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Atiyah, Sir Michael (Francis)

mathematical fields medal complex

[atty-ah] (1929– ) British mathematician.

Atiyah, the son of a Lebanese father and a Scottish mother, attended schools in Cairo and Manchester before his military service and then became a student, and later a fellow, of Trinity College, Cambridge. Further work at Princeton and Oxford followed, and led to professorships at both.

In 1963 he developed the Atiyah–Singer index theorem, and his subsequent publications in topology and algebra have contributed to a variety of areas in pure mathematics. He developed further the theory of complex manifolds, which had started with the Riemann surface (a multilayered surface) being used to understand multivalued functions of a single complex variable. Atiyah considered what happened when there was more than one complex variable. He received the Fields Medal in 1966 primarily for his work on topology.

The Fields Medal is awarded every four years to two, three or four mathematicians under the age of 40 and having outstanding distinction and promise in mathematics. The Canadian mathematician John Fields initiated, and provided money for, this international medal for high mathematical ability. The first medals were awarded in Oslo in 1936; and it is recognized as the mathematical equivalent of a Nobel Prize. Later Atiyah renewed interest in quaternions by showing their relationship with string theory, now widely used in mathematical physics. From Oxford he returned to Cambridge as Master of Trinity College and director of the Isaac Newton Institute for Mathematical Sciences, in 1990.

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