Kurt Mahler

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Kurt Mahler

Kurt Mahler (born July 26, 1903 in Krefeld , † February 25, 1988 in Canberra , Australia ) was a German-born British mathematician who primarily dealt with number theory (theory of p-adic numbers).

life and work

At the age of five, Kurt Mahler fell ill with tuberculosis . Due to health problems - he had to undergo several operations and from then on had a stiff leg - he left school at the age of thirteen to train as a toolmaker. In addition, he taught himself the basics of mathematics in the fields of analysis, analytical geometry and trigonometry by reading works by important mathematicians such as Edmund Landau , David Hilbert and Felix Klein . With the help of his education and mathematical knowledge, he hoped to be able to study at a technical university.

However, Mahler's father had secretly passed the little mathematical articles Mahler wrote on to the local school director, a mathematician. He sent them to Klein, with whom he had once studied, who in turn passed them on to Carl Ludwig Siegel . Thanks to Siegel's advocacy, Mahler was able to enroll in mathematics at the University of Frankfurt in 1923 , where he a. a. heard from Max Dehn , Ernst Hellinger , Siegel and Otto Szász . In 1925 he moved to Göttingen, where he heard lectures by Emmy Noether , Richard Courant , Edmund Landau , Max Born , David Hilbert , Alexander Markowitsch Ostrowski , Werner Heisenberg and worked as an unpaid assistant for Norbert Wiener . He published his dissertation on zeroing the incomplete gamma function , dedicated to the school director, in Frankfurt in 1929.

In 1933 he was appointed to Koenigsberg , but had to emigrate because of his Jewish origins and went to Manchester to Louis Mordell in 1933/34 . A year later he went to Groningen , where a bicycle accident in 1936 caused his old knee pain again and he therefore moved on to Switzerland to relax. In 1937 he returned to Manchester, but in 1940 was interned for three months as an " enemy alien " on the Isle of Man .

After his return to Manchester in 1941 Mahler got an assistant position and in 1944 he became a lecturer. He became a British citizen in 1946, and a year later he was given the university's first personal professorship. In 1948 the Royal Society accepted Mahler. Mahler stayed in Manchester until 1963 before accepting a professorship at the Australian National University in Canberra. In 1968 he left Australia to teach mathematics at Ohio State University in Columbus, Ohio . In 1972 he retired and returned to Australia.

In 1934/35 he proved the p-adic analog of the transcendence proof by Alexander Gelfond for the seventh Hilbert problem.

Mahler showed in 1946 that the number 0.1234567891011 .., which arises from the sequence of the decimal digits of all natural numbers, is transcendent. His main field of work was the p-adic numbers , Diophantine approximations, geometry of numbers and measures in the space of polynomials . ( Mahler's measure , which is the subject of Lehmer's conjecture, is named after him .) From him comes the division of the transcendental numbers into S, T, U classes (which are algebraically independent), Mahler proving that almost all real numbers are Belong to the S class (an example is Euler's number e).

The Mahler volume in convex geometry is named after him (a volume invariant under linear transformations, defined for centrally symmetric convex bodies in Euclidean space) and Mahler's unsolved conjecture says that it is minimal for a hypercube .

One of his doctoral students is Alf van der Poorten .

Fonts

  • Introduction to p-adic numbers and their functions, Cambridge UP 1973
  • Lectures on transcendental numbers, Lecture notes in mathematics, Springer 1976 (editor Bohuslav Diviš)

Awards

Web links

Individual evidence

  1. ↑ Published as About the zeros of the incomplete gamma functions , Rend. Circolo Math. Palermo, Volume 54, 1930
  2. ^ Mahler, On transcendent p-adic numbers, Composition Math., Volume 2, 1935, pp. 259–275
  3. ↑ Mahler on the approximation of the exponential function and the logarithm , part 1,2, Journal für Reine und Angewandte Mathematik, Vol. 166, 1932, pp. 118–150. Jurjen Koksma found an equivalent classification in 1939.
  4. ↑ The U-class is uncountable , the Liouville numbers belong to it . The existence of a number in the T-Class was proven by Wolfgang Schmidt in 1968 .
personal data
SURNAME Mahler, Kurt
BRIEF DESCRIPTION British mathematician of German origin
DATE OF BIRTH July 26, 1903
PLACE OF BIRTH Krefeld
DATE OF DEATH February 25, 1988
Place of death Canberra , Australia