46 Facts About Michael Atiyah

Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry.

Michael Atiyah was awarded the Fields Medal in 1966 and the Abel Prize in 2004.

Michael Atiyah's mother was Scottish and his father was a Lebanese Orthodox Christian.

Michael Atiyah had two brothers, Patrick and Joe, and a sister, Selma.

Michael Atiyah went to primary school at the Diocesan school in Khartoum, Sudan, and to secondary school at Victoria College in Cairo and Alexandria ; the school was attended by European nobility displaced by the Second World War and some future leaders of Arab nations.

Michael Atiyah was a doctoral student of William V D Hodge and was awarded a doctorate in 1955 for a thesis entitled Some Applications of Topological Methods in Algebraic Geometry.

Michael Atiyah became Savilian Professor of Geometry and a professorial fellow of New College, Oxford, from 1963 to 1969.

Michael Atiyah took up a three-year professorship at the Institute for Advanced Study in Princeton after which he returned to Oxford as a Royal Society Research Professor and professorial fellow of St Catherine's College.

Michael Atiyah was president of the London Mathematical Society from 1974 to 1976.

Michael Atiyah was president of the Pugwash Conferences on Science and World Affairs from 1997 to 2002.

Michael Atiyah contributed to the foundation of the InterAcademy Panel on International Issues, the Association of European Academies, and the European Mathematical Society.

Michael Atiyah was President of the Royal Society, Master of Trinity College, Cambridge, Chancellor of the University of Leicester, and president of the Royal Society of Edinburgh.

Michael Atiyah was a Trustee of the James Clerk Maxwell Foundation.

Michael Atiyah was awarded the Fields Medal in 1966 and the Abel Prize in 2004.

Michael Atiyah said that the mathematician he most admired was Hermann Weyl, and that his favourite mathematicians from before the 20th century were Bernhard Riemann and William Rowan Hamilton.

The seven volumes of Michael Atiyah's collected papers include most of his work, except for his commutative algebra textbook; the first five volumes are divided thematically and the sixth and seventh arranged by date.

Michael Atiyah studied double points on surfaces, giving the first example of a flop, a special birational transformation of 3-folds that was later heavily used in Shigefumi Mori's work on minimal models for 3-folds.

Michael Atiyah showed how primary operations in K-theory could be used to give a short solution taking only a few lines, and in joint work with Adams proved analogues of the result at odd primes.

Michael Atiyah showed that for a finite group G, the K theory of its classifying space, BG, is isomorphic to the completion of its character ring:.

Michael Atiyah introduced the J-group J of a finite complex X, defined as the group of stable fiber homotopy equivalence classes of sphere bundles; this was later studied in detail by J F Adams in a series of papers, leading to the Adams conjecture.

Michael Atiyah found a proof of several generalizations using elliptic operators; this new proof used an idea that he used to give a particularly short and easy proof of Bott's original periodicity theorem.

Michael Atiyah noticed the homotopy invariance of the index, and asked for a formula for it by means of topological invariants.

Hirzebruch and Borel had proved the integrality of the A genus of a spin manifold, and Michael Atiyah suggested that this integrality could be explained if it were the index of the Dirac operator.

Michael Atiyah solved a problem asked independently by Hormander and Gel'fand, about whether complex powers of analytic functions define distributions.

Michael Atiyah used Hironaka's resolution of singularities to answer this affirmatively.

In collaboration with Bott and Lars Garding, Michael Atiyah wrote three papers updating and generalizing Petrovsky's work.

Michael Atiyah showed how to extend the index theorem to some non-compact manifolds, acted on by a discrete group with compact quotient.

An early example of this which Michael Atiyah used repeatedly is the Penrose transform, which can sometimes convert solutions of a non-linear equation over some real manifold into solutions of some linear holomorphic equations over a different complex manifold.

Michael Atiyah reformulated this construction using quaternions and wrote up a leisurely account of this classification of instantons on Euclidean space as a book.

Michael Atiyah deduced from this that the intersection form must be a sum of one-dimensional ones, which led to several spectacular applications to smooth 4-manifolds, such as the existence of non-equivalent smooth structures on 4-dimensional Euclidean space.

Donaldson went on to use the other moduli spaces studied by Michael Atiyah to define Donaldson invariants, which revolutionized the study of smooth 4-manifolds, and showed that they were more subtle than smooth manifolds in any other dimension, and quite different from topological 4-manifolds.

Michael Atiyah described some of these results in a survey talk.

Michael Atiyah used the Penrose transform to convert the Green's function for the conformally invariant Laplacian into a complex analytic object, which turned out to be essentially the diagonal embedding of the Penrose twistor space into its square.

Michael Atiyah proved a generalization of this that applies to all compact symplectic manifolds acted on by a torus, showing that the image of the manifold under the moment map is a convex polyhedron, and with Pressley gave a related generalization to infinite-dimensional loop groups.

Michael Atiyah and Bott showed that this could be deduced from a more general formula in equivariant cohomology, which was a consequence of well-known localization theorems.

Michael Atiyah showed that instantons in 4 dimensions can be identified with instantons in 2 dimensions, which are much easier to handle.

Michael Atiyah continued to publish subsequently, including several surveys, a popular book, and another paper with Segal on twisted K-theory.

Michael Atiyah introduced the concept of a topological quantum field theory, inspired by Witten's work and Segal's definition of a conformal field theory.

Michael Atiyah studied skyrmions with Nick Manton, finding a relation with magnetic monopoles and instantons, and giving a conjecture for the structure of the moduli space of two skyrmions as a certain subquotient of complex projective 3-space.

Michael Atiyah gave an affirmative answer to this question, but felt his solution was too computational and studied a conjecture that would give a more natural solution.

Michael Atiyah related the question to Nahm's equation, and introduced the Atiyah conjecture on configurations.

Michael Atiyah was appointed as a Honorary Fellow of the Royal Academy of Engineering in 1993.

Michael Atiyah was made a Knight Bachelor in 1983 and made a member of the Order of Merit in 1992.

The Michael Atiyah building at the University of Leicester and the Michael Atiyah Chair in Mathematical Sciences at the American University of Beirut were named after him.

Michael Atiyah married Lily Brown on 30 July 1955, with whom he had three sons, John, David and Robin.

Lily Atiyah died on 13 March 2018 at the age of 90 while Sir Michael Atiyah died less than a year later on 11 January 2019, aged 89.