Angus Macintyre

Who is Angus Macintyre?

Angus John Macintyre is a British mathematician known for his contributions to Model theory and logic. He is professor of mathematics at the Queen Mary, University of London.

He completed his PhD under the supervision of Dana Scott in 1968 with a thesis entitled "Classifying Pairs of Real-Closed Fields". After a career as Professor of Mathematics at Yale University from 1972 until 1984, he was Professor of Mathematical Logic at Oxford University until 1999, then Professor at the University of Edinburgh until 2002, and then at Queen Mary. He was the first Scientific Director of the International Center for Mathematical Sciences in Edinburgh. He was elected a Fellow of the Royal Society in 1993, and in 2003 he was awarded the Pólya Prize by the London Mathematical Society. From 2009 to 2011, he served as the President of the London Mathematical Society.

Angus Macintyre has been a leading figure in model theory and its applications. His 1971 papers on Aleph-One categorical theories of groups and fields opened up avenues on stability-theoretic methods in algebra and geometry and was influential in geometric stability theory. His many works on logic of groups, rings, and fields has been highly influential. His paper form 1976 on quantifier elimination for p-adic fields opened up a theory of p-adic geometry and has had remarkable applications, most notably by Jan Denef in proving a conjecture of J-P. Serre on rationality of certain p-adic Poincare series. This and his later work on uniform rationality of p-adic integrals from 1992 was used in the work of Jan Denef and Francois Loeser in the theory of motivic integration. His work on model theory of difference fields, on logic of finite fields and Lang-Weil estimates for definable sets over finite fields, the model theory of difference fields, logic of Frobenius maps have had enormous importance in the connections of model theory with algebra, geometry, and number theory and have opened up active research avenues. His work with Alex Wilkie on decidability of real exponential fields settled a problem of Alfred Tarski modulo Schanuel's Conjecture. His has many other influential works, just to mention a few: on models of Peano arithmetic, on model theory of local-global principles, on logic of real and complex exponentiaion, of logarithmic-exponential series, on model theory of restricted analytic fields with exponentiation, model theory of Frobenius on Witt vectors, model theory of intersection theory and Weil cohomology theories in algebraic geometry, model theory of the adele ring over a number field, model theory of Zilber's field, and the study of VC-dimension which has had applications in computer science and neural networks.