Geiser's father was a butcher and innkeeper. The famous Swiss mathematician Jakob Steiner was Carl F. Geiser's great-uncle. Geiser studied for four semesters from 1859 to 1861 at the Zürich Polytechnikum and then went to Berlin for four semesters from 1861 to 1863 to study under Karl Weierstrass and Leopold Kronecker. Since the support from his parents was not sufficient, he gave private lessons to students, some of whom were found for him by Weierstrass and Kronecker. He graduated in 1863 and returned to Switzerland as a Privatdozent at Zürich Polytechnikum. He pursued graduate studies at the University of Bern with doctorate in 1866 under Ludwig Schläfli with dissertation Beiträge zur synthetischen Geometrie. At the Zürich Polytechnikum, Geiser, together with Theodor Reye, temporarily fulfilled the duties of a professorial chair upon the death of Joseph Wolfgang von Deschwanden, until the professorial chair was given in 1867 to Wilhelm Fiedler. Geiger had already fulfilled the habilitation requirements in 1863; at the Zürich Polytechnikum, he was appointed from 1863 to 1869 a Privatdozent for pure and applied mathematics, from 1869 to 1873 a professor extraordinarius, and from 1873 to 1913 a professor ordinarius for higher mathematics and synthetic geometry. From 1881 to 1887 and from 1891 to 1895 Geiser was the director of the Zürich Polytechnikum. Geiser taught algebraic geometry, differential geometry, and the theory of invariants. He published research on algebraic geometry and minimal surfaces. In addition to his research results, Geiser's participation in the development of Switzerland's education system is remarkable. He was helped by his relationships with eminent politicians and mathematicians. Geiser published previously unpublished lecture notes and treatises from Steiner's Nachlass. Geiser and Ferdinand Rudio were two of the main organizers of the International Congress of Mathematicians in 1897 in Zürich. Geiser was elected in 1888 a foreign member of the German Academy of Sciences Leopoldina. He was elected an honorary member of the Swiss Mathematical Society at its session in 1911–1912.
Monographs
as editor: Die Theorie der Kegelschnitte in elementarer Darstellung. Auf Grund von Universitätsvorträgen und mit Benutzung hinterlassener Manuscripte Jacob Steiner’s, B. G. Teubner, Leipzig 1867
, B. G. Teubner, Leipzig 1869
Articles
', Mittheilungen der naturforschenden Gesellschaft in Bern 580–602, 1865, pp. 97–107
