**Georg Sidler**was born on 31 August 1831 to Georg Joseph Sidler (1782-1861) and Verena Maria Sidler née Moos (1806-1886). He was their only child, but had two half-sisters from his father's first marriage with Josepha Landtwing. One of the girls died at the age of seven; the other one, Elisabetha Carolina, later married Heinrich Schweizer, professor for German and Sanskrit philology at the University of Zürich.

Both of Georg's parents came from old-established families in canton Zug; many of his ancestors had been involved in local and cantonal politics. His paternal grandfather Georg Damian held a number of offices; most notably he served as a Landvogt (bailiff) in the Valle Maggia in Ticino. Georg's father Georg Joseph made a name for himself as a politician, first in his home canton Zug, then in Zürich and in the newly established federal government. From 1810-1833 he served as delegate of canton Zug in the Tagsatzung, the legislative and executive council of the old Swiss confederacy. In addition, he also served as Landamman (the chief magistrate in a Swiss canton; similar to a Scottish provost) in Zug from 1813-1834. Sidler senior was a liberal politician, but as the conservatives gained power in Zug his influence dwindled, and as a result the family moved to Unterstrass, near Zürich, in 1839. From 1845-1861 he was a member of the cantonal parliament in Zürich; furthermore, he represented the canton Zürich in the National Council five times, each time serving as Father of the House. (The National Council or Nationalrat is the lower, but bigger, house of the Swiss federal government. The upper house is the Council of States or Ständerat). He fervently advocated the foundation of the Federal Polytechnic in the Swiss parliament, calling out to his colleagues in 1854: 'Let us trust the government and put its finest idea into practice!' [1, p. 68]. Sidler senior also had a great interest in astronomy and mathematics, having attended lectures in both subjects during his law studies. In his house, both in Zug and in Unterstrass, he had a little observatory, and Graf reports in [2] that 'he always took Kästner's *Foundations of Mathematics* or Lacroix's *Introduction to Differential and Integral Calculus* along to meetings of the National Court'. Sidler senior did not publish any scientific papers, but it is likely that he helped spark his son's interest in mathematics and astronomy.

Let us now return to Georg Sidler junior. He attended primary school first in Zug and then in Unterstrass. His father had bought a small manor there, which the family shared with the Cramer family. The son Carl Cramer (1831-1901), a future botanist, became a life-long friend of Sidler. Sidler attended the Gymnasium in Zürich from 1843-1850, excelling in mathematics and ancient languages. After having obtained his Matura, he matriculated at the University of Zürich to study mathematics. His teachers there were J L Raabe and J Amsler, who was Privatdozent at the university at the time. In 1852, Sidler moved to Paris to study there for a further two years. He attended lectures by J Bertrand (analysis), M Chasles (geometry), H Faye (astronomy), G Lamé (mathematical physics), U J Le Verrier (popular astronomy), J Liouville (differential equations) and V Puiseux (celestial mechanics). In his memoirs, partly quoted in [4] and retold in [2], Sidler describes his activities and acquaintances in Paris as well as the political events he witnessed, such as the newly crowned Emperor Napoleon III parading around Paris, and the population's restrained reaction.

It was Puiseux's lectures that inspired Sidler's doctoral dissertation *Sur les inégalités du moyen mouvement d'Uranus dues à l'action perturbatrice de Neptun* Ⓣ, published after his return from Paris in 1854. His father had offered to pay for a trip to England, but Sidler was anxious to get back to Switzerland and receive his doctorate. In addition to submitting his thesis, which he wrote during his stay in Paris, Sidler reports in [4] that he had to pass two written exams, one set by Raabe, the other one set by A Müller, and an oral exam. Furthermore, he had to give a public talk, *Über die Bewegungen im Sonnensystem und die allgemeine Anziehung*. Ⓣ A more succinct version of Sidler's thesis was published as *Über die Acceleration des Uranus durch Neptun *in *Astronomische Nachrichten* in 1858.

After having received his doctorate, Sidler habilitated as Privatdozent at the University of Zürich with a lecture entitled *Methode der kleinsten Quadrate* Ⓣ. Instead of starting to teach, however, he went to Berlin for a year, as he wanted to get to know a German university [4]. There he attended lectures on a range of mathematical topics by Dirichlet, on theoretical astronomy by Encke, on geodesy by Bremiker, on mathematical physics by Clausius and on geometry by Steiner. Sidler often went for a walk with Steiner; the two mathematicians stayed in touch for the rest of Steiner's life.

