# Alex Wilkie

**Alex James Wilkie** FRS (born 1948 in Northampton[1]) is a British mathematician known for his contributions to model theory and logic. Previously Reader in Mathematical Logic at the University of Oxford, he was appointed to the Fielden Chair of Pure Mathematics at the University of Manchester in 2007.[2][3][4]

Alex Wilkie | |
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Alex Wilkie FRS, pictured in 2007 | |

Born | Alex James Wilkie 1948 (age 70–71) |

Residence | United Kingdom |

Nationality | British |

Alma mater | University College London Bedford College, University of London |

Known for | Wilkie's theorem |

Awards | Karp Prize (1993) Fellow of the Royal Society (2001) Pólya Prize (LMS) (2017) |

Scientific career | |

Fields | Mathematics, Model theory |

Institutions | Manchester University |

Doctoral advisor | Wilfrid Hodges |

## Education

Alex Wilkie attended Aylesbury Grammar School and went on to gain his BSc in mathematics with first class honours from University College London in 1969, his MSc (in mathematical logic) from the University of London in 1970, and his PhD from the Bedford College, University of London in 1973 under the supervision of Wilfrid Hodges with a dissertation titled *Models of Number Theory*.

## Career and research

After his PhD he went on to an appointment as a lecturer in mathematics at Leicester University from 1972 to 1973, then a research fellow at the Open University from 1973 until 1978. He spent two periods as a junior lecturer in mathematics at Oxford University (1978–80 and 1981-2) with (1980-1) as a visiting assistant professor at Yale University. In 1980 Wilkie solved Tarski's high school algebra problem.

In October 1982 Wilkie was appointed as a research fellow in the department of mathematics at the University of Paris VII, then returned to England the following year to take up a three-year SERC (now EPSRC) advanced research fellowship at the University of Manchester. After two years he was appointed lecturer in the Department of Mathematics. In 1986 he went on to Oxford where he was appointed to the readership in mathematical logic there which had become vacant upon the retirement of Robin Gandy. He remained in this post until appointment to the Fielden Chair at Manchester.

## Awards and honours

Wilkie was elected a Fellow of the Royal Society in 2001. To quote the citation

*Wilkie has combined logical techniques and differential-geometric techniques to establish fundamental Finiteness Theorems for sets definable using the exponential function, and more general Pfaffian functions. The results, going far beyond those obtained by conventional methods, have already had striking applications to Lie groups.*[5]

Wilkie received the Carol Karp Prize (the highest award made by the Association for Symbolic Logic, every five years) jointly with Ehud Hrushovski in 1993.[6][7] He was elected to the Council of the London Mathematical Society in 2007, vice-president of the Association for Symbolic Logic (2006) and president of the Association for Symbolic Logic in 2009. In 2012 he became a fellow of the American Mathematical Society.[8] He received the Karp Prize again in 2013, jointly with Moti Gitik, Ya'acov Peterzil, Jonathan Pila, and Sergei Starchenko.[7] In 2017, Wilkie was awarded the Pólya Prize.[9]

He was an Invited Speaker of the International Congress of Mathematicians in Berkeley in 1986[10] and in Berlin in 1998.[11]

## References

- Wilkie, Alex James, Who's Who in Education,Inglewood Books, 2003
- Homepage of Alex Wilkie at Manchester
- Alex Wilkie at the Mathematics Genealogy Project
- List of publications from Microsoft Academic
- NOTICES, Bulletin of Symbolic Logic, Vol 7, No 3, p436, 2001
- NOTICES Carol Karp Prize, J. Symbolic logic, Volume 58, Number 2, June 1993
- "Karp Prize Recipients". Association for Symbolic Logic. Archived from the original on 6 March 2017. Retrieved 10 May 2018.
- List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
- A list of Pólya Prizewinners. Retrieved 2019-10-10.
- Wilkie, A. J. "On schemes axiomatizing arithmetic".
*Proceedings of the ICM, 1986, Berkeley*. pp. 331–337. - Wilkie, A. J. (1998). "O-minimality".
*Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I*. pp. 633–636.

Preceded by Mark Pollicott |
Fielden Chair of Pure Mathematics2007- |
Succeeded byCurrent Holder |