# Alan Baker (mathematician)

Alan Baker
Alan Baker
Born 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)

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.

## Life

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.[1] 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.[2]

## Accomplishments

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.[3] 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.