**Giulio Vivanti**'s parents were Guglielmo Vivanti (1831-1903) and Regina Colorni (1831-1863). Guglielmo Vivanti, the son of Giuseppe Vivanti and Ester Rossena, was a landowner who had qualified with a law degree. It was a Jewish family and at the time Giulio was born they were living at No 3 via Tubo Casa in Mantua (now renamed via Bertani). In 1862 Giulio's sister Clelia was born. The city of Mantua, where the Vivanti family lived, had become part of the Austrian Empire under the Congress of Vienna in 1815 but just a few years before Giulio was born there was a revolt against Austrian rule which was suppressed by the Austrian army. This episode was an important step in the beginning of the unification of Italy. Before Giulio began his secondary school studies, the family moved to No 3 Agnello Casa (now renamed via Agnelli) in Mantua.

In 1869 Vivanti began his studies at the Liceo-ginnasio Virgilio of Mantua. His achievements there were outstanding and on 27 September 1876 he was examined for his high school diploma earning the top mark in all his subjects. His examiners gave him a special merit in Italian and in physics. 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 Arzelà 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.

On 25 January 1887, Vivanti married Enrichetta Bianchini, the daughter of a 'landowner' from Padua. Giulio and Enrichetta Vivanti had five children: Eduardo Guglielmo Isacco Vivanti (born in 1887), Regina Vivanti (born 1888), Anna Vivanti (born 1890), Leo Vivanti (born 1892) and Alberto Vivanti (born 1893).

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. This was transferred to the University of Pavia in 1893. He had entered several competitions for professorships before this date, for example he entered one for Modena in 1887 and in the one for Turin in 1890.

On 23 October 1892 Vivanti sent a note to Giuseppe Peano from Mantua entitled *Sull'uso della rappresentazione geometrica nella teoria aritmetica dei numeri complessi* Ⓣ for publication in the *Rivista di Matematica, *of which Peano was the editor-in-chief. Vivanti introduced the note having arisen from the course he was teaching on this topic (see, for example [1]):-

He worked at Pavia as professor in theWhile teaching a course on the general theory of algebraic numbers, I came to observe that the theory of complex whole numbers assumes a fairly clear and intuitive form thanks to the constant recourse to geometrical representation. Here I outline the part of my lessons that refers to the above mentioned theme, in the hope that it might be of some interest to readers of the 'Rivista' from a didactic point of view. For brevity's sake. I will omit all that reflects the extension of elementary operations to complex numbers, an extension to be carried out in conformity with Hankel's 'principle of the permanence of formal rules'.

*Scuola Normale*for three years until 1895. His work there was described in a letter dated 19 December 1895 by Carlo Formenti, Dean of the Faculty of Mathematics, written to the rector of the university [4]:-

In December 1895 he was appointed as extraordinary professor of infinitesimal calculus at the University of Messina. In 1897 he entered a competition for the chair of infinitesimal calculus at the University of Modena. A committee, with Ulisse Dini as president, considered Vivanti's application along with that of seven other candidates, namely Italo Zignago, Mineo Chini, Onorato Nicoletti, Rodolfo Bettazzi, Domenico Amanzio, Orazio Tedone and Giuseppe Lauricella. A report of the findings of the committee appeared in [3] and we give a version of their evaluation of Vivanti:-Prof Giulio Vivanti, in addition to the service provided in this Royal University, as Internal Professor of the normal school, mathematical section, annexed to the Faculty of Science, and in addition to acting as substitute in algebraic analysis and analytical geometry that he did during the last year during the illness of Prof G Platner, he also held a free course on 'The theory of the algebraic resolution of equations' a course approved by the Faculty of Science[...]The service provided by Prof Vivanti in this university was constantly praiseworthy for zeal and diligence, all the more because he knew how to be loved by the students for his skill in educating them and for the love and the patience with which he advised them and followed them in their studies, as well as being able to be appreciated by the professors who were his colleagues for the firm and extended culture which he required for the office of which he was in charge.

