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Kurt Mahler FRS (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. 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. 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. He became a British citizen in 1946. Mahler held the following positions: University of Groningen Assistant 1934–1936 University of Manchester Assistant Lecturer at 1937–1939, 1941–1944 Lecturer, 1944–1947; Senior Lecturer, 1948–1949; Reader, 1949–1952 Professor of Mathematical Analysis, 1952–1963 Professor of Mathematics, Institute of Advanced Studies, Australian National University, 1963–1968 and 1972–1975 Professor of Mathematics, Ohio State University, USA, 1968–1972 Professor Emeritus, Australian National University, from 1975. Mahler worked in a broad variety of mathematical disciplines, including transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers. Mahler proved that the Prouhet–Thue–Morse constant and the Champernowne constant 0.1234567891011121314151617181920... are transcendental numbers. Mahler was the first to give an irrationality measure for pi, in 1953. 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. He was elected a member of the Royal Society in 1948 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.

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Kurt Mahler

Champernowne constant

In mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933. For base 10, the number is defined by concatenating representations of successive integers: C10 = 0.12345678910111213141516... . Champernowne constants can also be constructed in other bases, similarly, for example: C2 = 0.11011100101110111... 2 C3 = 0.12101112202122..

Transcendental number theory

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways. Transcendental number The fundamental theorem of algebra tells us that if we have a non-constant polynomial with rational coefficients (or equivalently, by clearing denominators, with integer coefficients) then that polynomial will have a root in the complex numbers.

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