Michael Atiyah

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HonFREng
Michael Atiyah in 2007
Born	Michael Francis Atiyah (1929-04-22)22 April 1929 Hampstead , London, England
Died	11 January 2019(2019-01-11) (aged 89) Edinburgh, Scotland
Education	PhD )
Known for	Atiyah algebroid Atiyah conjecture Atiyah conjecture on configurations Atiyah flop Atiyah–Bott formula Atiyah–Bott fixed-point theorem Atiyah–Floer conjecture Atiyah–Hirzebruch spectral sequence Atiyah–Jones conjecture Atiyah–Hitchin–Singer theorem Atiyah–Singer index theorem Atiyah–Segal completion theorem ADHM construction Fredholm module Eta invariant K-theory KR-theory Pin group Toric manifold
Awards	Berwick Prize (1961) Fields Medal (1966) Royal Medal (1968) De Morgan Medal (1980) Copley Medal (1988) Abel Prize (2004)
Scientific career
Fields	Mathematics
Institutions	University of Oxford Institute for Advanced Study University of Leicester University of Edinburgh University of Cambridge
Thesis	Some Applications of Topological Methods in Algebraic Geometry (1955)
Doctoral advisor	W. V. D. Hodge[1][2]
Doctoral students	Simon Donaldson K. David Elworthy Nigel Hitchin[3] Lisa Jeffrey Frances Kirwan Peter Kronheimer Ruth Lawrence George Lusztig Ian R. Porteous Graeme Segal David O. Tall[2]
Other notable students	Edward Witten

Sir Michael Francis Atiyah

in 2004.

Early life and education

Master

Atiyah was born on 22 April 1929 in

Atiyah was a member of the

During his time at Cambridge, he was president of The Archimedeans.^[11]

Career and research

Atiyah spent the academic year 1955–1956 at the

Atiyah was president of the

Within the United Kingdom, he was involved in the creation of the

Atiyah's mathematical collaborators included Raoul Bott, Friedrich Hirzebruch^[17] and Isadore Singer, and his students included Graeme Segal, Nigel Hitchin, Simon Donaldson, and Edward Witten.^[18] Together with Hirzebruch, he laid the foundations for topological K-theory, an important tool in algebraic topology, which, informally speaking, describes ways in which spaces can be twisted. His best known result, the Atiyah–Singer index theorem, was proved with Singer in 1963 and is used in counting the number of independent solutions to differential equations. Some of his more recent work was inspired by theoretical physics, in particular instantons and monopoles, which are responsible for some corrections in quantum field theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.

Collaborations

Mathematical Institute (now the Department of Statistics) in Oxford

, where Atiyah supervised many of his students

Atiyah collaborated with many mathematicians. His three main collaborations were with

His later research on

Atiyah's students included Peter Braam 1987, Simon Donaldson 1983, K. David Elworthy 1967, Howard Fegan 1977, Eric Grunwald 1977, Nigel Hitchin 1972, Lisa Jeffrey 1991, Frances Kirwan 1984,

1986, Ruth Lawrence 1989, George Lusztig 1971, Jack Morava 1968, Michael Murray 1983, Peter Newstead 1966, Ian R. Porteous 1961, John Roe 1985, Brian Sanderson 1963, Rolph Schwarzenberger 1960, Graeme Segal 1967, David Tall 1966, and Graham White 1982.^[2]

Other contemporary mathematicians who influenced Atiyah include Roger Penrose, Lars Hörmander, Alain Connes and Jean-Michel Bismut.^[25] Atiyah said that the mathematician he most admired was Hermann Weyl,^[26] and that his favourite mathematicians from before the 20th century were Bernhard Riemann and William Rowan Hamilton.^[27]

The seven volumes of Atiyah's collected papers include most of his work, except for his commutative algebra textbook;^[28] the first five volumes are divided thematically and the sixth and seventh arranged by date.

Algebraic geometry (1952–1958)

twisted cubic curve

, the subject of Atiyah's first paper

Atiyah's early papers on algebraic geometry (and some general papers) are reprinted in the first volume of his collected works.^[29]

As an undergraduate Atiyah was interested in classical projective geometry, and wrote his first paper: a short note on

His PhD thesis with Hodge was on a sheaf-theoretic approach to

K-theory (1959–1974)

Möbius band is the simplest non-trivial example of a vector bundle

.

Atiyah's works on K-theory, including his book on K-theory^[39] are reprinted in volume 2 of his collected works.^[40]

The simplest nontrivial example of a vector bundle is the

Topological K-theory was discovered by Atiyah and

generalized cohomology theory

.

