Michael Francis Atiyah

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Michael Francis Atiyah (2007)

Sir Michael Francis Atiyah , OM (born April 22, 1929 in London - † January 11, 2019 ) was a British mathematician and recipient of the Fields Medal and the Abel Prize .


He was the son of the Anglo-Lebanese writer and temporary secretary of the Arab League in London Edward Atiyah (1903-1964) and the Scot Jean Levens. Atiyah had a sister and two brothers, including law professor Patrick Atiyah (1931-2018). He went to school in Khartoum until 1941, with the family mostly spending the summers in England. Then the family went to Lebanon. Atiyah was soon sent to the Victoria School in Cairo, and when his father moved to England in 1945 he attended Manchester Grammar School. In 1947 he won a scholarship to Cambridge University (Trinity College), but preferred to do his two years of military service first before beginning his studies at Trinity College in 1949. In 1952 he received his bachelor's degree. After completing his doctorate with William Vallance Douglas Hodge (dissertation: Some Applications of Topological Methods in Algebraic Geometry ), he became a "Fellow" of Trinity College in 1954 . In 1955/56 he was a Commonwealth Fellow at the Institute for Advanced Study in Princeton , where he met Jean-Pierre Serre , Friedrich Hirzebruch , with whom he was friends and worked closely, Kunihiko Kodaira , Donald Spencer , Raoul Bott and Isadore Singer , among others . In 1957 he became a Lecturer and 1958 Fellow of Pembroke College , Cambridge, before he went to Oxford University as a reader in 1961 , where he became a Fellow of St. Catherine's College and in 1963 the Savilian Professorship in Geometry . From 1969 to 1972 he was Professor at the Institute for Advanced Study at Princeton and then Royal Society Research Professor at Oxford and Fellow at St. Catherine's College. In 1990 he became director of the newly founded Isaac Newton Institute for Mathematics in Cambridge and at the same time "Master" of Trinity College.

In 1955 he married the mathematician Lily Brown (1928-2018), with whom he had three sons. She received her PhD from Mary Cartwright and was a lecturer at Bedford College before giving up her mathematical career.


Atiyah initially studied algebraic geometry as a student of Hodge . As a student, he won the Smith Prize in 1954 for a thesis on the theoretical treatment of ruled surfaces . His dissertation dealt with a theory of the second kind of integrals on algebraic varieties by Solomon Lefschetz .

In the 1960s he and Friedrich Hirzebruch were one of the founders of the topological K-theory , a cohomology theory defined with the help of vector bundles . The suggestion for this came from the generalization of the Riemann-Roch theorem by Alexander Grothendieck and the periodicity theorem by Raoul Bott . For example, Atiyah applied topological K-theory to a simplification of the complicated solution of the Hopf invariant 1 problem by John Frank Adams and other topological problems. In 1963, together with Isadore M. Singer , he proved the Atiyah-Singer index theorem , which is considered one of the most important mathematical theorems of the 20th century. The theorem expresses the analytic index of an elliptic linear differential operator ( e.g. Laplace operator , Dirac operator ) on a compact manifold M by topological invariants of M (different depending on the type of operator, in the simplest case by the Euler-Poincare characteristic ). So it combines analysis with topology and has applications in modern physics. The “index” of the differential operator is the difference between the dimensions of its solution vector space and that of its adjoint operator. He also took part in the new, simpler proofs of this theorem with the help of the heat conduction equation (diffusion equation) in the 1970s (with Raoul Bott, Patodi 1973). The index theorem also has applications in algebraic geometry - it contains the Riemann-Roch theorem as a special case. In connection with the index theorem, Atiyah and Singer also “discovered” the Dirac operator for mathematics. The motivation for the famous theorem came from Israel Gelfand ( On elliptic equations , Russ. Math. Surveys 1960).

Atiyah and Friedrich Hirzebruch 1977

With Raoul Bott he proved Atiyah-Bott's fixed point theorem , a generalization of Lefschetz's fixed point theorem .

Atiyah has worked as a tireless mediator between mathematics and physics for decades. He was particularly interested in the non-Abelian gauge theories ( Yang-Mills theories ), which are nonlinear differential equations on manifolds. The ADHM construction of instantons in self-dual Euclidean Yang-Mills theories comes from him and Nigel Hitchin , Vladimir Drinfeld and Yuri Manin . But he also took up the quantum field theoretical methods introduced into mathematics by Edward Witten in particular (from new knot invariants to topological quantum field theories to supersymmetry and string theory ). In this way, many of Atiyah's ideas were reversed from the 1980s onwards by physicists (including new proofs of his index theorem with supersymmetry) and developed further.

He was a driving force behind the establishment of the Isaac Newton Institute , the formation of the Inter Academy Panel (IAP), the Association of European Academies ( ALLEA ), and the formation of the European Mathematical Society .

His students include Simon Donaldson , Nigel Hitchin , Peter Kronheimer , Graeme Segal , Frances Kirwan and Ruth Lawrence .

Awards and memberships

1974 to 1976 he was President of the London Mathematical Society and 1990 to 1995 President of the Royal Society. He was also President of the Royal Society of Edinburgh , of which he was a Fellow. He was a foreign member of numerous academies such as the Académie des Sciences , the Russian, Norwegian, Spanish, Swedish, Irish and Australian Academy of Sciences. He also received numerous honorary doctorates.

From 1997 to 2002 he was President of the Pugwash Conferences on Science and World Affairs .

