Upon his return to Switzerland, Weiler first worked as a mathematics lecturer at the Ryffel Institute in Stäfa (canton Zürich). In 1878 he was appointed to a teaching post for mathematics at the women teachers' college in Zürich. Weiler also habilitated as Privatdozent at both the Polytechnic and the University of Zürich. He stayed at the Polytechnic, where he was also Wilhelm Fiedler's assistant, from 1875-1901 and started his job at the University in 1891. There he taught analytic and descriptive geometry, later on he also lectured on map projection. In 1899 he became a Titularprofessor for geometry at the university. At the beginning of the 20th century Weiler supervised five doctoral students in total, but none of them became influential mathematicians.
Weiler's research interests lay in Steiner geometry; in particular, he was interested in complexes and congruencies of rays. He published a range of papers on problems in descriptive geometry, axonometry and map projections. Two examples of his papers are Neue Behandlung der Parallelprojektionen und der Axonometrie (1889) and Geometrisches über einige Abbildungen der Kugel in der Kartenprojektion (1903).
Weiler joined the organising committee of the first International Congress of Mathematicians in December 1896, but he did not have a specific position and is not mentioned in the committee minutes (except for the attendance records).
Article by: Stefanie Eminger, University of St Andrews