Alan Baker FRS[1] (19 August 1939 – 4 February 2018[2]) was 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 attended Stratford Grammar School, East London, and his academic career started as a student of Harold Davenport, at University College London and later at Trinity College, Cambridge, where he received his PhD.

[3] He was a visiting scholar at the Institute for Advanced Study in 1970 when he was awarded the Fields Medal at the age of 31.

[4] In 1974 he was appointed Professor of Pure Mathematics at Cambridge University, a position he held until 2006 when he became an Emeritus.

He was a fellow of Trinity College from 1964 until his death.

[3] His interests were in number theory, transcendence, linear forms in logarithms, effective methods, Diophantine geometry and Diophantine analysis.

[5] He has also been made a foreign fellow of the National Academy of Sciences, India.

[6] Baker generalised the Gelfond–Schneider theorem, which itself is a solution to Hilbert's seventh problem.

are irrational algebraic numbers such that the set

Baker made significant contributions to several areas in number theory, such as the Gauss class number problem,[8] diophantine approximation, and to Diophantine equations such as the Mordell curve.