Wolfgang M. Schmidt
Encyclopedia
Wolfgang M. Schmidt is a mathematician
born in 1933. He studied mathematics at the University of Vienna
, where he received his PhD, which was supervised by Edmund Hlawka
, in 1955. Wolfgang Schmidt is professor at the University of Colorado at Boulder
and a member of the Austrian Academy of Sciences
and the Polish Academy of Sciences
.
He was awarded the eighth Frank Nelson Cole Prize in Number Theory
for work on Diophantine approximation
. He is known for his subspace theorem.
In 1960, he proved that every normal number
in base r is normal in base s if and only if log r / log s is a rational number. He also proved the existence of T numbers. His series of papers on irregularities of distribution contained landmark results; see J.Beck and W.Chen, Irregularities of Distribution, Cambridge University Press, for more information.
Schmidt is in a small group of number theorists who have been invited to address the International Congress of Mathematicians
three times. The others are Iwaniec, Shimura
, and Tate
.
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....
born in 1933. He studied mathematics at the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
, where he received his PhD, which was supervised by Edmund Hlawka
Edmund Hlawka
Edmund Hlawka was an Austrian mathematician. He was a leading number theorist. Hlawka did most of his work at the Vienna University of Technology. He was also a visiting professor at Princeton University and the Sorbonne...
, in 1955. Wolfgang Schmidt is professor at the University of Colorado at Boulder
University of Colorado at Boulder
The University of Colorado Boulder is a public research university located in Boulder, Colorado...
and a member of the Austrian Academy of Sciences
Austrian Academy of Sciences
The Austrian Academy of Sciences is a legal entity under the special protection of the Federal Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every field, particularly in fundamental research...
and the Polish Academy of Sciences
Polish Academy of Sciences
The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...
.
He was awarded the eighth Frank Nelson Cole Prize in Number Theory
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
for work on Diophantine approximation
Diophantine approximation
In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers....
. He is known for his subspace theorem.
In 1960, he proved that every normal number
Normal number
In mathematics, a normal number is a real number whose infinite sequence of digits in every base b is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b2 pairs of digits are equally likely with density b−2,...
in base r is normal in base s if and only if log r / log s is a rational number. He also proved the existence of T numbers. His series of papers on irregularities of distribution contained landmark results; see J.Beck and W.Chen, Irregularities of Distribution, Cambridge University Press, for more information.
Schmidt is in a small group of number theorists who have been invited to address the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
three times. The others are Iwaniec, Shimura
Goro Shimura
is a Japanese mathematician, and currently a professor emeritus of mathematics at Princeton University.Shimura was a colleague and a friend of Yutaka Taniyama...
, and Tate
John Tate
John Torrence Tate Jr. is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry.-Biography:...
.
Books
- Diophantine approximation. Lecture Notes in Mathematics 785. Springer. (1980 [1996 with minor corrections])
- Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, Springer Verlag 2000
- Equations Over Finite Fields: An Elementary Approach, 2nd edition, Kendrick Press 2004
- On normal numbers. Pacific Journal of Mathematics, 10:661-672, 1960.
Further reading
- Diophantine approximation: festschrift for Wolfgang Schmidt, Wolfgang M. Schmidt, H. P. Schlickewei, Robert F. Tichy, Klaus Schmidt, Springer, 2008, ISBN 9783211742792