Kurt Mahler FRS (26 July 1903,

Krefeld Krefeld ( , ; li, Krieëvel ), also spelled Crefeld until 1925 (though the spelling was still being used in British papers throughout the Second World War), is a city in North Rhine-Westphalia, Germany. It is located northwest of Düsseldorf, i ...

Germany Germany, officially the Federal Republic of Germany (FRG),, is a country in Central Europe. It is the most populous member state of the European Union. Germany lies between the Baltic and North Sea to the north and the Alps to the sou ...

– 25 February 1988, Canberra, Australia) was a German mathematician who worked in the fields of

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. Transcendence ...

diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by ...

, ''p''-adic analysis, and the

geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental informatio ...

Career

Mahler was a student at the universities in

Frankfurt Frankfurt, officially Frankfurt am Main (; Hessian: , " Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on its ...

and

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

, graduating with a Ph.D. from

Johann Wolfgang Goethe University of Frankfurt am Main Goethe University (german: link=no, Johann Wolfgang Goethe-Universität Frankfurt am Main) is a university located in Frankfurt am Main, Germany. It was founded in 1914 as a citizens' university, which means it was founded and funded by the wealt ...

in 1927; his advisor was

Carl Ludwig Siegel Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation ...

. He left Germany with the rise of

Adolf Hitler Adolf Hitler (; 20 April 188930 April 1945) was an Austrian-born German politician who was dictator of Nazi Germany, Germany from 1933 until Death of Adolf Hitler, his death in 1945. Adolf Hitler's rise to power, He rose to power as the le ...

and accepted an invitation by

Louis Mordell Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

to go to

Manchester Manchester () is a city in Greater Manchester, England. It had a population of 552,000 in 2021. It is bordered by the Cheshire Plain to the south, the Pennines to the north and east, and the neighbouring city of City of Salford, Salford to ...

. However, at the start of

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

he was interned as an

enemy alien In customary international law, an enemy alien is any native, citizen, denizen or subject of any foreign nation or government with which a domestic nation or government is in conflict and who is liable to be apprehended, restrained, secured and ...

in Central Camp in

Douglas Douglas may refer to: People * Douglas (given name) * Douglas (surname) Animals * Douglas (parrot), macaw that starred as the parrot ''Rosalinda'' in Pippi Longstocking * Douglas the camel, a camel in the Confederate Army in the American Civi ...

Isle of Man ) , anthem = " O Land of Our Birth" , image = Isle of Man by Sentinel-2.jpg , image_map = Europe-Isle_of_Man.svg , mapsize = , map_alt = Location of the Isle of Man in Europe , map_caption = Location of the Isle of Man (green) in Europ ...

, where he met

Kurt Hirsch Kurt August Hirsch (12 January 1906 – 4 November 1986) was a German mathematician who moved to England to escape the Nazi persecution of Jews. His research was in group theory. He also worked to reform mathematics education and became a county ...

, although he was released after only three months. He became a British citizen in 1946. Mahler held the following positions: *

University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a public research university of more than 30,000 students in the city of Groningen in the Netherlands. Founded in 1614, the university is the ...

** Assistant 1934–1936 *

University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The university owns and operates majo ...

** 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 The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...

, 1963–1968 and 1972–1975 * Professor of Mathematics,

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best pu ...

, USA, 1968–1972 *

Professor Emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

, from 1975.

Research

Mahler worked in a broad variety of mathematical disciplines, including

, ''p''-adic analysis, and the

. Mahler proved that the

Prouhet–Thue–Morse constant In mathematics, the Prouhet–Thue–Morse constant, named for Eugène Prouhet, Axel Thue, and Marston Morse, is the number—denoted by —whose binary expansion 0.01101001100101101001011001101001... is given by the Thue–Morse sequence. Th ...

and the

Champernowne constant In mathematics, the Champernowne constant 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 ...

0.1234567891011121314151617181920... are

transcendental number In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are and . Though only a few classe ...

s. Mahler was the first to give an

irrationality measure In number theory, a Liouville number is a real number ''x'' with the property that, for every positive integer ''n'', there exists a pair of integers (''p, q'') with ''q'' > 1 such that :0 1 + \log_2(d)~, the last inequality above implies :\left ...

for pi, in 1953.Kurt Mahler, "On the approximation of π", ''Nederl. Akad. Wetensch. Proc. Ser. A.'', t. 56 (1953), p. 342–366. 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 Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics. Education and career He received his doctorate from the Weizmann Institute of Science in 1976, ...

and

Wadim Zudilin Wadim Zudilin (Вадим Валентинович Зудилин) is a Russian mathematician and number theorist who is active in studying hypergeometric functions and zeta constants. He studied under Yuri V. Nesterenko and worked at Moscow St ...

Awards

He was elected a member of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

in 1948 and a member of the

Australian Academy of Science The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The academy is modelled after the Royal So ...

in 1965. He was awarded the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

Senior Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...

in 1950, the

De Morgan Medal The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the societ ...

, 1971, and the Thomas Ranken Lyle Medal, 1977.

Personal life

Mahler spoke fluent

Japanese Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspor ...

and was an expert photographer.

References

External links