Klaus Friedrich Roth

Klaus Friedrich Roth (born October 25, 1925 in Breslau , Province of Lower Silesia ; † November 10, 2015 in Inverness , Scotland ) was a British mathematician from Germany who was awarded the Fields Medal in 1958 for his outstanding achievements in mathematics .

Life

Klaus Friedrich Roth was born in Breslau in 1925 to Jewish parents. He came to England as a youth on the run from the National Socialists and attended St Paul's School in London from 1939 to 1943 and then studied at the Peterhouse College of Cambridge University , among others with Harold Davenport . After graduation in 1945 he became an assistant at the internationally renowned Gordonstoun School near Elgin in Scotland . The boarding school was founded in 1934 by the German educator Kurt Hahn as a boys' school and was intended to serve the development of character and academic education. But Roth returned to London in 1946 to do research at the university. He graduated with a master's degree in 1948. Two years later he received his doctorate and in 1961 was appointed professor. In 1966 he accepted a professorship in mathematics at the University of London and held this position until 1988.

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Roth worked mainly in the field of number theory , especially the Diophantine approximation . His most significant result was reflected in the Thue-Siegel-Roth theorem . It says that for every algebraic number and every the inequality ( p , q relatively prime ) ${\displaystyle \alpha }$ ${\displaystyle \varepsilon >0}$

${\displaystyle \left|\alpha -{\frac {p}{q}}\right|<q^{-(2+\varepsilon )}}$

only has a finite number of solutions. This is the "best" possible such sentence and improves the previous versions of Axel Thue and Carl Ludwig Siegel . However, it does not provide an effective method for determining such solutions.

In 1953 he proved a theorem ( Roth's Theorem ) about the minimum density of sets of natural numbers, which ensure the existence of nontrivial arithmetic progressions with three terms (a special case of a theorem later proved by Endre Szemerédi and named after him). The sentence was later tightened by Jean Bourgain , Roger Heath-Brown and Tom Sanders .

In the 1960s, at the same time as Enrico Bombieri , he further developed the method of the "Great Sieve" by Juri Linnik and Alfréd Rényi in analytical number theory. With Halberstam he is the author of a book "Sieve Methods" .

In addition to the Fields Medal, Roth received other honors for his work. In 1960 he became an honorary member of the Royal Society of London , in 1966 of the American Academy of Arts and Sciences and in 1983 of the Royal Society of Edinburgh . He received the De Morgan Medal from the London Mathematical Society in 1983 and the New Year's Eve Medal from the Royal Society in 1991 . In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh (Rational Approximations to Algebraic Numbers).

Web links

• John J. O'Connor, Edmund F. Robertson :  Klaus Friedrich Roth. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Klaus Roth. In: chalkdustmagazine.com , November 10, 2015, accessed November 10, 2015.
2. ↑ Klaus Friedrich Roth: Rational approximations to algebraic numbers and Corrigendum . In: Mathematika , Vol. 2 (1955), pp. 1-20 and 168, ISSN  0025-5793 .
3. ^ Klaus Friedrich Roth: On certain sets of integers . In: Journal of the London Mathematical Society / 1. Series , Vol. 28 (1953), pp. 104-109, ISSN  0024-6107 .