by I. M. James, rev.

© Oxford University Press 2004 All rights reserved

**Adams, (John) Frank** (1930-1989), mathematician, was born on 5 November 1930 in Woolwich, London, the elder son (there were no daughters) of William Frank Adams, civil engineer, and his wife, Jean Mary Baines, biologist, both of London. He was educated at Bedford School and then spent the years 1948 and 1949 doing national service in the Royal Engineers. He went to Trinity College, Cambridge, where he was a wrangler in part two (1951) and gained special credit in part three (1952) of the mathematical tripos. He continued at Cambridge as a research student, first under A. S. Besicovitch and then, more significantly, under Shaun Wylie. His PhD dissertation (1955) was on algebraic topology, which remained his main research interest for the rest of his life. Adams spent the year 1954 at Oxford, as a junior lecturer, where he came under the influence of J. H. C. Whitehead, then the leading topologist in the country. In 1953 he married Grace Rhoda, daughter of Charles Benjamin Carty, time and motion engineer. Soon after their marriage she became a minister in the Congregational church. They had a son and three daughters (one adopted). Family life was extremely important to Adams, though he preferred to keep it separate from his professional life. The family used to do many things together, especially fell-walking in the Lake District.

Adams returned to Cambridge in 1956 as a research fellow at Trinity College and developed the spectral sequence which bears his name, linking the cohomology of a topological space to its stable homotopy groups. In 1957-8 he was a Commonwealth fellow at the University of Chicago, where he proved a famous conjecture about the existence of H-structures on spheres, using the same ideas. On his return from the United States he became fellow, lecturer, and director of studies at Trinity Hall, Cambridge. There, in 1961, he confirmed his already high international reputation by solving another famous problem, concerning vector fields on spheres. For this he invented some operations in K-theory, which later bore his name, and these proved to be of fundamental importance.

In 1962 Adams left Cambridge for Manchester University, where in 1964 he became Fielden professor in succession to M. H. A. Newman and was elected a fellow of the Royal Society at the early age of thirty-four. At Manchester he took much further the powerful methods he had originated at Cambridge in a celebrated series of papers 'On the groups J(X)', which opened up a new era in homotopy theory. In the first of these he made a bold conjecture about the relation between the classification of vector bundles by stable isomorphism and their classification by stable homotopy equivalence of the associated sphere-bundles. Reformulated in various ways this Adams conjecture (later a theorem) became one of the key results in homotopy theory.

By 1970 Adams was the undisputed leader in his field and his reputation was such that he was seen as the obvious person to succeed Sir William Hodge as Lowndean professor of astronomy and geometry at Cambridge. He was delighted to return to Trinity, his old college, though he never became very active in its affairs. Among his various research interests in this later phase of his career three subjects predominated: finite H-spaces, equivariant homotopy theory, and the homotopy properties of classifying spaces of topological groups. Although he published important papers on these and other subjects throughout this period he also began to publish more expository work, notably his lecture notes on *Stable Homotopy and Generalised Homology* (1974) and his monograph, *Infinite Loop Spaces* (1978), based on the Hermann Weyl lectures he gave at Princeton University. The latter, especially, gives a good idea of his magisterial expository style and particular brand of humour.

Adams was an awe-inspiring teacher who expected a great deal of his research students and whose criticism of work which did not impress him could be withering. For those who were stimulated rather than intimidated by this treatment, he was generous with his help. The competitive instinct in Adams was highly developed, for example in his attitude to research. Priority of discovery mattered a great deal to him and he was known to argue such questions not just as to the day but as to the time of day. In a subject where 'show and tell' is customary he was extraordinarily secretive about research in progress.

Although Adams enjoyed excellent physical health he suffered a serious episode of depressive illness in 1965 and there were further episodes of depression later. To what extent his professional work was adversely affected by the nature of the treatments he received to help control the condition is not clear, but certainly his contributions to research in later years were not as innovative as those of his youth. Moreover, he never played the prominent role in the academic and scientific world to which his professional standing would have entitled him. Even so, his influence was great; those who turned to him for an opinion were seldom left in any doubt as to his views.

Adams's great contributions to mathematics were recognized by the awards of the junior Berwick (1963) and senior Whitehead (1974) prizes of the London Mathematical Society and the Sylvester medal (1982) of the Royal Society. He received the degree of ScD from Cambridge in 1982. He was elected a foreign associate of the National Academy of Sciences of Washington, DC (1985), and an honorary member of the Royal Danish Academy of Sciences (1988), and was made an honorary ScD at the University of Heidelberg in 1986. His collected works were published in 1992. He acted as treasurer of the local branch of the Labour Party and might be described as an intellectual Fabian in outlook. Adams died immediately following a night-time accident in the car he was driving on the A1 near Brampton, Huntingdonshire, on 7 January 1989.

I. M. JAMES, *rev.*

**Sources **

I. M. James, *Memoirs FRS,* 36 (1990), 1-16

*CGPLA Eng. & Wales* (1989)

**Archives **

Trinity Cam., corresp. and papers

**Likenesses **

bronze head, priv. coll.

photograph, repro. in James, *Memoirs FRS*

photograph, repro. in N. Ray and G. Walker, eds., *Adams memorial symposium on algebraic topology,* 2 vols. (1992)

**Wealth at death **

£154,180: probate, 7 March 1989, *CGPLA Eng. & Wales*

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