F. K. Schmidt
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Friedrich Karl Schmidt (22 September 1901 – 25 January 1977) was a German
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, who made notable contributions to
algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
and
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
. Schmidt studied from 1920 to 1925 in Freiburg and Marburg. In 1925 he completed his doctorate at the
Albert-Ludwigs-Universität Freiburg The University of Freiburg (colloquially ), officially the Albert Ludwig University of Freiburg (), is a public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany. The university was founded in 1457 by the Habsburg ...
under the direction of
Alfred Loewy Alfred Loewy (20 June 1873 – 25 January 1935) was a German mathematician who worked on representation theory. Loewy rings, Loewy length, Loewy decomposition and Loewy series are named after him. His graduate students included Wolfgang Krull ...
. In 1927 he became a ''Privatdozent'' (lecturer) at the
University of Erlangen A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...
, where he received his
habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...
and in 1933 became a professor extraordinarius. In 1933/34 he was a ''Dozent'' at the
University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...
, where he worked with
Helmut Hasse Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and ...
. Schmidt was then a professor ordinarius at the
University of Jena The University of Jena, officially the Friedrich Schiller University Jena (, abbreviated FSU, shortened form ''Uni Jena''), is a public research university located in Jena, Thuringia, Germany. The university was established in 1558 and is cou ...
from 1934 to 1945. During WW II, he was at the ''Deutsche Versuchsanstalt für Segelflug'' (German Research Station for Gliding) in
Reichenhall Bad Reichenhall (; Central Bavarian: ''Reichahoi'') is a spa town, and administrative center of the Berchtesgadener Land district in Upper Bavaria, Germany. It is located near Salzburg in a basin encircled by the Chiemgau Alps (including Mount Stau ...
. He was a professor from 1946 to 1952 at Westfälischen Wilhelms-Universität in Münster and from 1952 to 1966 at the
University of Heidelberg Heidelberg University, officially the Ruprecht Karl University of Heidelberg (; ), is a public university, public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is List ...
, where he retired as professor emeritus. In the mid-1930s Schmidt was on the editorial staff of . Schmidt was elected in 1954 a member of the
Heidelberger Akademie der Wissenschaften The Heidelberg Academy of Sciences and Humanities (German: ''Heidelberger Akademie der Wissenschaften''), established in 1909 in Heidelberg, Germany, is an assembly of scholars and scientists in the German state of Baden-Wuerttemberg. The acade ...
Gabriele Dörflinger
Mathematik in der Heidelberger Akademie der Wissenschaften
2014, pp. 68–70
and was made in 1968 an honorary doctor of the
Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public university, public research university in Berlin, Germany. It was founded in West Berlin in 1948 with American support during the early Cold War period a ...
. Schmidt is known for his contributions to the theory of algebraic function fields and in particular for his definition of a
zeta function In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function : \zeta(s) = \sum_^\infty \frac 1 . Zeta functions include: * Airy zeta function, related to the zeros of the Airy function * A ...
for
algebraic function field In mathematics, an algebraic function field (often abbreviated as function field) of ''n'' variables over a field ''k'' is a finitely generated field extension ''K''/''k'' which has transcendence degree ''n'' over ''k''. Equivalently, an algebrai ...
s and his proof of the generalized
Riemann–Roch theorem The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It re ...
for algebraic function fields (where the base field can be an arbitrary
perfect field In algebra, a field ''k'' is perfect if any one of the following equivalent conditions holds: * Every irreducible polynomial over ''k'' has no multiple roots in any field extension ''F/k''. * Every irreducible polynomial over ''k'' has non-zero f ...
). He also made contributions to
class field theory In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credit ...
and
valuation theory In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of siz ...
.


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* 1901 births 1977 deaths Algebraists 20th-century German mathematicians German number theorists University of Freiburg alumni German academic journal editors {{Germany-mathematician-stub