Carl Friedrich Geiser (26 February 1843,

Langenthal Langenthal is a town and a Municipalities of Switzerland, municipality in the district of Oberaargau (administrative district), Oberaargau in the canton of Bern in Switzerland. On 1 January 2010 the municipality of Untersteckholz merged into the ...

– 7 March 1934,

Küsnacht Küsnacht () is a municipality in the district of Meilen in the canton of Zürich, Switzerland. History Küsnacht is first mentioned in 1188 as ''de Cussenacho''. Earliest findings of settlement date back to the Stone Age. There are also findi ...

) was a Swiss mathematician, specializing in algebraic geometry. He is known for the Geiser involution and Geiser's minimal surface.

Education and career

Geiser's father was a butcher and innkeeper. The famous Swiss mathematician

Jakob Steiner Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards st ...

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 Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school t ...

and

Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker as having said, ...

. 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 ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifi ...

'' at Zürich Polytechnikum. He pursued graduate studies at the

University of Bern The University of Bern (, , ) is a public university, public research university in the Switzerland, Swiss capital of Bern. It was founded in 1834. It is regulated and financed by the canton of Bern. It is a comprehensive university offering a br ...

with doctorate (

Promotion Promotion may refer to: Marketing * Promotion (marketing), one of the four marketing mix elements, comprising any type of marketing communication used to inform or persuade target audiences of the relative merits of a product, service, brand or i ...

) in 1866 under

Ludwig Schläfli Ludwig Schläfli (; 15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spac ...

with dissertation ''Beiträge zur synthetischen Geometrie''. At the Zürich Polytechnikum, Geiser, together with

Theodor Reye Karl Theodor Reye (born 20 June 1838 in Ritzebüttel, Germany and died 2 July 1919 in Würzburg, Germany) was a German mathematician. He contributed to geometry, particularly projective geometry and synthetic geometry. He is best known for his ...

, temporarily fulfilled the duties of a professorial chair upon the death of Joseph Wolfgang von Deschwanden (1819–1866), 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 Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

, 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 (partly due to his family connection with Jakob Steiner) with eminent politicians and mathematicians. Geiser published previously unpublished lecture notes and treatises from Steiner's ''

Nachlass ''Nachlass'' (, older spelling ''Nachlaß'') is a German language, German word, used in academia to describe the collection of manuscripts, notes, correspondence, and so on left behind when a scholar dies. The word is a compound word, compound in ...

''. Geiser and Ferdinand Rudio were two of the main organizers of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in 1897 in Zürich. Geiser was elected in 1888 a foreign member of the

German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (), in short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on 1 January 1652, based on academic models in Italy, it was originally named the ''Academi ...

. He was elected an honorary member of the

Swiss Mathematical Society The Swiss Mathematical Society, SMS (, SMG; ), founded in Basel on 4 September 1910, is the national mathematical society of Switzerland. It is a member of the European Mathematical Society. History The SMS was established on 4 September 1910 ...

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 (first part ''Jacob Steiner’s Vorlesungen über synthetische Geometrie''
Google Booksdittoditto
*
Einleitung in die synthetische Geometrie. Ein Leitfaden beim Unterrichte an höheren Realschulen und Gymnasien
', B. G. Teubner, Leipzig 1869
Internet-ArchivJahrbuch-Bericht

Articles

*
Ueber eine geometrische Verwandtschaft des zweiten Grades
', Mittheilungen der naturforschenden Gesellschaft in Bern 580–602, 1865, pp. 97–107 *
Ueber die Normalen der Kegelschnitte
', Journal für die reine und angewandte Mathematik 65, 1866, pp. 381–383
Google Booksditto
*
Ueber zwei geometrische Probleme
', Journal für die reine und angewandte Mathematik 67, 1867, pp. 78–89
Google Books
* as editor:
Construction der Fläche zweiten Grades durch neun Punkte. (Nach den hinterlassenen Manuscripten Jacob Steiners dargestellt von Herrn C. F. Geiser in Zürich.)
' Journal für die reine und angewandte Mathematik 68, 1868, pp. 191–192
Google Booksditto
*
Zur Theorie der Flächen zweiten und dritten Grades
', Journal für die reine und angewandte Mathematik 69, 1868, pp. 197–221
Google Books
*
Ueber die Doppeltangenten einer ebenen Curve vierten Grades
', Mathematische Annalen 1, 1869, pp. 129–138
Jahrbuch-Bericht
*
Ueber die Flächen vierten Grades, welche eine Doppelcurve zweiten Grades haben
', Journal für die reine und angewandte Mathematik 70, 1869, pp. 249–257
Jahrbuch-Bericht
*
Ueber die Steinerschen Sätze von den Doppeltangenten der Curven vierten Grades
', Journal für die reine und angewandte Mathematik 72, 1870, pp. 370–378
Jahrbuch-Bericht
*
Notiz über die algebraischen Minimumsflächen
', Mathematische Annalen 3, 1871, pp. 530–534
Jahrbuch-Bericht
*
Zum Hauptaxenproblem der Flächen zweiten Grades
', Journal für die reine und angewandte Mathematik 82, 1877, pp. 47–53 *
Ueber einen fundamentalen Satz aus der kinematischen Geometrie des Raumes
', Journal für die reine und angewandte Mathematik 90, 1881, pp. 39–43
Jahrbuch-Bericht

Sources

*
† Prof. Dr. C. F. Geiser
', Schweizerische Bauzeitung 103, 17 March 1934 * Henri Fehr:
C.-F. Geiser
', L’Enseignement Mathématique 32, 1933, pp. 410–411 * Louis Kollros:
† Prof. Dr. Carl Friedrich Geiser
', Schweizerische Bauzeitung 103, 31 March 1934, pp. 157–158 *

Arnold Emch Arnold F. Emch (24 March 1871 – 1959) was an American mathematician, known for his work on the inscribed square problem. Emch received his Ph.D. in 1895 at the University of Kansas under the supervision of Henry Byron Newson. In the late 1890s u ...

: ''Carl Friedrich Geiser'', National Mathematics Magazine 12, 1938, pp. 286–289 *

References

{{DEFAULTSORT:Geiser, Carl Friedrich 1843 births 1934 deaths 19th-century Swiss mathematicians 20th-century Swiss mathematicians University of Bern alumni Academic staff of ETH Zurich People from Langenthal ETH Zurich alumni