Several results showed that the newly introduced K-theory was in some ways more powerful than ordinary cohomology theory. Atiyah and Todd

also proved analogues of the result at odd primes.

The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory.^[43] (Atiyah and Hirzebruch used the case of K-theory, but their method works for all cohomology theories).

Atiyah showed

:

${\displaystyle K(BG)\cong R(G)^{\wedge }.}$

The same year

isomorphic

to the ordinary K-theory of a space, ${\displaystyle X_{G}}$, which fibred over BG with fibre X:

${\displaystyle K_{G}(X)^{\wedge }\cong K(X_{G}).}$

The original result then followed as a corollary by taking X to be a point: the left hand side reduced to the completion of R(G) and the right to K(BG). See Atiyah–Segal completion theorem for more details.

He defined new generalized homology and cohomology theories called bordism and cobordism, and pointed out that many of the deep results on cobordism of manifolds found by René Thom, C. T. C. Wall, and others could be naturally reinterpreted as statements about these cohomology theories.^[51] Some of these cohomology theories, in particular complex cobordism, turned out to be some of the most powerful cohomology theories known.

He introduced

.

With Hirzebruch he extended the Grothendieck–Riemann–Roch theorem to complex analytic embeddings,^[53] and in a related paper^[54] they showed that the Hodge conjecture for integral cohomology is false. The Hodge conjecture for rational cohomology is, as of 2008, a major unsolved problem.^[55]

The

Index theory (1963–1984)

Atiyah's work on index theory is reprinted in volumes 3 and 4 of his collected works.^[61][62]

The index of a differential operator is closely related to the number of independent solutions (more precisely, it is the differences of the numbers of independent solutions of the differential operator and its adjoint). There are many hard and fundamental problems in mathematics that can easily be reduced to the problem of finding the number of independent solutions of some differential operator, so if one has some means of finding the index of a differential operator these problems can often be solved. This is what the Atiyah–Singer index theorem does: it gives a formula for the index of certain differential operators, in terms of topological invariants that look quite complicated but are in practice usually straightforward to calculate.^{[citation needed]}

Several deep theorems, such as the

]

The index problem for

(which was rediscovered by Atiyah and Singer in 1961).

The first announcement of the Atiyah–Singer theorem was their 1963 paper.[65] The proof sketched in this announcement was inspired by Hirzebruch's proof of the Hirzebruch–Riemann–Roch theorem and was never published by them, though it is described in the book by Palais.^[66] Their first published proof^[67] was more similar to Grothendieck's proof of the Grothendieck–Riemann–Roch theorem, replacing the cobordism theory of the first proof with K-theory, and they used this approach to give proofs of various generalizations in a sequence of papers from 1968 to 1971.

Instead of just one elliptic operator, one can consider a family of elliptic operators parameterized by some space Y. In this case the index is an element of the K theory of Y, rather than an integer.

With Bott, Atiyah found an analogue of the

Atiyah and Segal combined this fixed point theorem with the index theorem as follows. If there is a compact . For trivial groups G this gives the index theorem, and for a finite group G acting with isolated fixed points it gives the Atiyah–Bott fixed point theorem. In general it gives the index as a sum over fixed point submanifolds of the group G.[72]

Atiyah

As an application of the equivariant index theorem, Atiyah and Hirzebruch showed that manifolds with effective circle actions have vanishing

(Lichnerowicz showed that if a manifold has a metric of positive scalar curvature then the Â-genus vanishes.)

With Elmer Rees, Atiyah studied the problem of the relation between topological and holomorphic vector bundles on projective space. They solved the simplest unknown case, by showing that all rank 2 vector bundles over projective 3-space have a holomorphic structure.^[76] Horrocks had previously found some non-trivial examples of such vector bundles, which were later used by Atiyah in his study of instantons on the 4-sphere.

Atiyah, Bott and Vijay K. Patodi^[77] gave a new proof of the index theorem using the heat equation.

If the

, in particular in Witten's work on anomalies.

The fundamental solutions of linear

, who found topological conditions describing which regions were lacunas. In collaboration with Bott and Lars Gårding, Atiyah wrote three papers updating and generalizing Petrovsky's work.^[79]

Atiyah

With H. Donnelly and I. Singer, he extended Hirzebruch's formula (relating the signature defect at cusps of Hilbert modular surfaces to values of L-functions) from real quadratic fields to all totally real fields.[83]

Gauge theory (1977–1985)

Many of his papers on gauge theory and related topics are reprinted in volume 5 of his collected works.

