# Alan Baker (mathematician)

**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 | |
---|---|

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 |

## Life

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.[2] 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.[3] 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.[2]

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

## Accomplishments

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.[6] 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**(2): 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**(2): 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.[7] - 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
- 1973: Fellowship of the Royal Society

## References

- Trinity College website, accessed 5 February 2018
- "BAKER, Prof. Alan".
*Who's Who*.*ukwhoswho.com*.**2019**(online ed.). A & C Black, an imprint of Bloomsbury Publishing plc. (subscription or UK public library membership required) (subscription required) - 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.

## External links

- O'Connor, John J.; Robertson, Edmund F., "Alan Baker",
*MacTutor History of Mathematics archive*, University of St Andrews. - Alan Baker at the Mathematics Genealogy Project
- Masser, David (January 2019). "Alan Baker 1939–2018" (PDF).
*Notices of the American Mathematical Society*.**66**(1): 32–35.