Kurt Mahler

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Kurt Mahler
Kurt Mahler in 1970
Born(1903-07-26)26 July 1903
Died25 February 1988(1988-02-25) (aged 84)
Canberra, Australia
Alma materJohann Wolfgang Goethe-Universität
Known forMahler's inequality
Mahler measure
Mahler polynomial
Mahler volume
Mahler's theorem
Mahler's compactness theorem
Skolem–Mahler–Lech theorem
AwardsFellow of the Royal Society (1948)
Member of the Australian Academy of Science (1965)
Senior Berwick Prize (1950)
De Morgan Medal (1971)
Thomas Ranken Lyle Medal (1977)
Scientific career
InstitutionsOhio State University
Australian National University
University of Manchester
University of Groningen
ThesisÜber die Nullstellen der unvollständigen Gammafunktion (1927)
Doctoral advisorCarl Ludwig Siegel

Kurt Mahler FRS[1] (26 July 1903, Krefeld, Germany – 25 February 1988, Canberra, Australia) was a German mathematician who worked in the fields of transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers.[1]


Mahler was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D. from Johann Wolfgang Goethe University of Frankfurt am Main in 1927; his advisor was Carl Ludwig Siegel.[2] He left Germany with the rise of Adolf Hitler and accepted an invitation by Louis Mordell to go to Manchester. However, at the start of World War II he was interned as an enemy alien in Central Camp in Douglas, Isle of Man, where he met Kurt Hirsch, although he was released after only three months.[3] He became a British citizen in 1946.

Mahler held the following positions:


Mahler worked in a broad variety of mathematical disciplines, including transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers.[1]

Mahler proved that the Prouhet–Thue–Morse constant and the Champernowne constant 0.1234567891011121314151617181920... are transcendental numbers.[4][5]

Mahler was the first to give an irrationality measure for pi,[6] in 1953.[7] Although some have suggested the irrationality measure of pi is likely to be 2, the current best estimate is 7.103205334137…, due to Doron Zeilberger and Wadim Zudilin.[8]


He was elected a member of the Royal Society in 1948[1] and a member of the Australian Academy of Science in 1965. He was awarded the London Mathematical Society's Senior Berwick Prize in 1950, the De Morgan Medal, 1971, and the Thomas Ranken Lyle Medal, 1977.[1]

Personal life[edit]

Mahler spoke fluent Japanese and was an expert photographer.[1]

See also[edit]


  1. ^ a b c d e f Coates, J. H.; Van Der Poorten, A. J. (1994). "Kurt Mahler. 26 July 1903-26 February 1988". Biographical Memoirs of Fellows of the Royal Society. 39: 264. doi:10.1098/rsbm.1994.0016.
  2. ^ Kurt Mahler at the Mathematics Genealogy Project
  3. ^ Biography of Kurt Mahler available from www.educ.fc.ul.pt
  4. ^ Kurt Mahler, "Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen", Math. Annalen, t. 101 (1929), p. 342–366.
  5. ^ Kurt Mahler, "Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen", Proc. Konin. Neder. Akad. Wet. Ser. A. 40 (1937), p. 421–428.
  6. ^ Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B.; Mahler, Kurt (2004). Pi, a source book. New York: Springer. pp. 306–318. ISBN 0-387-20571-3. OCLC 53814116.
  7. ^ Kurt Mahler, "On the approximation of π", Nederl. Akad. Wetensch. Proc. Ser. A., t. 56 (1953), p. 342–366.
  8. ^ Zeilberger, Doron; Zudilin, Wadim (5 November 2020). "The irrationality measure of π is at most 7.103205334137…". Moscow Journal of Combinatorics and Number Theory. Mathematical Sciences Publishers. 9 (4): 407–419. arXiv:1912.06345. doi:10.2140/moscow.2020.9.407. ISSN 2640-7361. S2CID 209370638.

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