Professor Douglas Northcott, who was elected a member of the LMS on 17 November 1949, died on 8 April 2005. Born in London on 31 December 1916, he was educated at Christs Hospital and St Johns College, Cambridge. He started work as a research student in analysis under the supervision of G.H. Hardy in 1938, but then war intervened.
Douglas Northcott endured appalling conditions and poor health during the war years, particularly after he became a prisoner of war following the fall of Singapore.
Northcotts original intention, when visiting Princeton during 1946-48, had been to study Banach spaces. However, Emil Artins kindnesses in explaining fundamental algebraic ideas converted him to algebra. He returned to St Johns College as a Research Fellow in 1948, and almost all his post-doctoral work was concerned with commutative algebra and its links with algebraic geometry. He held the Town Trust Chair of Pure Mathematics, and was Head of Department, at Sheffield University for thirty years from 1952 until his retirement. He was awarded the LMSs Junior Berwick Prize in 1953 and served as LMS Vice-President during 1968-69. He was elected to the Royal Society in 1961.
Northcotts name will be known to many LMS members through his seven books. He was delighted when his two Cambridge Tracts, Ideal theory (1953) and Finite free resolutions (1976), were reprinted in 2004.
Several of Douglas Northcotts many important contributions to research in commutative algebra continue to be mentioned at present-day top-level international conferences. In particular, his joint work with David Rees in 1954 on reductions, integral closures and analytic spreads of ideals is of lasting significance and has strong connections with the modern theory of tight closure.
SAUNDERS MAC LANE
Saunders Mac Lane, who has died aged 95, was the joint creator (with Samuel Eilenberg) of the subject of category theory. He will also be remembered as the co-author (with Garrett Birkhoff) of A Survey of Modern Algebra, which for at least thirty years remained the definitive English-language treatment of abstract algebra.
Mac Lane was born in Taftville, Connecticut on 4 August 1909. His father, who was a Congregationalist minister, died when he was 15, and an uncle made it possible for him to go to Yale where he quickly excelled in mathematics. After a year of postgraduate working Chicago, he moved to Göttingen to study for a PhD in mathematical logic under the supervision of Paul Bernays. On returning to the United States he spent the next five years in fixed-term appointments before becoming an assistant professor at Harvard in 1938.
Although his PhD thesis had been in logic, his early published papers were in algebra (particularly valuation theory), a subject which he had imbibed deeply at Göttingen from Emmy Noether and her students. It was in 1941, the year the Survey was published, that the EilenbergMac Lane collaboration began. Eilenberg had arrived in the US from Poland two years earlier, and was then at the University of Michigan. He recognized the similarity of Mac Lane's calculations to ones he was encountering in algebraic topology, and suggested to Mac Lane that they collaborate. The partnership lasted 14 years, and produced 15 major papers which changed the direction of twentieth-century mathematics.
The common calculations led to the development of homological algebra, and in particular to the discovery of EilenbergMacLane spaces, which provided the definitive link between the cohomology of groups and that of topological spaces. But Mac Lane and Eilenberg went further. In seeking to provide a sound conceptual framework for the subject, they invented the notions of category, functor and natural transformation. These notions were slow to gain acceptance on account of their seeming lack of content: for a decade or so, category theory was derided by other mathematicians as abstract nonsense. But in time the substantial new advances made possible by the categorical way of thinking about mathematics won it acceptance. Mac Lane remained at the forefront of these advances until well into the 1970s.
In 1947 Mac Lane moved to the University of Chicago, where he spent the rest of his career, becoming Professor Emeritus in 1982. His distinction was recognized by honorary degrees from several universities, and by the award of the National Medal of Science in 1989. His list of PhD students is both long and distinguished, including many mathematicians (such as Irving Kaplansky, Anil Nerode, Robert Solovay and John Thompson) who went on to eminence in fields quite different from his own. He greatly enjoyed the company of younger colleagues, and remained an active participant in international conferences right up to his 90th year.
In addition to the best-selling Survey of Modern Algebra, Mac Lane was author or co-author of five books. His accounts of homological algebra (1963) and category theory (1971) both carry the authority of a founder of the subject, and his last book (1992), a textbook on topos theory written jointly with Ieke Moerdijk, was one of the major new developments in mathematics that category theory made possible.