Klaus Roth

Not to be confused with Leonard Roth.

Klaus Roth
Born	Klaus Friedrich Roth (1925-10-29)29 October 1925 Breslau, Province of Lower Silesia, Weimar Germany
Died	10 November 2015(2015-11-10) (aged 90) Inverness, Scotland
Citizenship	Germany United Kingdom
Alma mater	Peterhouse, Cambridge
Known for	diophantine approximation discrepancy theory
Awards	Sylvester Medal (1991) LMS De Morgan Medal (1983) Fellow of the Royal Society (1960) Fields Medal (1958)
Scientific career
Fields	Mathematics
Institutions	University College London Imperial College London
Doctoral advisor	Theodor Estermann

Klaus Friedrich Roth (29 October 1925 – 10 November 2015) was a German-born British mathematician known for work on diophantine approximation, the large sieve, and irregularities of distribution.

Early life

He was born in Breslau, Prussia, but was raised and educated in the UK, where his family settled in 1933. He was pupil at St Paul's School in London from 1939 to 1943 and then attended Cambridge University, graduating from Peterhouse, Cambridge in 1945. In 1946 he began research at University College London, under the supervision of Theodor Estermann.

Career

In 1952, Roth proved that subsets of the integers of positive density must contain infinitely many arithmetic progressions 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 in 1988. He then remained at Imperial College as Visiting Professor until 1996. He died in 2015 at the age of 90.

The Imperial College Department of Mathematics instituted the Roth Doctoral Fellowship in his honour.

Publications

• Roth, Klaus Friedrich (1955), "Rational approximations to algebraic numbers", Mathematika, 2: 1–20, 168, doi:10.1112/S0025579300000644, ISSN 0025-5793, MR 0072182
• Halberstam, Heini; Roth, Klaus Friedrich (1983) [1966], Sequences (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-90801-4, MR 0210679

References

• Davenport, H. (1960), "The work of K. F. Roth", Proc. Internat. Congress Math. 1958, Cambridge University Press, pp. lvii–lx, Zbl 0119.24901

Further reading

• Chen, W. W. L.; Gowers, W. T.; Halberstam, H.; Schmidt, W. M.; Vaughan, R. C., eds. (2009), "Klaus Roth at 80", Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday, Cambridge: Cambridge University Press, ISBN 978-0-521-51538-2, Zbl 1155.11004

External links

• O'Connor, John J.; Robertson, Edmund F., "Klaus Roth", MacTutor History of Mathematics Archive, University of St Andrews