|Born||1941 (age 72–73)|
|Institutions||Queen Mary University of London
University of Oxford
|Alma mater||Cambridge University
|Thesis||Classifying Pairs of Real-Closed Fields (1968)|
|Doctoral advisor||Dana Scott|
|Notable awards||Polya Prize|
Angus John Macintyre FRS, FRSE (born 1941) is a British mathematician and logician and Professor of Mathematics at the Queen Mary, University of London. He is known for many fundamental and widely influential contributions to Model theory, logic and their applications in algebra, algebraic geometry, and number theory.
After undergraduate studies in Cambridge University, he completed his PhD at Stanford University under the supervision of Dana Scott in 1968. From 1973 to 1985, he was Professor of Mathematics at Yale University. From 1985 to 1999, he was Professor of Mathematical Logic at the University of Oxford and Fellow of Merton College, Oxford. He then moved to the University of Edinburgh until 2002, then to Queen Mary.
Macintyre was the first Scientific Director of ICMS, the International Centre for Mathematical Sciences in Edinburgh. He was elected a Fellow of the Royal Society in 1993. In 2003, he was awarded the Pólya Prize by the London Mathematical Society. From 2009 to 2011, he was the President of the London Mathematical Society. He has supervised a number of doctoral students who have become leaders in the field.
Macintyre's papers from 1971 on Aleph-one categorical theories of groups and fields started a whole field of model theory and its applications to areas of mathematics, and were influential in the development of geometric stability theory. His works on model theory of various structures related to algebra, geometry and number theory have been widely influential. His work in 1976 on quantifier elimination for p-adic fields created a theory of p-adic semi-algebraic geometry and has had applications to arithmetic geometry and motivic integration, including solution by Jan Denef to a conjecture of Jean-Pierre Serre on rationality of p-adic Poincare series.
Macintyre's work with Zoe Chatzidakis and Lou van den Dries re-visited Ax's work on model theory of finite and pseudo-finite fields and generalized the Lang-Weil estimates (of Serge Lang and Andre Weil) over finite fields to definable sets. This has had applications to model theory of finite and asymptotic structures, simple theories and topics in analytic number theory. He introduced the model theory of difference fields and proved results on model theory of Frobenius automorphisms. He is one of the pioneers of the model theory of real and complex exponentiation. With Alex Wilkie he proved the decidability of real exponential fields (solving a problem of Alfred Tarski) modulo Schanuel's conjecture from transcendental number theory. With Lou van den Dries he initiated the model theory of logarithmic-exponential series and Hardy fields. His work with David Marker and Lou van den Dries gave fundamental results on the model theory of restricted analytic functions and exponentiation and O-minimality. Macintyre has worked on Zilber's theory of the complex exponentiation and Zilber's pseudo-exponential fields. Macintyre's work with Jamshid Derakhshan develops a model theory for the adele ring of a number field which is of importance in number theory. With Marek Karpinski, he proved decisive results on VC-dimention which has had applications to theoretical computer science and neural networks.