# 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 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 |

## Contents

## LifeEdit

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]}

## AccomplishmentsEdit

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 publicationsEdit

- 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 awardsEdit

- 1970: Fields Medal
- 1972: Adams Prize

## ReferencesEdit

**^**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.

## External linksEdit

- 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.