-------------------------------------------------------------------------= Dear Ms or Sir, On Tuesday I was asked by Maria Cleminson to write an obituary on Saunders Mac Lane, about 1000-1200 words long. Below, you find my proposed text. I have not written the standard closing paragraph, which I assume you will add yourself. I understand that an editor will go over it, but would ask you to show me the final version before I will give my consent to publish it. ... Yours sincerely, I. Moerdijk. ----------------------------------------------- Saunders Mac Lane, a former Professor at the University of Chicago and one of the most influential mathematicians of the twentieth century, died on April 14 in San Francisco, California. He is widely known as the creator, together with Samuel Eilenberg, of the language of CATEGORY THEORY, now an indispensable tool in many parts of mathematics, and having more and more applications in other fields, notably computer science and theoretical physics. Moreover, he was an inspiring teacher to many students, and served the mathematical community as a president of the American Mathematical Society, as a member of the National Science Board, and in various other important functions. He was awarded the National Medal of Science in 1989. During his productive life, he was strongly supported by his first wife Dorothy, with whom he had two daughters, Gretchen and Cynthia, and later, after Dorothy's death in 1985, by his second wife Osa Mac Lane-Skotting. Saunders Mac Lane was born on the 4th of August, 1909, in Norwich, Connecticut, as the son of a Congregetional minister, Donald Mac Lane, and a school teacher Winifred Saunders - Mac Lane. His father died when Saunders was only 15 years old, and after he graduated from high school in Leominster, Massachusetts, it was an uncle who in 1926 sent him to Yale. He graduated from Yale in 1930, and then moved to the University of Chicago where he obtained a Master's degree in 1931. During that year, he met Dorothy Jones who was reading economics at the same university, and whom he was to marry in 1933. Subsequently Mac Lane went to Goettingen in Germany, to work on a PhD thesis. In those days, it was not uncommon for talented mathematicians from the USA to study in Europe, and Goettingen was a world center of mathematics, where Mac Lane was able to attend lectures by the mathematical elite of the time, including David Hilbert, Gustav Herglotz, Hermann Weyl and Emmy Noether. One of the new developments that was taking place in Goettingen was the shaping of a "modern algebra", of which Emmy Noether was one of the main proponents. Mac Lane did not stay in Goettingen long. Pressed for time by the political climate in Germany, he hurried to complete his thesis in Mathematical Logic, under the supervision of Hermann Weyl and Paul Bernays. He returned to the US in the summer of 1933, to take a one year job at Yale. After working as an instructor at Harvard, Cornell and Chicago, he went to Harvard as an assistant professor in 1938, where he became full professor in 1946. In 1947, Mac Lane accepted an offer from the University of Chicago, where he was to spend the rest of his lon= g career. He served as Chairman of the Mathematics Department there from 1952 to 1958, and was appointed Max Mason Distinguished Service Professor in 1963, and Professor Emeritus in 1982. After his return from Germany to the US, Mac Lane's research interests had shifted from logic to algebra. Together with Garrett Birkhoff, he took it upon himself to spread the modern algebra of Emmy Noether on the American continent, and in 1941 Birkhoff and Mac Lane published their celebrated "Survey of Modern Algebra", the first English language text on the subject, a book which has seen many editions, and has influenced the lives of many generations of mathematics students in America and Europe alike. In his own research, Mac Lane had moved on and, together with Samuel Eilenberg and others, he developed an entirely new field of algebra, designed to provid= e the methods for a quantative, "algebraic" study of geometric objects, called homological algebra. They discovered a class of mathematical objects which combine algebraic and geometric features in a miraculous way, which are now known as Eilenberg-Mac Lane spaces, and which continue to play a central role in the field. In his work on homological algebra, Mac Lane showed the rare combination of being capable of doing long and complicated calculations (using new concepts to be developed simultaneously!), and of being a clear teacher and expositor at the same time. It was in the course of this work with Eilenberg, that the two mathematicians became increasingly aware of the lack of tools, even of a language, that would enable one to move from a domain like geometry, to another such as algebra, in a way which not only relates geometric objects to algebraic ones, but also translates - in an informative way - relations between different geometric objects into algebraic relations. This lead to their development of category theory. The first publication on category theory by Mac Lane and Eilenberg in 1945 was received by the mathematical community with mixed feelings, as it seemed just to express known facts in a new language. But gradually the force and wide applicability of the new language became clear, and now many important modern insights in mathematics cannot even be formulated without this language. Moreover, it turned out to be an effective vehicle, not only for exhibiting existing as well as newly discovered relations between different areas of mathematical research, but also between mathematics and other disciplines. Mac Lane wrote two influential text books on these subjects he partly created himself, "Homological Algebra" first published in 1963 and "Categories for the Working Mathematician", first published in 1971 and still the prevailing textbook in the field. Mac Lane was responsible for important breakthroughs in mathematical research, wrote several important books, and served the mathematical community in important functions. In addition, he was a gifted teacher, who was able at the same time to teach, to challenge and to listen to young students. He was a fervent hiker, leading the troops at mathematical conferences when he was already well into his seventies. Moreover, he had many interests besides mathematics, notably English poetry and philosophy. I was very fortunate to get to know him closely as a person and directly experience these qualities when in the late eighties we were collaborating on our joint book on topos theory, a field which - not surprisingly - uses categorical language to relate geometry to logic. We would have seemingly endless discussions about how (and how not!), to present mathematical concepts. Mac Lane would argue fiercely for his own point of view, but would always concentrate on the content of the matter, and never impose his authority or seniority. In the evenings, we would sit on the terrace of his weekend house in the Indiana Dunes overlooking Lake Michigan, and discuss philosophy, from Hegel and Heidegger to Kant and beyond, and Mac Lane would explain at length why Wittgenstein's view on the philosophy of mathematics was all wrong. Like many of his younger students and colleagues, I also had the privilege of listening to his colourful stories about how mathematics was before the war, about Hermann Weyl in Goettingen, or about his encounters with Bertrand Russell at a seminar at Harvard. We would go on long walks, on which he would lead the way at a brisk pace. It was only many years later,- when he would suggest I go alone on a walk while he would rest after lunch -, that his physical strength started to fade. Ieke Moerdijk. -------------------- Add standard form paragraph. ------------------- --=20 --=20 --=20 --=20 --=20 --=20 --=20 --=20 --=20 --=20