# Alan Baker (mathematician)

Alan Baker FRS | |
---|---|

| |

Born |
London, England | 19 August 1939

Died |
4 February 2018 78) Cambridge, England | (aged

Nationality | British |

Alma mater |
University College London University of Cambridge |

Known for |
Number theory Diophantine equations Baker's theorem |

Awards |
Fields Medal (1970) Adams Prize (1972) |

Scientific career | |

Fields | Mathematics |

Institutions | University of Cambridge |

Thesis |
Some Aspects of Diophantine Approximation (1964) |

Doctoral advisor | Harold Davenport |

Doctoral students |
John Coates Yuval Flicker Roger Heath-Brown David Masser Cameron Stewart |

**Alan Baker** FRS (19 August 1939 – 4 February 2018^{[1]}) 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 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, where he received his PhD. He was a visiting scholar at the Institute for Advanced Study in the fall of 1970.^{[2]}
He was a fellow of Trinity College, Cambridge.

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

In 2012 he became a fellow of the American Mathematical Society.^{[3]} He has also been made a foreign fellow of the National Academy of Sciences, India.^{[4]}

## Accomplishments

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.^{[5]} Specifically, Baker showed that if
are algebraic numbers (besides 0 or 1), and if
are irrational algebraic numbers such that the set
are linearly independent over the rational numbers, then the number
is transcendental.

## Selected publications

- Baker, Alan (1966), "Linear forms in the logarithms of algebraic numbers. I",
*Mathematika*,**13**: 204–216, doi:10.1112/S0025579300003971, ISSN 0025-5793, MR 0220680 - Baker, Alan (1967a), "Linear forms in the logarithms of algebraic numbers. II",
*Mathematika*,**14**: 102–107, doi:10.1112/S0025579300008068, ISSN 0025-5793, MR 0220680 - Baker, Alan (1967b), "Linear forms in the logarithms of algebraic numbers. III",
*Mathematika*,**14**: 220–228, doi:10.1112/S0025579300003843, ISSN 0025-5793, MR 0220680 - Baker, Alan (1990),
*Transcendental number theory*, Cambridge Mathematical Library (2nd ed.), Cambridge University Press, ISBN 978-0-521-39791-9, MR 0422171 ;*1st edition*. 1975.^{[6]} - Baker, Alan; Wüstholz, G. (2007),
*Logarithmic forms and Diophantine geometry*, New Mathematical Monographs,**9**, Cambridge University Press, ISBN 978-0-521-88268-2, MR 2382891

## Honours and awards

- 1970: Fields Medal
- 1972: Adams Prize

## References

- ↑ Trinity College website, accessed 5 February 2018
- ↑ Institute for Advanced Study: A Community of Scholars Archived 6 January 2013 at the Wayback Machine.
- ↑ List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
- ↑ "National Academy of Sciences, India: Foreign Fellows". Retrieved 2 June 2018.
- ↑ Biography in Encyclopædia Britannica. http://www.britannica.com/eb/article-9084909/Alan-Baker
- ↑ Stolarsky, Kenneth B. (1978). "Review:
*Transcendental number theory*by Alan Baker;*Lectures on transcendental numbers*by Kurt Mahler;*Nombres transcendants*by Michel Waldschmidt" (PDF).*Bull. Amer. Math. Soc*.**84**(8): 1370–1378. doi:10.1090/S0002-9904-1978-14584-4.