Klaus Roth
Encyclopedia
Klaus Friedrich Roth is a British
mathematician
known for work on diophantine approximation
, the large sieve, and irregularities of distribution
. He was born in Breslau, Prussia
, but raised and educated in the UK. He graduated from Peterhouse, Cambridge
in 1945. In 1946 he began research at University College London
, under the supervision of Theodor Estermann
.
In 1952, Roth proved that subsets of the integer
s of positive density
must contain infinitely many arithmetic progression
s of length three, thus establishing the first non-trivial case of what is now known as Szemerédi's theorem
. His definitive result, now known usually as the Thue–Siegel–Roth theorem
, but also just Roth's theorem, dates from 1955, when he was a lecturer at University College London
. He was awarded a Fields Medal
in 1958 on the strength of it. He became a professor at University College London in 1961, and moved to a chair at Imperial College London
in 1966, a position he retained until official retirement at 1988. He then changed his status to visiting professor and remained at Imperial College until 1996.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
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....
known 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....
, the large sieve, and irregularities of distribution
Discrepancy theory
In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be. It is also called theory of irregularities of distribution. This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly...
. He was born in Breslau, Prussia
Prussia
Prussia was a German kingdom and historic state originating out of the Duchy of Prussia and the Margraviate of Brandenburg. For centuries, the House of Hohenzollern ruled Prussia, successfully expanding its size by way of an unusually well-organized and effective army. Prussia shaped the history...
, but raised and educated in the UK. He graduated from Peterhouse, Cambridge
Peterhouse, Cambridge
Peterhouse is a constituent college of the University of Cambridge, England. It is the oldest college of the University, having been founded in 1284 by Hugo de Balsham, Bishop of Ely...
in 1945. In 1946 he began research at University College London
University College London
University College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
, under the supervision of Theodor Estermann
Theodor Estermann
Theodor Estermann was a mathematician, working in the field of analytic number theory.He was born in Neubrandenburg, Germany. His doctorate, completed in 1925, was supervised by Hans Rademacher. Heini Halberstam, Klaus Roth and Robert Charles Vaughan were Ph.D. students of his.-External links:*...
.
In 1952, Roth proved that subsets of the integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s of positive density
Szemerédi's theorem
In number theory, Szemerédi's theorem is a result that was formerly the Erdős–Turán conjecture...
must contain infinitely many arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...
s of length three, thus establishing the first non-trivial case of what is now known as Szemerédi's theorem
Szemerédi's theorem
In number theory, Szemerédi's theorem is a result that was formerly the Erdős–Turán conjecture...
. His definitive result, now known usually as the Thue–Siegel–Roth theorem
Thue–Siegel–Roth theorem
In mathematics, the Thue–Siegel–Roth theorem, also known simply as Roth's theorem, is a foundational result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that a given algebraic number α may not have too many rational number approximations, that are 'very...
, but also just Roth's theorem, dates from 1955, when he was a lecturer at University College London
University College London
University College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
. He was awarded a Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1958 on the strength of it. He became a professor at University College London in 1961, and moved to a chair at Imperial College London
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
in 1966, a position he retained until official retirement at 1988. He then changed his status to visiting professor and remained at Imperial College until 1996.