Carl Johannes Thomae

Carl Johannes Thomae (sometimes called Johannes Thomae, Karl Johannes Thomae, or Johannes Karl Thomae; 11 December 1840 in Laucha an der Unstrut – 1 April 1921 in Jena) was a German mathematician.

Carl Johannes Thomae
Born11 December 1840
Laucha an der Unstrut, North German Confederation
Died1 April 1921(1921-04-01) (aged 80)
Jena, Weimar Republic
NationalityGerman
Alma materUniversity of Göttingen
Known forThomae's function, Thomae's formula
Scientific career
FieldsMathematics
InstitutionsUniversity of Jena
Doctoral advisorErnst Schering

Biography

Thomae, son of Karl August Thomae (head master) and Emilie Gutsmuths, grew up in Laucha an der Unstrut and in 1864 attained a doctorate under Ernst Schering at the University of Göttingen. In 1866 Thomae attained the habilitation qualification at the University of Göttingen and one year later also at the University of Halle. In the year 1874, Thomae married Anna Uhde in Balgstädt in the proximity of his native city Laucha an der Unstrut. Their son Walter Thomae was born one year later on 5 November 1875, but Thomae's wife died 5 days after giving birth.

In 1879 Thomae became ordentliche professor at the University of Jena. In 1892 he married his second wife Sophie Pröpper in Jena. One year later was born Susanne Thomae. In 1914 Thomae, at that time dean of the philosophical faculty at the University of Jena, retired. In 1921 he died in Jena after a short illness.

Carl Johannes Thomae's research was concerned with function theory and with what German-speaking mathematicians often call "Epsilontik", the precise development of analysis, differential geometry, and topology using epsilon-neighborhoods in the style of Weierstrass. The Thomae function, the Thomae transformation formula (aka, Thomae's transformation and Thomae's theorem),[1][2] the Thomae formula for hyperelliptic curves,[3] and the Sears–Thomae transformation formula[4] are named after him. He called himself Riemann's student, although he never attended a lecture by Riemann.

Works
  • Thomae, Carl Johannes (1870), "Beitrag zur Bestimmung von θ(0,0,...0) durch die Klassenmoduln algebraischer Funktionen", Journal für die reine und angewandte Mathematik, 71: 201–222
  • Elementare Theorie der analytischen Funktionen einer komplexen Veränderlichen. Nebert, Halle (Saale) 1880.

References
  1. Thomae's Theorem from mathworld.wolfram.com
  2. Hardy, G. H. (1999) [1940]. Ramanujan: twelve lectures on subjects suggested by his life and work. Am. Math. Soc. pp. 104––105. ISBN 0-8218-2023-0. Ramanujan independently rediscovered both the statement and proof of Thomae's transformation formula.
  3. Nakayashiki, Atsushi (1996). "On the Thomae formula ZN curves". arXiv:alg-geom/9608016. Bibcode:1996alg.geom..8016N. {{cite journal}}: Cite journal requires |journal= (help)
  4. Andrews, George E.; Berndt, Bruce C. (2008). Ramanujan's lost notebook, Part 2. Springer. p. 45. ISBN 978-0-387-77765-8.
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