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From:"Peter_McCrae" <>Subject:MAC LANE; SAUNDERS-2005-USDate:Tue, 10 May 2005 13:00:36 +0100Saunders Mac Lane

(Filed: 06/05/2005) The Telegraph & telegraph.co.uk

Saunders Mac Lane, the mathematician who has died aged 95, developed

category theory, upon which the language of much modern mathematics depends.

Saunders Mac Lane was born at Taftville, Connecticut, on August 4 1909, the

son of Donald Mac Lane, a Congregationalist minister who died when his son

was 15. Young Saunders's schooling was interrupted, and he went to live with

his grandfather, also a Congregationalist preacher, before going up to Yale

in 1926. He graduated with a PhB in 1930 and took his Masters at the

University of Chicago the following year, where he came under the influence

of EH Moore, who persuaded him to move to Göttingen, then the world's

foremost mathematical research centre, for his doctoral work.

Mac Lane began his thesis, completed as Abbreviated Proofs in the Logical

Calculus (1933), under the supervision of the Swiss mathematician Paul

Bernays, who was removed from his post when the Nazis came to power. Mac

Lane, seeing that things were likely to get worse, returned to America as

soon as he could, spending a year at Yale and the following two at Harvard.

After stints at Cornell and back at Chicago, he became an assistant

professor at Harvard.

During this period he wrote (with G Birkhoff) A Survey of Modern Algebra

(1941), which had an immediate effect on the subject, introducing

undergraduates to the abstract algebra which had been explored in van der

Waerden's Moderne Algebra, and until then known only to research scholars.

When America entered the war, Mac Lane worked for the Applied Mathematics

Group at Columbia, before becoming professor of mathematics at Chicago in

1947.

Mac Lane, working with Samuel Eilenberg, began to concentrate his research

on homology, or the algebraic description of topological objects; a class of

objects which combine geometrical and algebraic properties are now known as

Eilenberg-Mac Lane spaces, have become essential tools in the study of

mathematical convergence and continuity, and opened up the study of group

cohomology in general.

As a result of this work, in 1945 Mac Lane and Eilenberg laid the

foundations of category theory, which provides a framework to show how

mathematical structures and families of structures relate to one another, in

a widely-influential paper. The theory has since been used to help define

philosophical concepts, and in fields as diverse as linguistics,

mathematical physics and computer science.

Mac Lane continued to lecture and research over a wide range. He worked on

and off throughout his career on mathematical logic and was one of the first

to undertake work on planar graphs. He also studied valuations and their

extensions to polynomial rings. In 1963 he published Homology and, in 1971,

Categories for the Working Mathematician; both remain significant textbooks.

In 1985 he produced Mathematics: Form and Function, and he also published

(with I Moerdijk) an introduction to topos theory, Sheaves in Geometry and

Logic (1992).

He received many awards (including membership of the Royal Society of

Edinburgh) and served on several learned bodies.

Mac Lane married, first, in 1933, Dorothy Jones; they had two daughters. She

died in 1985, and the following year he married Osa Segal.

© Copyright of Telegraph Group Limited 2005.

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