Fonts (selection)


  • with Ian G. Macdonald : Introduction to commutative algebra. Addison-Wesley 1969
  • Elliptic operators and compact groups, Lecture Notes in Mathematics 401, Springer 1974
  • (Ed. And co-author) The representation theory of Lie groups. 1977
  • Geometry of Yang-Mills Fields , Fermi Lecture, Accademia dei Lincei, Pisa 1979
  • Collected works. Clarendon Press, Oxford, 7 volumes, 1988 to 2014
  • K-theory. Benjamin 1967, 1989
  • with Nigel Hitchin : The geometry and dynamics of magnetic monopoles , MB Porter Lectures, Princeton University Press, 1988
  • The geometry and physics of knots. Cambridge 1990
  • with Daniel Iagolnitzer (ed. and co-author): Fields medaillist lectures. World Scientific 1997, 2003, 3rd edition with Chitat Chong 2015


  • with Isadore M. Singer : The index of elliptic operators on compact manifolds. Bull. AMS 1963, proof then in a series of essays in the Annals of Mathematics, reprinted in Volume 3 of the Collected Works. See also the references in Atiyah-Singer index set .
  • with Raoul Bott : A Lefschetz Fixed Point Formula for Elliptic Differential Operators, Bulletin of the American Mathematical Society, Volume 72, 1966, p. 245 (Atiyah-Bott Fixed Point Theorem )
  • Thom Complexes , Proc. London Math. Soc., Series 3, Volume 11, 1961, pp. 291-310
  • The role of algebraic topology in mathematics , Journal of the London Mathematical Society, Volume 41, 1966, pp. 63-69
  • Change and progress in mathematics , picture of science, 1969, issue 4, pp. 314–323, reprint in: Michael Otte (ed.), Mathematician about mathematics. Science and the public , Berlin Heidelberg 1974, ISBN 978-3-540-06898-3 , doi: 10.1007 / 978-3-642-80866-1_8 .
  • with Bott, Patodi: On the heat equation and the index theorem , Invent. Math., Vol. 19, 1973, pp. 279-330, Errata Vol. 28, 1975, pp. 277-280
  • with Richard S. Ward : Instantons and algebraic geometry , Comm. Math. Phys. Vol. 55, 1977, pp. 117-124, Project Euclid
  • with Wilfried Schmid : A geometric construction of the discrete series for semisimple Lie groups , Inventiones Mathematicae, Volume 42, 1977, pp. 1-62, Errata, Volume 54, 1979, pp. 189-192
  • with I. Singer, N. Hitchin: Self-duality in four dimensional Riemannian geometry, Proc. Roy. Soc. A, Volume 362, 1978, pp. 425-461
  • What is geometry? (Presidential Address), The Mathematical Gazette, Vol. 66, 1982, pp. 179-182
  • Topological Quantum Field Theory , Pub. Math. IHES, vol. 68, 1988, pp. 175-186
  • Quantum Field Theory and low dimensional geometry, Progress in Theoretical Physics, Supplement No. 102, 1990, p. 1
  • Geometry and Physics , The Mathematical Gazette, Volume 80, 1996, pp. 78-82
  • Global Geometry (Bakerian Lecture), American Mathematical Monthly, Volume 111, 2004, pp. 716-723
  • Advice to a young mathematician , in Timothy Gowers June Barrow-Green , Imre Leader (Ed.): The Princeton Companion to Mathematics , Princeton University Press 2008, pp. 1006-1010
  • Edinburgh Lectures on Geometry, Analysis and Physis , 2010, Arxiv


  • Michael J. Barany: Michael F. Atiyah (1929-2019) . In: Nature . tape 566 , February 1, 2019, p. 40 , doi : 10.1038 / d41586-019-00358-9 ( nature.com [accessed February 9, 2019]).
  • S.-T. Yau (Ed.): The founders of index theory: reminiscences of Atiyah, Bott, Hirzebruch and Singer , International Press, Somerville 2003, with biography of Atiyah, Online, Celebratio Mathematica

Web links

Individual evidence

  1. Michael Francis Atiyah in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. Textbook representations are for example: Peter Gilkey: "Invariance theory, the heat equation, and the Atiyah-Singer-Indextheorem", online book , Melrose: The Atiyah-Patodi-Singer index theorem , online book
  3. Atiyah, Hitchin, Drinfeld, Manin, Construction of Instantons, Phys. Lett. A, Vol. 65, 1978, pp. 185-187
  4. ^ Atiyah: Topological quantum field theories, Publications Mathématiques de l'IHÉS. Volume 68, 1988, pp. 175-186
  5. ^ Atiyah and Singer receive Abel prize , Notices AMS, June / July 2004, pp. 649–650
  6. ^ American Academy of Arts and Sciences. Book of Members ( PDF ). Retrieved April 15, 2016
  7. Member entry of Sir Michael F. Atiyah at the German Academy of Natural Scientists Leopoldina , accessed on October 25, 2017.
  8. ^ Member Directory: Michael Atiyah. National Academy of Sciences, accessed October 25, 2017 .
  9. ^ Past Members: Michael Francis Atiyah. Royal Irish Academy, accessed March 31, 2019 .
  10. ^ Membership directory: Michael Atiyah. Academia Europaea, accessed on October 25, 2017 (English, with biographical and other information).
  11. ^ Abel Prize for Atiyah and Singer 2004
  12. ^ Abel Lecture by Atiyah, ICM 2018