Whilst teaching in Langenthal he also studied towards a doctorate at the University of Bern. He completed his thesis Ein mit der Theorie algebraischer Flächen zusammenhängendes planimetrisches Problem Ⓣ in 1888. The doctorate was conferred "summa cum laude", with highest honours . Bützberger was the 11th of Schläfli's 12 doctoral students.
Bützberger became a mathematics teacher at the Kantonsschule in Zürich in 1896. From 1899 onwards he taught in the school's technical track only, thus preparing future engineers for their university studies. Furthermore, he also taught mathematics at Zürich's adult education centre. At the University of Zürich he delivered lectures on descriptive geometry to future secondary school teachers. In 1903 he took up a teaching post at the technical school in Burgdorf.
Bützberger was a 'first-rate teacher and author of several much valued textbooks with ample exercises' . His textbooks include Lehrbuch der ebenen Trigonometrie mit vielen Aufgaben und Anwendungen Ⓣ (Zürich, 4th edition 1910), Lehrbuch der Stereometrie Ⓣ (Zürich, 3rd edition 1916), and Lehrbuch der Arithmetik und Algebra für Mittelschulen Ⓣ (Zürich, 2nd edition 1920). All of them were reviewed favourably and were reprinted several times. Salkowski calls Lehrbuch der Stereometrie Ⓣ an 'established book' , whilst Barneck comments on Bützberger's style in Lehrbuch der Arithmetik Ⓣ ...: 'The presentation is broad and comprehensible for pupils' . Zacharias commends Lehrbuch der ebenen Trigonometrie Ⓣ... for similar reasons :
The [writing] is succinct and clear; the definitions and theorems are succinct and easy to learn throughout; historic remarks make for interesting reading; numerous exercises, partly theoretical, partly practical, are included in the individual sections [...]Moreover, Bützberger published several papers, among them Eiförmige Drehkörper Ⓣ (1917), which is aimed at secondary school pupils. In this paper he determines centroids of ovoids, using the Guldinus theorem. As he mentions in the introduction, 'one of my pupils, a keen ornithologist, inspired me to solve [the problems treated here]' . Bützberger also wrote a very readable biography of the Bernese mathematician Georg Sidler , his friend and former teacher. In 1912 he gave a talk at the annual meeting of the Swiss Mathematical Society.
He had a particular interest in Jakob Steiner and published a couple of biographical papers on the geometer. More importantly, he organised and edited Steiner's papers from 1823-26 on the request of the Bernese Society for Natural Scientists. As Bützberger remarks in , Graf discovered Steiner's handwritten manuscripts covering the period from 1814 - 1826 in the attic of the Town Library in Bern. Graf then passed the documents on to Bützberger 'to put them in order and to good use' . The collection of Bützberger's papers is now stored in the ETH Library Archive.
More details of Bützberger's work on Steiners papers are at THIS LINK
Bützberger joined the organising committee of the first International Congress of Mathematicians (or enlarged committee as it is called in the minutes) in December 1896. At his first committee meeting on 8 December he joined the reception committee chaired by Hurwitz. At the meeting on 31 July 1897, Rudio suggested that a 'correspondence and mail room should be established and a postal service organised' ; Bützberger accepted this task.
Bützberger was married to Rosa Kohler. The couple had two children: a son, Fritz, and a daughter, Marie. There is little information about Bützberger's personal life in the obituaries and his estate. In a letter to U Hoepli and his wife in 1920 , Bützberger mentions his son and daughter. Presumably he would have mentioned any further children. He also refers to his brother Ernst and his brother-in-law Hardmeyer. Ulrico Hoepli (1847-1935) was a Swiss bookseller who emigrated to Milan. He became one of Italy's most important publishers, specialising in sciences and Italian classics, and an influential art patron.
Article by: Stefanie Eminger, University of St Andrews