For a list of Vivanti's publications, including the 52 that he submitted for the competition for the chair at Modena, see THIS LINK.Dr Giulio Vivanti, a graduate with a laurea in mathematics from Bologna in1883, obtained a 'libera docenza' teaching position in infinitesimal calculus, which was then transferred to Pavia. He taught there as an internal professor in the school of education. Since December1895he has been an extraordinary professor of infinitesimal calculus in Messina. He presents52original printed works, reviews, translations and lithographed courses. The first19works were already judged in the calculus competition in Modena in1887and in the one in Turin in1890. The Commissions said that these works demonstrate a lot of ease of assimilation and versatility of talent, in spite of some errors that were detected there. The numerous works that Vivanti published after1890refer in part strictly to calculus, and partly to the most varied branches of mathematics with greater relevance to the chair in this competition. It would be too much to expose here in this place the complete and minute analysis made by the Commission. To remember the works that are most pertinent to questions of calculus, we will limit ourselves to hinting at the interesting question proposed with the memoir: "On the series of powers whose coefficients depend on a variable". - The attempts made with the work "Preliminaries for the study of the functions of two variables", are praiseworthy. The book "The concept of the infinitesimal and its application to mathematics" shows that Vivanti has a vast historical, literary and bibliographical knowledge. These qualities are further confirmed by the work "Theory of sets", where Vivanti publishes the complete collection of the propositions so far known relative to the interesting continuous groups, connected sets of points, of transfinite numbers, on the order types, etc., with the bibliographic list of70works on this subject. There Vivanti tries also to understand and know how to handle the theories of mathematical logic. The works on the application of the function can also be noted in the Poncelet polygons, on the surfaces of constant mean curvature, icosahedral irrationality, contact transformations, the theory of partial derivatives of the2nd order, the extension of the Ampère method, on the integral polydromes of differential equations, and not a few others. 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. Finally one must take into account the various years of lecturing, in which he gave splendid evidence of talented teaching. Together with all these works, Vivanti shows that he continues to be an indefatigable worker, and if he does not leave deep footprints in the various parts he has dealt with, he knows how to make himself master of each one, using it with ease. His mathematical culture is undoubtedly the most varied; and he demonstrates a special aptitude for his own research.

The committee ranked Vivanti first followed by Bettazzi and Tedone. However, Vivanti must have turned down the chair at the University of Modena for he remained at the University of Messina where he became a full professor in 1901. In addition to the regular mathematics courses he also taught a course of mathematics aimed at students of natural science since it was felt that such students did not have the necessary background in the subject.

On 1 December 1907 Vivanti requested a transfer to the University of Pavia. He was Dean of the Faculty of Science of the University of Pavia for the three years 1914-17, resigning from that position in March 1917; he was also Dean of the same Faculty from 1920 until 1924. In 1924 Vivanti moved to the University of Milan. This was a new university, founded in 1924 from the merger of two older institutions. At this new university he taught Higher Analysis, Differential Geometry, Mathematical Analysis, Algebraic Analysis and Infinitesimal Analysis. He was head of the Faculty of Science from 1930 to 1932, a member of the board of directors from 1926 to 1934, and director of the advanced course in applied mathematics from 1932 to 1934. Salvatore Coen writes [1]:-

For reviews of theThanks to his mastery of modern languages, he was solidly inserted in the international mathematical community, above all in that of Germany, where his indefatigable activity as reviewer for the 'Jahrbuch über die Fortschriften der Mathematik'Ⓣwas well-known(he published a total of1,740reviews between1884and1938). Vivanti was, moreover, sensitive to didactic issues. The clearest testimony to his teaching skills lies in his nineteen university and six secondary school textbooks, together with the clearly-explained booklets published by Hoepli on analytic functions, on integral equations, and on polyhedric and modular functions, some of which were translated into German and favourably received in Italy and abroad. Given his training and his academic activities, it was natural that Vivanti's collaboration on the 'Enciclopedia delle Matematiche Elementari' was primarily focused on analytic slope. He contributed two articles on this matter and oversaw their coordination with other related entries. Member of the Pavia section of Mathesis, and later, starting from1925, President of the Milan section, he was nonetheless only fully involved in the first volume of the Enciclopedia. Subsequently, his role became increasingly marginal and eventually ceased altogether, partly as a result of his blindness, and partly because of the racial laws, which led to his marginalisation from the academic world.