Encke asked Sidler to calculate the ephemeris of Neptune for the year 1856, to be published in the *Berliner Astronomisches Jahrbuch 1856*, and allowed him to use the Berlin observatory. As a result, Sidler spent many nights in the observatory, observing and mapping recently discovered minor planets. He gives a detailed account of the method they used in his memoirs, parts of which are quoted in [4], but also remarks that:

Despite this, Sidler retained an interest in astronomy for the rest of his life. All of his biographers praise his exemplary lecture notes - not only did he carefully write up the lectures that he attended, he also copied entire lecture courses by for example Steiner and Dirichlet from friends and asked the respective professors to fill in any gaps.The ongoing work on the Berlin Observatory redounded more to my detriment than to my advantage, for spending entire winter nights in the cold rooms came back to haunt me by day in the form of sleepiness. Thus, my notes of important lectures became incomplete.

After his return to Zürich in August 1855, Sidler habilitated at the newly founded Polytechnic. He taught arithmetic, trigonometry and theoretical astronomy as a Privatdozent. Moreover, he also took on P F Servient's lectures on differential and integral calculus in French. Rudio remarks in [4] that out of the teaching staff in the Polytechnic's first year, Sidler was the last to die.

After a year in Zürich, Sidler was appointed to a teaching position at the newly founded Kantonsschule (secondary school) in Bern. The school had two departments, one specialising in arts and the other one in sciences, but Sidler taught mathematics, and for a few years mechanics, in both departments. For a decade he also taught history in the science department.

In addition to his duties at the school, Sidler also lectured at the University of Bern. He started as a Privatdozent in 1857 and was promoted to Honorarprofessor for mathematics and astronomy in 1866. This meant that he became a full member of the teaching staff, but he continued to teach only a few hours a week. The promotion was proposed by his colleagues, who recognised Sidler's contribution to mathematics and astronomy both at the university and in Switzerland; in particular they highlighted his commitment to the university's observatory. In 1880, when the Kantonsschule had to close down, he was appointed to an extraordinary professorship, which he held until 1898. He would have been appointed to Schläfli's chair in 1891, but explicitly refused this position and Graf was appointed instead. Sidler remained a member of the university's academic staff and lectured occasionally even after resigning from his post. Throughout the years he lectured on a wide variety of topics, including algebra, analysis, arithmetic, astronomy, various areas of geometry, and mathematical physics. In [2] Graf gives a detailed list of when Sidler taught which lecture course; the summary of this fills almost a page in Rudio's biography [4]. We note that Sidler had a particular interest in the geometry of triangles and collected books on this topic.

In 1893 he asked for a sabbatical in order to spend another year in Berlin. He attended lectures on mathematical topics by H A Schwarz, Du Bois-Reymond and Knoblauch, and also on botany by S Schwendener. Bützberger reports in [1] that Schwarz occasionally called Sidler his 'mathematical conscience', as Sidler discussed his lectures with him very critically and in great detail. Despite his academic titles, he joined the student mathematical society. Sidler spent his free time visiting Berlin's many museums with his wife Hedwig née Schiess, whom he had married in 1866.

The University of Zürich renewed Sidler's doctorate in 1904 to mark the 50^{th} anniversary of obtaining it. Furthermore, Geiser dedicated his paper *Die konjugierten Kernflächen des Pentaeders* Ⓣ and Rudio his paper *Die Möndchen des Hippokrates* Ⓣ to Sidler. Two years later, Sidler's 50^{th} year in the Bernese educational service was celebrated officially as well, on Graf's instigation.

Apart from in his teaching positions, Sidler also made a name for himself as a member of the Bernese cantonal Matura Examination Committee (1880-1905) and of the Examination Committee for teachers in higher education. At the time, three secondary schools in Bern awarded the Matura (in Bern, Burgdorf and Pruntrut), and Sidler had to examine all pupils in mathematics. As every canton had its own education system, the examination regulations in canton Bern differed considerably from those in other cantons. As examiner, Sidler had to set the problems for the written exam and do all the marking, as well as conduct every oral examination in the canton. The respective teachers were excluded completely. Bützberger, a teacher himself, criticizes this system in [1]: Not only did it create a lot of work for the examiner, it also failed to reflect a teacher's abilities adequately. It seems that in most cantons the teachers were allowed to set the questions for the oral exam at least, thus giving the examiner the chance to better assess the pupils' performances. Bützberger remarks that the Polytechnic had only good experiences with pupils from his own school in Zürich, where the teachers were even allowed to conduct the written exams. He comments that Sidler was an excellent examiner, making the pupils work independently and encouraging them to develop their own thoughts.

