Copyright 2005 Telegraph Group Limited THE DAILY TELEGRAPH(LONDON) May 06, 2005, Friday SECTION: News; End Column Pg. 031 LENGTH: 538 words HEADLINE: Saunders Mac Lane Creator of category theory, which provided a framework for much of modern mathematics BODY: 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 Gttingen, 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. 13-May-2005 17:28:05 -0300,4138;000000000000-00000005