## Professor Douglas Northcott

### Mathematician dedicated to commutative algebra

Douglas Geoffrey Northcott, mathematician: born London 31 December 1916; Commonwealth Fund Fellow, Princeton University 1946-48; Research Fellow, St John's College, Cambridge 1948-52; Assistant Lecturer in Mathematics, Cambridge University 1949-51, Lecturer in Mathematics 1951-52; Town Trust Professor of Pure Mathematics, Sheffield University 1952-82 (Emeritus); FRS 1961; married 1949 Rose Austin (died 1992; two daughters); died Sheffield 8 April 2005.Douglas Northcott, who held the Town Trust Chair of Pure Mathematics at Sheffield University for 30 years, will be remembered for his fundamental contributions to the branch of pure mathematics known as "commutative algebra", and as the author of seven carefully written, detailed and informative books.

Northcott's parents were not well off, but an opportunity arose for him to be nominated for a "presentation vacancy" at Christ's Hospital; he was admitted in 1927. The school, which has a fine record in the production of outstanding mathematicians, recognised his mathematical aptitude at an early stage, and he benefited from the teaching of the Senior Mathematics Master, C.J.A. Trimble. (Northcott became the Royal Society's representative on the Council of Almoners of Christ's Hospital in 1976, and he found this re-establishment of links with the school most interesting.)

In 1935, Northcott was awarded an open Bayliss Scholarship in Mathematics and entered St John's College, Cambridge; he was a Wrangler in 1937 and obtained a Distinction in Part III of the Mathematical Tripos in 1938.

During Part III, he attended lectures by G.H. Hardy, the Sadleirian Professor of Pure Mathematics responsible for many major contributions to mathematical analysis and number theory, and came to know Hardy quite well. Hardy agreed to supervise him as a research student, starting in the 1938-39 session, and Northcott's initial research was in mathematical analysis. He was awarded a Commonwealth Fund Fellowship to enable him to study the theory of Banach spaces at the University of Princeton, but on the day that he was due to sail to the United States, Britain declared war on Germany.

The war years affected Northcott dramatically. He volunteered for military service, even though it had been recommended that he "be held in a pool to be employed in technical services" and some who knew him hoped that he would take that route. He was drafted to the Far East; he contracted several serious illnesses; and he was a prisoner of war from the fall of Singapore until liberation in 1945. During those years, he endured appalling conditions and poor health; his survival strategy included his concealment of a notebook, in which he wrote down mathematical arguments, in his gas-mask case; he believed that the atomic bombs saved his life. It was only well into retirement that he talked much about those years.

After the Second World War, Northcott was able to pick up the threads of his academic career: G.H. Hardy, who accorded him the exceptional (for Hardy) honour of shaking his hand to welcome him back to Cambridge, had retired, and Frank Smithies became his supervisor; Northcott was allowed to take up the Commonwealth Fund Fellowship in 1946.

Although, on arrival in Princeton, Northcott still had the intention of studying Banach spaces, he there encountered Emil Artin, whose many kindnesses in explaining fundamental algebraic ideas resulted in Northcott's becoming a dedicated algebraist. After 21 exciting months in the US, he returned to St John's College as a Research Fellow, and, once his much-delayed PhD was completed, almost all of his subsequent scholarly work was concerned with commutative algebra, that is, the study of the local rings that are used in algebraic geometry together with related algebraic structures.

He was appointed to the Town Trust Chair of Pure Mathematics at Sheffield in 1952, and he held that post until his retirement in 1982. He was awarded the London Mathematical Society's Junior Berwick Prize in 1953 (for his paper "On integrally closed geometric quotient rings" in the society's Proceedings) and elected to the Royal Society in 1961.

Northcott was a very organised person who liked to be prepared for whatever lay ahead. As a result, he had a reputation for making many lists. His natural inclination to think carefully before speaking meant that conversations with him would sometimes be punctuated by lengthy pauses, which could be unnerving for young members of his staff.

In 1949, he married Rose Austin, a charming and vivacious person whose unstinting support helped him to cope with the demands of the headship of the department in Sheffield; she even looked after babies of members of staff in times of crisis. Even though he served as head for 30 years, he was, with Rose's support, able to make time for writing seven books and about 70 research papers following his PhD.

His writing is characterised by careful attention to detail; his books were principally aimed at graduate students, but their clarity, detailed discussion of difficult points and reliable accuracy means that they also serve as informative and reassuring references for experienced researchers. Northcott was delighted when his two Cambridge Tracts, Ideal Theory (1953) and Finite Free Resolutions (1976), were reprinted in 2004.

Northcott had comparatively few research collaborators, but a visit to Sheffield in the 1960s by John A. ("Jack") Eagon resulted in what is nowadays called (by others) the "Eagon-Northcott complex". However, Northcott's most famous collaboration was with David Rees, a friend from Cambridge days but later Professor of Mathematics at Exeter University. In a joint paper in 1954, they introduced the concepts of reduction and analytic spread of an ideal, and developed their connections with integral closures. These ideas have turned out to be important in much modern research in commutative algebra; they have provided one of several motivations for the exciting development of tight closure theory in the last 18 years, so much so that the Northcott-Rees theory of reductions and integral closures, now more than 50 years old, is still mentioned at most top-level international conferences on commutative algebra.

This means that Northcott's name is destined to live on, well after his death, among the international community of commutative algebraists, in a way that most research mathematicians can only dream about.

**Rodney Sharp**

Published: 2 May 2005 © Independent