# Sir Michael Francis Atiyah

# Sir Michael Francis Atiyah

**1929-**

**English Mathematician**

Sir Michael Atiyah is best known as one of the mathematicians responsible for K-theory, a technique in topology that made possible the solution of numerous problems. (Friedrich Hirzenbruch and Alexander Grothendieck (1928- ) also made significant contributions to the creation of K-theory.) He also helped create a significant theorem relating to the number of possible solutions for elliptic differential equations, called the index theorem. This discovery in turn led to a number of other advances, including a fixed-point theorem, which Atiyah helped define. These discoveries earned him the Fields Medal in 1966.

The son of a Lebanese father and a Scottish mother, Atiyah received his grade-school education in Egypt at Cairo's Victoria College and in England at the Manchester Grammar School. He later performed military service, then enrolled at Trinity College, Cambridge.

After earning his B.A., Atiyah immediately commenced work on his doctorate. He became a fellow of Trinity College in 1954 and the following year went to the Institute of Advanced Study in Princeton, New Jersey, as a Commonwealth Fellow. Upon his return to Cambridge, Atiyah became a lecturer in 1957, then a Fellow of Pembroke College in 1958. In 1961 he took a readership at Oxford and became a Fellow of St. Catherine's College.

During the 1950s and 1960s, Atiyah undertook some of his most important work in the field of cohomology, an area of topological theory that uses groups or vector bundles to study the properties of topological spaces. Later, while working with Isadore Manuel Singer, Atiyah developed the index theorem. This work, along with K-theory, earned him the Fields Medal, awarded at the International Congress in Moscow in 1966.

The following year Atiyah published *K-Theory,* in which he explained both the new concept and the index theorem. The latter gained new definition as Atiyah and Raoul Bott (1923- ) developed the fixed-point theorem. In time, these ideas would be applied to quantum theory, and theoretical physicists made extensive use of
them. This was particularly so when Simon Donaldson (1957- ), one of Atiyah's students, applied the index theorem to four-dimensional geometry. Atiyah's ideas also made possible advances in the theories of superspace and super-gravity, which attempt to unify relativity and quantum theory; they have also been applied to the string theory of fundamental particles.

In 1962 Atiyah was named a Fellow of the Royal Society, and in 1968 received its Royal Medal. He was knighted in 1983, and in 1988 received the Royal Society's Copley Medal. He has received numerous other awards as well, including election as a foreign member of national academies in a variety of countries, and honorary degrees from more than a dozen universities.

Atiyah remained at Oxford until 1990, when he was named Master of Trinity College, as well as first director of the Isaac Newton Institute for Mathematical Sciences in Cambridge. From 1990 to 1995 he served as President of the Royal Society. His work at Trinity College has focused on the application of mathematics to physics, and specifically on the linkage between geometry and particle physics.

**JUDSON KNIGHT**

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**Sir Michael Francis Atiyah**