Wolfgang Gröbner
Encyclopedia
Wolfgang Gröbner was an Austria
n mathematician
. His name is best known for the Gröbner basis
, used for computations in algebraic geometry
. However, the theory of Gröbner bases for polynomial rings was developed by Bruno Buchberger
in 1965, who named them Gröbner, who was his advisor.
He was born in Gossensaß, which at that time was in part of the County of Tyrol
of the Austro-Hungarian Empire and is now part of Italy
.
Gröbner first studied engineering at the University of Technology
in Graz
, Austria, but switched in 1929 to mathematics
.
He wrote his dissertation Ein Beitrag zum Problem der Minimalbasen in 1932 at the University of Vienna; his advisor was Phillip Furtwängler. After his promotion, he did further studies in Göttingen
under Emmy Noether
, in what is now known as commutative algebra
.
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. His name is best known for the Gröbner basis
Gröbner basis
In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating subset of an ideal I in a polynomial ring R...
, used for computations in algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. However, the theory of Gröbner bases for polynomial rings was developed by Bruno Buchberger
Bruno Buchberger
Bruno Buchberger 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. He named these objects after his advisor Wolfgang Gröbner...
in 1965, who named them Gröbner, who was his advisor.
He was born in Gossensaß, which at that time was in part of the County of Tyrol
County of Tyrol
The County of Tyrol, Princely County from 1504, was a State of the Holy Roman Empire, from 1814 a province of the Austrian Empire and from 1867 a Cisleithanian crown land of Austria-Hungary...
of the Austro-Hungarian Empire and is now part of Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
.
Gröbner first studied engineering at the University of Technology
Graz University of Technology
The Graz University of Technology is the second largest university in Styria, Austria, after the University of Graz. Austria has three universities of technology – in Graz, in Leoben, and in Vienna. The Graz University of Technology was founded in 1811 by Archduke John of Austria. TUG, as the...
in Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...
, Austria, but switched in 1929 to mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
He wrote his dissertation Ein Beitrag zum Problem der Minimalbasen in 1932 at the University of Vienna; his advisor was Phillip Furtwängler. After his promotion, he did further studies in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
under Emmy Noether
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...
, in what is now known as commutative algebra
Commutative algebra
Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra...
.