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Frank Adams's family was evacuated from London during World War II and he attended school in a number of places. He entered Trinity College, Cambridge in 1949. After taking his degree he started graduate work at Cambridge with Besicovitch on geometric measure theory. He changed to working on algebraic topology with Wylie.
Adams became influenced by Henry Whitehead who led the foremost British school of algebraic topology. In fact Adams was appointed to a post at Oxford shortly before completing his doctorate. After a year at Oxford he returned to Cambridge have won a Fellowship with his doctoral thesis on spectral sequences.
Adams visited Chicago as a research associate, then he moved to Princeton. Adams said:-
... I regard the progress of my researches in America as most successful. ... By good luck, moreover, my new methods were sufficiently powerful to answer one of the classical problems of my subject, that proposed by H Hopf in 1935.On his return from the USA he became a College Lecturer at Trinity Hall Cambridge. His work turned towards K-theory, the generalised cohomology theory on vector bundles.
After spendind further time in Princeton, Adams took up a post at Manchester as a Reader, being appointed to Newman's chair when he retired. During this time he wrote a series of papers which were highly influential in homotopy theory.
In 1964 Adams was elected a Fellow of the Royal Society. In  James says:-
It was in 1965, however, that he suffered the first attack of a psychiatric illness, as a result of which he was on sick leave for some months. It was apparently brought on by the worry caused by his responsibilities as head of department ...In 1970 Adams succeeded Hodge as Lowndean Professor of Astronomy and Geometry at Cambridge. His research continued to be of fundamental importance in homotopy theory of the classifying spaces of topological groups, finite H-spaces and equivariant homotopy theory.
He wrote a number of books of major importance, Lectures on Lie groups (1969), Algebraic topology: a student's guide (1972), Stable homotopy theory and generalized homology (1974) and Infinite loop spaces (1978).
His lectures were well prepared but usually hard. He once received a letter from a second year undergraduate class saying:-
The class wishes to inform Professor Adams that it has been left behind.He replied:-
At any rate I have done exterior algebra, even if the second year haven't.Adams received many awards for his work. Among these was the Sylvester Medal of the Royal Society of London which was awarded to him in 1982:-
... in recognition of his solution of several outstanding problems of algebraic topology and of the methods he invented for this purpose which have proved of prime importance in the theory of that subject.His health continued to cause him problems with another psychiatric illness in 1986. Perhaps his health contributed to his death since he decided to go to London to celebrate the retiral of a friend despite feeling unwell. He was killed in a car crash only a few miles from his home on the return journey. He had apparently always had a reputation as a car driver. According to 
He drove cars with remarkable skill but in a style that left a lasting impression on his passengers.References (4 books/articles)
References elsewhere in this archive:
J Frank Adams was elected to the Royal Society of London in 1964. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.
He was awarded the Sylvester Medal of the Royal Society in 1982. You can see a history of the Sylvester Medal and a list of the winners.
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