Baker, Alan (1939– )

English mathematician. Baker's chief work has been devoted to the study of transcendental numbers (numbers that cannot be expressed as roots or as the solution of an algebraic equation with rational coefficients).

Baker was born in London and studied mathematics there and at Cambridge. He remained at Cambridge, except for many visiting professorships abroad, becoming professor in 1974.

In 1966 he extended French mathematician Joseph Liouville's original proof of the existence of transcendental numbers by means of continued fractions, by obtaining a result on linear forms in the logarithms of algebraic numbers. This solution opened the way to the resolution of a wide range of Diophantine problems (see Diophantus), and in 1967 Baker used his results to provide the first useful theorems concerning the theory of these problems.

Apart from individual papers, Baker's most important publication is Transcendental Number Theory (1975).