Christoph Gudermann (25 March 1798 – 25 September 1852) was a German mathematician noted for introducing the
Gudermannian function and the concept of
uniform convergence, and for being the teacher of
Karl Weierstrass, 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. He was the son of a school teacher and became a teacher himself after studying at the
University of Göttingen, where his academic advisor was
Karl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
. He began his teaching career in
Kleve and then transferred to a school in
Münster.
Gudermann introduced the concept of
uniform convergence 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 functions focused on particular cases, so that he did not receive the credit given to those who published more general works. The
Gudermannian function, or hyperbolic amplitude, is named after him.
Gudermann died in Münster.
References
External links
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{{DEFAULTSORT:Gudermann, Christoph
1798 births
1852 deaths
People from Goslar (district)
19th-century German mathematicians
University of Göttingen alumni