, 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.

In a series of papers with several authors, Atiyah classified all instantons on 4-dimensional Euclidean space. It is more convenient to classify instantons on a sphere as this is compact, and this is essentially equivalent to classifying instantons on Euclidean space as this is conformally equivalent to a sphere and the equations for instantons are conformally invariant. With Hitchin and Singer

invariants of 4-manifolds

. Atiyah and Ward used the Penrose correspondence to reduce the classification of all instantons on the 4-sphere to a problem in algebraic geometry.[86] With Hitchin he used ideas of Horrocks to solve this problem, giving the ADHM construction of all instantons on a sphere; Manin and Drinfeld found the same construction at the same time, leading to a joint paper by all four authors.^[87] Atiyah reformulated this construction using quaternions and wrote up a leisurely account of this classification of instantons on Euclidean space as a book.^[88]

Atiyah's work on instanton moduli spaces was used in Donaldson's work on

Green's functions for linear partial differential equations can often be found by using the Fourier transform to convert this into an algebraic problem. Atiyah used a non-linear version of this idea.^[91] He 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. This allowed him to find an explicit formula for the conformally invariant Green's function on a 4-manifold.

In his paper with Jones,

Harder and M. S. Narasimhan described the cohomology of the moduli spaces of stable vector bundles over Riemann surfaces by counting the number of points of the moduli spaces over finite fields, and then using the Weil conjectures to recover the cohomology over the complex numbers.^[94] Atiyah and

An old result due to Schur and Horn states that the set of possible diagonal vectors of an Hermitian matrix with given eigenvalues is the convex hull of all the permutations of the eigenvalues. 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,^[96] and with Pressley gave a related generalization to infinite-dimensional loop groups.^[97]

Duistermaat and Heckman found a striking formula, saying that the push-forward of the

With Hitchin he worked on

Atiyah showed[104] that instantons in 4 dimensions can be identified with instantons in 2 dimensions, which are much easier to handle. There is of course a catch: in going from 4 to 2 dimensions the structure group of the gauge theory changes from a finite-dimensional group to an infinite-dimensional loop group. This gives another example where the moduli spaces of solutions of two apparently unrelated nonlinear partial differential equations turn out to be essentially the same.

Atiyah and Singer found that anomalies in quantum field theory could be interpreted in terms of index theory of the Dirac operator;^[105] this idea later became widely used by physicists.

Later work (1986–2019)

topological quantum field theories

was influenced by Atiyah

Many of the papers in the 6th volume^[106] of his collected works are surveys, obituaries, and general talks. Atiyah continued to publish subsequently, including several surveys, a popular book,^[107] and another paper with Segal on twisted K-theory.

One paper^[108] is a detailed study of the Dedekind eta function from the point of view of topology and the index theorem.

Several of his papers from around this time study the connections between

.

He studied

.

Several papers

.

With

. These papers seem to be the first time that Atiyah worked on exceptional Lie groups.

In his papers with M. Hopkins^[117] and G. Segal^[118] he returned to his earlier interest of K-theory, describing some twisted forms of K-theory with applications in theoretical physics.

In October 2016, he claimed^[119] a short proof of the non-existence of complex structures on the 6-sphere. His proof, like many predecessors, is considered flawed by the mathematical community, even after the proof was rewritten in a revised form.^[120][121]

At the 2018 Heidelberg Laureate Forum, he claimed to have solved the Riemann hypothesis, Hilbert's eighth problem, by contradiction using the fine-structure constant. Again, the proof did not hold up and the hypothesis remains one of the six unsolved Millennium Prize Problems in mathematics, as of 2024.^[122][123]

Bibliography

Books

This subsection lists all books written by Atiyah; it omits a few books that he edited.

Selected papers

Awards and honours

In 1966, when he was thirty-seven years old, he was awarded the Fields Medal,^[124] for his work in developing K-theory, a generalized Lefschetz fixed-point theorem and the Atiyah–Singer theorem, for which he also won the Abel Prize jointly with Isadore Singer in 2004.^[125] Among other prizes he has received are the

Benjamin Franklin Medal for Distinguished Achievement in the Sciences of the American Philosophical Society in 1993,^[129]

the Jawaharlal Nehru Birth Centenary Medal of the Indian National Science Academy in 1993,^[130] the President's Medal from the Institute of Physics in 2008,^[131] the Grande Médaille of the French Academy of Sciences in 2010^[132] and the Grand Officier of the French Légion d'honneur in 2011.^[133]

He was elected a foreign member of the

Royal Spanish Academy of Science, the Accademia dei Lincei and the Moscow Mathematical Society.^[9][13] In 2012, he became a fellow of the American Mathematical Society.^[135] He was also appointed as a Honorary Fellow^[4] of the Royal Academy of Engineering^[4]

in 1993.

