**Maurice Auslander** studied at Columbia University in New York where he obtained his B.S. in 1949. Remaining at Columbia he worked for his doctorate on group theory under the supervision of R L Taylor. He left New York in 1953 when he was appointed as an Instructor at the University of Chicago. After submitting his doctoral thesis to Columbia University, he was awarded his Ph.D. in 1954.

After a year as an Instructor at Chicago University, Auslander was appointed as an Instructor at the University of Michigan. He held this post for two academic years, 1954-56, before being awarded an NSF Fellowship which enabled him to spend the year 1956-57 at the Institute for Advanced Study in Princeton. The year 1956 marks an important stage in his career for in that year he published his first joint paper with D Buchsbaum *Homological dimension in Noetherian rings.* It was to be the first of many joint papers that the two mathematicians produced in a long and fruitful collaboration.

In 1957 Auslander was appointed as an Assistant Professor at Brandeis University. Three years later he was promoted to Associate Professor and he became Chairman of the Mathematics Department at Brandeis. After holding this post for a year, Auslander was awarded an NSF Senior Postdoctoral Fellowship which enabled him to spend the academic year 1961-62 at the University of Paris. He published *Modules over unramified local rings* in 1961 which continued, and to a certain extent completed, the work which he had begun with Buchsbaum over five years before.

Auslander was invited to give a special lecture at the International Congress of Mathematicians in Stockholm in 1962. He chose to speak on his results on modules over unramified local rings. It was the first of two addresses he gave to the International Congress of Mathematicians, the second being in 1986 at Berkeley. Returning to Brandeis in 1962, Auslander was promoted to full Professor in 1963, a position that he held until his death in 1994.

Travel was one of Auslander's loves and he spent time in many different parts of the world holding visiting positions at many universities. After being awarded a Sloan Foundation Fellowship for 1963-64, he spent the summer of 1965 as a Fulbright Fellow at the University of Uruguay in Montevideo. The academic year 1965-66 was spent on a second year long visit to the University of Paris, and in 1970-71 he held two visiting positions, first at the University of Illinois at Urbana and then at Queen Mary College in London, England. In 1975 he visited Mexico setting up a research group there on the representation theory of Artin algebras. For a couple of years he travelled less and in this period he was Chairman of the Mathematics Department at Brandeis for a second time during 1976-78.

In 1978-79 Auslander made the first of several visits to the University of Trondheim in Norway, on this occasion as a Guggenheim Fellow. He made further visits to Trondheim in 1989-90 and 1991 being appointed as an Adjunct Professor there in 1992. It is interesting to note that half of Auslander's publications have a co-author from Trondheim. A visit to China in 1986 saw him help establish a successful research group on representation theory. Other universities he visited included Texas at Austin (1981-82), Bielefeld (1984, 1985), Virginia State (1986-87), and Paderborn (1988, 1990). The countries he visited are too numerous to mention but we should note in particular visits to Israel and Switzerland.

It is fitting that Auslander ended his days while travelling. Knowing that he had incurable cancer he set off for a last trip during which he visited again some of his favourite parts of the word [1]:-

He enjoyed the company of old friends, wandered through the streets and gardens of Paris; appreciated for the last time his favourite painting, a self-portrait of Rembrandt, in London; and enjoyed the Munch museum in Oslo. Shortly after arriving in Trondheim he was hospitalised. He died a week and a half later, among close friends and colleagues, in the middle of the European meeting on "invariants and representations of algebras" which he had looked forward to attending. He died the way he lived and worked - elegantly.

The authors of [4] write about his contributions to the representation theory of algebras:-

[

Maurice Auslander's]contributions to the modern representation theory of algebras as well as to other fields of mathematics were deep and influential. When Maurice Auslander entered representation theory he was already a widely known mathematician with important contributions in commutative and homological algebra. His discovery, with Idun Reiten, of almost split sequences in the early seventies is certainly one of the foundation stones of our subject. His contributions to various fields continued right up to his last days. The influence of Maurice Auslander was not limited to his papers. His lectures and personal discussions with colleagues and students were always a source of inspiration.

While on the theme of representation theory of algebras, Dieter Happel reviewing [2] writes:-

... one should highlight ... the famous "Queen Mary Notes", which were written at a very early stage of modern representation theory of Artin algebras, and also early papers on the use of functors. They show clearly the insight and influence of Auslander on the directions and developments of representation theory of Artin algebras.

To gain some insight into the range of Auslander's contributions we list the chapter headings that his papers are divided into in his *Selected Works* ([1] and [2]):-

(1)

Homological dimension and local rings,(2)Ramification theory,(3)Functors,(4)Almost split sequences and Artin algebras,(5)Some topics in representation theory,(6)Lattices over general orders,(7)Tilting theory and homologically finite subcategories,(8)Almost split sequences and commutative rings,(9) Grothendieck groups and Cohen-Macaulay approximations, and (10)Relative theory and syzygy modules ...

H Rossi writes about Auslander's personality in [1]:-

For[Maurice], the difference between pragmatics and theory was only theoretical: his complete comprehension of complex situations, and only that, guided his actions. There never was any suspicion of compromise with principle: in his life, his politics, his mathematics. He always delivered his message with charm, elegance and humour; because of this he was surprisingly effective ...

In [5] Peskine and Reiten also write of Auslander's personality:-

Maurice Auslander had a warm and sensitive personality. His door was always open to his friends. He enjoyed discussions, often provocative ones, about mathematics and its philosophy in particular. He had considerable administrative talent, doubling the size of the department during his first chairmanship at Brandeis. His interests outside mathematics included art, poetry and music, and he enjoyed playing the violin. He was himself a "homme libre", free of all influences, and wanted others to be the same. He would pin down clichés on the spot. In mathematics he had a sense of beauty; he truly enjoyed some results and their proofs.

Among the honours he received for his outstanding contributions we should mention his election to the American Academy of Arts and Science and to the Royal Norwegian Society of Science and Letters.

**Article by:** *J J O'Connor* and *E F Robertson*