Alan Baker (mathematician)

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## Life

## Accomplishments

## Selected publications

## Honours and awards

## References

## External links

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Alan Baker Mathematician

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

Born |
London, England | 19 August 1939

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

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.

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]}

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.

- 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

- 1970: Fields Medal
- 1972: Adams Prize

**^**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 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.

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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