As a result of his work as an examiner, Sidler published two papers, *Zur Theorie des Kreises* Ⓣ (1902) and *Zu den logarithmischen Reihen* Ⓣ (1904). Those were his last publications. For the annual publication (Schulprogramm) of the Kantonsschule in Bern he wrote three contributions: *Theorie der Kugelfunktionen* Ⓣ (1861), *Über die Wurflinie im leeren Raum* Ⓣ (1865), and *Zur Dreiteilung eines Kreisbogens* Ⓣ (1876). Out of these, the paper on spherical harmonics from 1861 was the most important and popular one. His friend Schläfli even dedicated a paper to it, commenting that [1]:

In addition, Sidler published a number of papers and talks on astronomical problems and phenomena as well as on problems in analysis and geometry. In his geometric papers he favoured historic problems, such as the trisection of an arc and the temple of Viviani. In his paperIn this academic work the author approached his topic historically by first deriving spherical harmonics and their properties from the development of inverse distance before examining them based on their general definition. I have learned a lot that I did not know before from this paper. The reader finds everything united that he would have to search for in scattered papers otherwise. Moreover, it is written in a way that he is not required to have any particular knowledge of infinitesimal calculus, such as gamma functions. Thus, every young man educated at our Swiss schools will read it with pleasure and success.

*Die Schale Vivianis*Ⓣ (1901) he showed an elementary solution to the problem and new results relating to Viviani's curve.

As most Swiss mathematicians of his time, Sidler was a member of the Schweizerische Naturforschende Gesellschaft, and of the societies for natural scientists in Bern and Zürich for most of his life. In addition, he was also an active member of the Swiss Alpine Club and a councillor in the synod of the Christian Catholic Church of Switzerland. As Rudio reports in [4], Sidler kept up to date with the scientific life in Zürich and corresponded with a number of his colleagues in Zürich, among them Rudio himself. Furthermore, he was very interested in everything that happened in his home canton Zug; he bequeathed charitable institutions in Zug a considerable amount of his fortune.

As mentioned above, Sidler was in touch with a number of mathematicians in Zürich. Most notable however are his friendships with Steiner and Schläfli, two of the great Swiss mathematicians of the 19^{th} century.

Sidler met Steiner during his first stay in Berlin. He reports in his memoirs that he could not attend all of Steiner's lectures, but he seems to have had a habit of demanding a great deal of himself, as in March 1855 Steiner wrote to Schläfli about his lectures [2]:

Teacher and student frequently went for walks together, discussing mathematics. Steiner spent a lot of time with Sidler during his stay in Bern in 1856-1858 and during the subsequent summers. He seems to have hoped that Sidler would help him formulate mathematical ideas, but this never came to fruition as Steiner suffered a stroke in 1862 and died half a year later. Bützberger reports in [1] that both Sidler and his mother looked after Steiner during those last few months. In the 1880s, Sidler donated a tombstone for Steiner's grave that has been rediscovered in the Bernese cemetery by Bützberger and Moser. He was also involved in placing a memorial plaque on Steiner's last residence in Bern.Only three listeners persevered; two of them are Swiss: old Sidler's son ... and the son of my colleague Prof Hagenbach in Basel, they are the only paying ones, the others deferred. As you can see, my monetary situation this semester was not much better than yours.

Schläfli was Sidler's colleague at the University of Bern for thirty-five years. Both had a reputation for being extremely helpful, yet making their lectures too difficult and abstract. Bützberger, who studied under both, rejects this allegation claiming that they advocated serious research [1]. He also nicely describes the friendship between these two Bernese lecturers [1]:

Although described as lank and bookish, Sidler enjoyed good health throughout his lifetime. On 9 November 1907 he died from a heart attack, and was buried in Zürich three days later.... Schläfli hardly could have hoped for a more ambitious, scholarly and congenial friend. Whilst he mainly lectured on analytic geometry, infinitesimal calculus, theory of functions and number theory, Sidler primarily gave lectures on theoretical astronomy and synthetic geometry. However, both had such a broad and thorough education that they could easily swap their duties, which indeed happened occasionally. No doubt one can imagine the autodidact Schläfli's interest when he asked Sidler to tell him about the famous lectures in Paris and Berlin, and how valuable Sidler's exemplary lecture notes were to him. Sidler introduced his older friend to the theory of spherical harmonics, ... and when Schläfli mastered this area through his inventions, Sidler, as a student, looked up to him without envy.

His main passions were mathematics and astronomy, but he also took great interest in botany, literature and arts. As Rudio put it [4]:

Who ... could ever forget Georg Sidler! Today we live in completely different times than just a few decades ago, and as the times change, so do the faces. The old type of scholar has disappeared; the modern scholars look different to those from fifty years ago. But according to the whole of his outward appearance, Georg Sidler belonged to the good old times, when we still had characters like Schweizer-Sidler, Mommsen, Weierstrass. And this appearance will live on in our memory for a long time to come.

**Article by:** Stefanie Eminger, University of St Andrews