Alex James Wilkie FRS (born 1948 in

Northampton Northampton () is a market town and civil parish in the East Midlands of England, on the River Nene, north-west of London and south-east of Birmingham. The county town of Northamptonshire, Northampton is one of the largest towns in England; ...

) is a British mathematician known for his contributions to

model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the ...

and

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...

. Previously Reader in Mathematical Logic at the

University of Oxford The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in contin ...

, he was appointed to the Fielden Chair of Pure Mathematics at the

University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The university owns and operates majo ...

in 2007.

Education

Alex Wilkie attended

Aylesbury Grammar School Aylesbury Grammar School is a grammar school in Aylesbury situated in the English county of Buckinghamshire, which educates approximately 1300 students. Founded in 1598 in Aylesbury, Buckinghamshire by Sir Henry Lee, Champion of Queen Eliza ...

and went on to gain his BSc in mathematics with first class honours from

University College London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = � ...

in 1969, his MSc (in mathematical logic) from the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degre ...

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 , mottoeng = So that they may have life , established = , type = public research university , endowment = £20.0 million , budget = £326 million , chancellor = David Willetts , vice_chancellor = Nishan Canagarajah , head_labe ...

from 1972 to 1973, then a research fellow at the

Open University The Open University (OU) is a British Public university, public research university and the largest university in the United Kingdom by List of universities in the United Kingdom by enrolment, number of students. The majority of the OU's underg ...

from 1973 until 1978. He spent two periods as a junior lecturer in mathematics at

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

(1978–80 and 1981-2) with (1980–1) as a visiting assistant professor at

Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...

. 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 The Engineering and Physical Sciences Research Council (EPSRC) is a British Research Council that provides government funding for grants to undertake research and postgraduate degrees in engineering and the physical sciences, mainly to unive ...

) 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 Robin Oliver Gandy (22 September 1919 – 20 November 1995) was a British mathematician and logician. He was a friend, student, and associate of Alan Turing, having been supervised by Turing during his PhD at the University of Cambridge, where ...

. He remained in this post until appointment to the Fielden Chair at Manchester.

Awards and honours

Wilkie was elected a

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

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.'' Wilkie received the Carol Karp Prize (the highest award made by the

Association for Symbolic Logic The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL is ...

, every five years) jointly with Ehud Hrushovski in 1993. He was elected to the Council of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

. He received the Karp Prize again in 2013, jointly with Moti Gitik, Ya'acov Peterzil,

Jonathan Pila Jonathan Solomon Pila (born 1962) FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: is an Australian mathematician at the University of Oxford. Education Pila earned his bachelor's degree at ...

, and Sergei Starchenko. In 2017, Wilkie was awarded the Pólya Prize. He was an Invited Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Berkeley in 1986 and in Berlin in 1998. In 2015, Wilkie held the

Gödel Lecture The Gödel Lecture is an honor in mathematical logic given by the Association for Symbolic Logic, associated with an annual lecture at the association's general meeting. The award is named after Kurt Gödel and has been given annually since 1990. ...

titled ''Complex continuations of functions definable in with a diophantine application.''

References

{{DEFAULTSORT:Wilkie, Alex 1948 births Living people People from Northampton People educated at Aylesbury Grammar School Alumni of University College London Alumni of Bedford College, London 20th-century English mathematicians 21st-century English mathematicians Model theorists Academics of the University of Oxford Academics of the University of Manchester Yale University faculty Fellows of Wolfson College, Oxford Fellows of the Royal Society Fellows of the American Mathematical Society Tarski lecturers Gödel Lecturers