*Enciclopedia delle Matematiche Elementari*Ⓣ, see THIS LINK.

In [4] Vivanti's activities relating to the Royal Virgilian Academy of Sciences, Letters and Arts of Mantua are discussed. We give some details below. On 12 June 1892 he addressed the Academy delivering the lecture "The infinite in nature and science". The lecture "was heard with the utmost attention, and when it ended it was greeted by long cordial applause." At the meeting of the Academy on 21 May 1893 a proposal was put forward, signed by seven members of the Academy, proposing that Vivanti be elected to the Academy which was unanimously approved. Vivanti responded with a letter sent from Mantua on 24 May expressing his "heartfelt gratitude for the high honour that the Academy wanted to appoint me as an effective member". As a member of the Academy he was involved in its activities, in particular writing obituaries. However, by the 1930s the political situation in Italy, with its Fascist government, made things increasingly difficult for Vivanti since he was a Jew. Vivanti wrote to the President of the Academy on 14 November 1935. In this letter, as well as providing some data concerning his academic career and information related to his own scientific production, he indicated that he did not want to be registered with the National Fascist Party. At this stage he continued to be a member of the Academy but the royal decree of 17 November 1938, "Provisions for the defence of the Italian race", led to the expulsion of Jews from universities and academies. Following this decree, eleven members of the Academy were expelled, including the mathematicians Gino Fano, Gino Loria and Giulio Vivanti. In a census of Jewish academics dated 8 October 1938 Vivanti is described as "registered with the Jewish community" and "professing the Jewish religion."

Vivanti had retired from teaching at the University of Milan in 1934 when he had reached the age of 75 and he had been appointed professor emeritus. However, the last ten years of his life must have been greatly saddened by the fact that his country Italy, which he had supported so passionately over the years, in some sense disowned him. Let us end this biography by looking a little at this passion he had shown for his country.

Italy entered World War I in May 1915. The country had remained neutral when war broke out in August 1914 and began to negotiate with both sides to see which would offer the most for their support. Eventually in April 1915, at the Treaty of London, Italy joined France, Britain and Russia and one month later began military advances towards Austria-Hungary. Vivanti was in Pavia at this time and he became President of the Pavia Section of the "General Union of Italian Teachers for the National War". In this capacity he circulated fifteen messages to his fellow teachers and presidents of other Sections during the period 1916-1918, the first being on 9 June 1916. In this message he said that during the first year of the war the Teachers of the Province of Pavia were worthy of the highest praise for the assistance they had given to soldiers [4]:-

He encourages the teachers to "dedicate their efforts to hasten the inevitable final victory." Later missives called for "a broad civil mobilization, which will leave all citizens who are fit for arms free for war" and one sent out on 14 May 1917 stated [4]:-... always first in every useful initiative, always ready to offer their personal work and their help, they have rendered invaluable service to the great national cause.

A month later he is proposing that school pupils assist in the war effort by working in military hospitals, and supporting the families of the military and of those killed in the war. The war had not gone well for Italy and in October 1917 they had a military disaster at Caporetto which left many Italians dead, injured or captured. After the battle the Austrians began to occupy much of the Veneto. By the beginning of 1918 Vivanti was urging support for refugees from invaded areas, and by the middle of 1918 he writes [4]:-May the inevitable victory crown the efforts of our marvellous army very soon! On that day we will celebrate, together with the triumph of freedom, of civilization, of law, also that of the schools; because from the schools came those young heroes who peacefully lost their lives on the Alps and the Carso, also from the schools came those beneficial forces which supported our people during the long struggle.

Vivanti was proposed for the honour of Knight of the Crown of Italy for his deep patriotic commitment during the war. One can only imagine how he must have suffered with the Fascist decrees to remove Jews from public offices.At this grave hour, in which the very existence of the Fatherland is at stake, it is our first need to render our work of assistance and propaganda more intense, assiduous, and more effective.

**Article by:** *J J O'Connor* and *E F Robertson*