Martin Hyland
Encyclopedia
John Martin Elliott Hyland is professor of mathematics at King's College
in the University of Cambridge
, England
where he is currently head of the Department of Pure Mathematics and Mathematical Statistics. His interests include mathematical logic
, category theory
, and theoretical computer science.
Martin Hyland is best known for his work on category theory applied to logic (proof theory
, recursion theory), theoretical computer science (lambda-calculus and semantics) and higher dimensional algebra. In particular he is known for work on the effective topos
(within topos theory) and on game semantics
.
King's College, Cambridge
King's College is a constituent college of the University of Cambridge, England. The college's full name is "The King's College of our Lady and Saint Nicholas in Cambridge", but it is usually referred to simply as "King's" within the University....
in the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
where he is currently head of the Department of Pure Mathematics and Mathematical Statistics. His interests include mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, and theoretical computer science.
Martin Hyland is best known for his work on category theory applied to logic (proof theory
Proof theory
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
, recursion theory), theoretical computer science (lambda-calculus and semantics) and higher dimensional algebra. In particular he is known for work on the effective topos
Effective topos
In mathematics, the effective topos is a topos introduced by , based on Kleene's notion of recursive realizability, that captures the idea of effectivity in mathematics....
(within topos theory) and on game semantics
Game semantics
Game semantics is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes. In the late 1950s Paul Lorenzen was the...
.