and their applications in Analysis), written in collaboration with Pincherle.
- Pompilj publications
- Giuseppe Pompilj, La mutabilita dell'universo dei campioni, in Scritti matematici in onore di Filippo Sibirani (Zuffi, Bologna, 1957), 225-232.
- Giuseppe Pompilj, La regressione, Statistica (Bologna) 20 (1960), 583-603.
- Mathematics at Aberdeen 1
- The University, based on those at Paris and Bologna, was to be under the control of the Roman Catholic Church with Bishop Elphinstone and his successors in the office of Chancellor.
- Charles Bossut on Leibniz and Newton Part 2
- The Institute of Bologna was founded in 1713 through the means of the celebrated count de Marsigli to whom natural history is so much indebted.
- Cotlar publications
- Mischa Cotlar, Quadratic inequalities for Hilbert transforms and Hankel forms in the spaces L2(F) and L2(B), Geometry and complex variables, Bologna, 1988/1990, Lecture Notes in Pure and Appl.
- W H Young addresses ICM 1928
- The International Congress of Mathematicians took place in Bologna from 3 September to 10 September 1928.
- Cafaro's publications
- E Cafaro, D Grasso, F Pegoraro, F Porcelli and A Saluzzi, Finite Larmor radius effects on nonlinear collisionless magnetic reconnection, in J W Connor, E Sindoni and J Vaclavik, Theory of Fusion Plasmas (SIF e Editrice Compositori, Bologna, 1996), 453-458.
- Hilbert quotes
- In 1928 the Congress was held in Bologna.
- Dubreil-Jacotin on Maria Gaetana Agnesi
- we have the Italian Maria Gaetana Agnesi (1718-1799), the first woman professor of mathematics on a faculty; indeed, she was appointed professor at the University of Bologna by Pope Benedict XIV.
- Hatzidakis papers
- N J Hatzidakis, Due proposte per l'insegnamento medio, Atti Congresso Bologna 3n(1930), 439-441.
- Dehn on Mathematical abilities
- In 1932 Dehn wrote the 16-page essay Das Mathematische im Menschen (Mathematical ability in humans) which he published in Scientia, an Italian journal produced in Bologna by Federigo Enriques.
- W H Young addresses ICM 1928 Part 2
- The International Congress of Mathematicians took place in Bologna from 3 September to 10 September 1928.
Quotations
- Quotations by Cardan
- Scipio Ferro of Bologna well-nigh thirty years ago discovered this rule and handed it on to Antonio Maria Fior of Venice, whose contest with Niccolo Tartaglia of Brescia gave Niccolo occasion to discover it.
Famous Curves
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Chronology
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EMS Archive
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BMC Archive
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Gazetteer of the British Isles
- References
- The first lectures in Italy on Galois theory: Bologna, 1886-1887.
Astronomy section
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JOC/BS August 2001