Wolfgang Gröbner
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Wolfgang Gröbner (11 February 1899 – 20 August 1980) was an
Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...
n
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 ...
. His name is best known for the
Gröbner basis In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K _1,\ldots,x_n/math> ove ...
, used for computations in
algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
. However, the theory of Gröbner bases for polynomial rings was developed by his student
Bruno Buchberger Bruno Buchberger (born 22 October 1942) is Professor of Computer Mathematics at Johannes Kepler University in Linz, Austria. In his 1965 Ph.D. thesis, he created the theory of Gröbner bases, and has developed this theory throughout his career ...
in 1965, who named them for Gröbner. Gröbner is also known for the Alekseev-Gröbner formula, which was actually proven by him.


Early life

Gröbner was born in Gossensaß, which at that time was in part of the
County of Tyrol The (Princely) County of Tyrol was an Imperial State, estate of the Holy Roman Empire established about 1140. After 1253, it was ruled by the House of Gorizia and from 1363 by the House of Habsburg. In 1804, the County of Tyrol, unified with th ...
of the
Austro-Hungarian Empire Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe between 1867 and 1918. A military and diplomatic alliance, it consist ...
and is now part of
Italy Italy, officially the Italian Republic, is a country in Southern Europe, Southern and Western Europe, Western Europe. It consists of Italian Peninsula, a peninsula that extends into the Mediterranean Sea, with the Alps on its northern land b ...
. Gröbner first studied engineering at the
University of Technology An institute of technology (also referred to as technological university, technical university, university of technology, polytechnic university) is an institution of tertiary education that specializes in engineering, technology, applied science ...
in
Graz Graz () is the capital of the Austrian Federal states of Austria, federal state of Styria and the List of cities and towns in Austria, second-largest city in Austria, after Vienna. On 1 January 2025, Graz had a population of 306,068 (343,461 inc ...
, Austria, but switched in 1929 to
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
.


Career

He wrote his dissertation ''Ein Beitrag zum Problem der Minimalbasen'' in 1932 at the
University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...
; his advisor was
Philipp Furtwängler Friederich Pius Philipp Furtwängler (April 21, 1869 – May 19, 1940) was a German number theorist. Biography Furtwängler wrote an 1896 doctoral dissertation at the University of Göttingen on cubic forms (''Zur Theorie der in Linearfaktoren z ...
. After his promotion, he did further studies 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 ...
under
Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
, in what is now known as
commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...
. Later he contributed with his students to numerical analysis of ordinary differential equations and the industrial applications of Lie-theoretic methods, including a book on Lie series.


Awards

*
Wilhelm Exner Medal The Wilhelm Exner Medal has been awarded by the Austrian Industry Association, (ÖGV), for excellence in research and science since 1921. The medal is dedicated to Wilhelm Exner (1840–1931), former president of the Association, who initialize ...
, 1969.Editor, ÖGV. (2015)
Wilhelm Exner Medal
Austrian Trade Association. ÖGV. Austria.


References

* {{DEFAULTSORT:Grobner, Wolfgang 1899 births 1980 deaths 20th-century Austrian mathematicians University of Vienna alumni Academic staff of the University of Innsbruck People from Brenner