Alan Baker (mathematician)

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.

Life

Alan Baker was born in London on 19 August 1939. He attended

Baker generalised the Gelfond–Schneider theorem, which itself is a solution to Hilbert's seventh problem.^[7] 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 ${\displaystyle \{1,\beta _{1},...,\beta _{n}\}}$ is

${\displaystyle \alpha _{1}^{\beta _{1}}\alpha _{2}^{\beta _{2}}\cdots \alpha _{n}^{\beta _{n}}}$

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.^[9][10]

Selected publications

• Baker, Alan (1966), "Linear forms in the logarithms of algebraic numbers. I",
  MR 0220680
• Baker, Alan (1967a), "Linear forms in the logarithms of algebraic numbers. II",
  MR 0220680
• Baker, Alan (1967b), "Linear forms in the logarithms of algebraic numbers. III",
  MR 0220680
• Baker, Alan (1990), Transcendental number theory, Cambridge Mathematical Library (2nd ed.),
  MR 0422171; 1st edition. 1975.^[11]
• Baker, Alan; Wüstholz, G. (2007), Logarithmic forms and Diophantine geometry, New Mathematical Monographs, vol. 9, Cambridge University Press,
  MR 2382891