Christoph Gudermann (25 March 1798 – 25 September 1852) was a German mathematician noted for introducing the

Gudermannian function In mathematics, the Gudermannian function relates a hyperbolic angle measure \psi to a circular angle measure \phi called the ''gudermannian'' of \psi and denoted \operatorname\psi. The Gudermannian function reveals a close relationship betwee ...

and the concept of

uniform convergence In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions (f_n) converges uniformly to a limiting function f on a set E if, given any arbitrarily s ...

, and for being the teacher of

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, 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 ...

, who was greatly influenced by Gudermann's course on

elliptic function In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those in ...

s in 1839–1840, the first such course to be taught in any institute.

Biography

Gudermann was born in

Vienenburg Vienenburg is a borough of Goslar, capital of the Goslar (district), Goslar district, in Lower Saxony, Germany. The former independent municipality was incorporated in Goslar on 1 January 2014. Geography It is situated in the north of the Harz mou ...

. He was the son of a school teacher and became a teacher himself after studying at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

, where his academic advisor was Karl Friedrich Gauss. He began his teaching career in

Kleve Kleve (; traditional en, Cleves ; nl, Kleef; french: Clèves; es, Cléveris; la, Clivia; Low Rhenish: ''Kleff'') is a town in the Lower Rhine region of northwestern Germany near the Dutch border and the River Rhine. From the 11th century ...

and then transferred to a school in

Münster Münster (; nds, Mönster) is an independent city (''Kreisfreie Stadt'') in North Rhine-Westphalia, Germany. It is in the northern part of the state and is considered to be the cultural centre of the Westphalia region. It is also a state distr ...

. Gudermann introduced the concept of

in an 1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and applied uniform convergence. His researches into

spherical geometry 300px, A sphere with a spherical triangle on it. Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sp ...

and

special function Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

s focused on particular cases, so that he did not receive the credit given to those who published more general works. The

, or hyperbolic amplitude, is named after him. Gudermann died in Münster.

References

External links

* * {{DEFAULTSORT:Gudermann, Christoph 1798 births 1852 deaths People from Goslar (district) 19th-century German mathematicians University of Göttingen alumni