Alan Baker (mathematician)

Alan Baker
Alan Baker
Born	(1939-08-19) 19 August 1939 (age 77) London, England
Nationality	British
Fields	Mathematics
Institutions	University of Cambridge
Alma mater	University College London University of Cambridge
Thesis	Some Aspects of Diophantine Approximation (1964)
Doctoral advisor	Harold Davenport
Doctoral students	John Coates Yuval Flicker Roger Heath-Brown Richard Clive Mason David Masser Robert Odoni Cameron Stewart
Known for	Number theory Diophantine equations Baker's theorem
Notable awards	Fields Medal (1970) Adams Prize (1972)

Alan Baker, FRS (born 19 August 1939) is an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.

Alan Baker was born in London on 19 August 1939. He was awarded the Fields Medal in 1970, at age 31. His academic career started as a student of Harold Davenport, at University College London and later at Cambridge. He was a visiting scholar at the Institute for Advanced Study in the fall of 1970. He is a fellow of Trinity College, Cambridge.

His interests are in number theory, transcendence, logarithmic forms, effective methods, Diophantine geometry and Diophantine analysis.

In 2012 he became a fellow of the American Mathematical Society.

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem. Specifically, Baker showed that if ${\displaystyle \alpha _{1},...,\alpha _{n}}$ are algebraic numbers (besides 0 or 1), and if ${\displaystyle \beta _{1},..,\beta _{n}}$ are irrational algebraic numbers such that the set ${\displaystyle \{1,\beta _{1},...,\beta _{n}\}}$ are linearly independent over the rational numbers, then the number ${\displaystyle \alpha _{1}^{\beta _{1}}\alpha _{2}^{\beta _{2}}\cdots \alpha _{n}^{\beta _{n}}}$ is transcendental.

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