Atiyah was awarded honorary degrees by the universities of Birmingham, Bonn, Chicago, Cambridge, Dublin, Durham, Edinburgh, Essex, Ghent, Helsinki, Lebanon, Leicester, London, Mexico, Montreal, Oxford, Reading, Salamanca, St. Andrews, Sussex, Wales, Warwick, the American University of Beirut, Brown University, Charles University in Prague, Harvard University, Heriot–Watt University, Hong Kong (Chinese University), Keele University, Queen's University (Canada), The Open University, University of Waterloo, Wilfrid Laurier University, Technical University of Catalonia, and UMIST.[9]^{[13][136][137]}

Atiyah was made a

Order of Merit in 1992.^[13]

The Michael Atiyah building[138] at the University of Leicester and the Michael Atiyah Chair in Mathematical Sciences^[139] at the American University of Beirut were named after him.

Personal life

Atiyah married Lily Brown on 30 July 1955, with whom he had three sons, John, David and Robin. Atiyah's eldest son John died on 24 June 2002 while on a walking holiday in the Pyrenees with his wife Maj-Lis.

Lily Atiyah died on 13 March 2018 at the age of 90^[5][7][9] while Sir Michael Atiyah died less than a year later on 11 January 2019, aged 89.^[140][141]

See also

• List of presidents of the Royal Society

References

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2. ^ ^{a b c d e} Michael Atiyah at the Mathematics Genealogy Project
3. EThOS uk.bl.ethos.459281
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4. ^ ^{a b c} "List of Fellows". Archived from the original on 8 June 2016. Retrieved 28 October 2014.
5. ^ ^{a b} O'Connor, John J.; Robertson, Edmund F., "Michael Atiyah", MacTutor History of Mathematics Archive, University of St Andrews
6. ^ "ATIYAH, Sir Michael (Francis)". Who's Who. Vol. 2014 (online edition via Oxford University Press ed.). A & C Black. (Subscription or UK public library membership required.)
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8. ^ Raafat, Samir, Victoria College: educating the elite, 1902−1956, archived from the original on 16 April 2008, retrieved 14 August 2008
9. ^ ^{a b c d e f g} Atiyah 1988a, p. xi
10. ^ "Distinguished mathematician and supporter of Humanism."
11. ^ "[Presidents Archimedeans]". Archimedeans: Previous Committees and Officers. Retrieved 10 April 2019.
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26. ^ Atiyah 1988a, p. 307
27. ^ Interview with Michael Atiyah, superstringtheory.com, archived from the original on 14 September 2008, retrieved 14 August 2008
28. ^ Atiyah & Macdonald 1969
29. ^ Atiyah 1988a
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31. ^ Atiyah 1988a, paper 2
32. ^ Atiyah 1988a, p. 1
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36. ^ Atiyah 1988a, paper 8
37. ^ Matsuki 2002.
38. ^ Barth et al. 2004
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41. arXiv:math/0012213
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44. ^ Atiyah 1988b, paper 26
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47. ^ Atiyah 1961
48. ^ Atiyah & Hirzebruch 1961
49. ^ Segal 1968
50. ^ Atiyah & Segal 1969
51. ^ Atiyah 1988b, paper 34
52. ^ Atiyah 2004, paper 160, p. 7
53. ^ ^{a b} Atiyah 1988b, paper 37
54. ^ Atiyah 1988b, paper 36
55. ^ Deligne, Pierre, The Hodge conjecture (PDF), The Clay Math Institute, archived from the original (PDF) on 27 August 2008, retrieved 14 August 2008
56. ^ Atiyah 1988b, paper 40
57. ^ Atiyah 1988b, paper 45
58. ^ Atiyah 1988b, paper 39
59. ^ Atiyah 1988b, paper 46
60. ^ Atiyah 1988b, paper 48
61. ^ Atiyah 1988c
62. ^ Atiyah 1988d
63. ^ Atiyah 1988a, paper 17, p. 76
64. ^ Gel'fand 1960
65. ^ Atiyah & Singer 1963
66. ^ Palais 1965
67. ^ Atiyah & Singer 1968a
68. ^ Atiyah 1988c, paper 67
69. ^ Atiyah 1988c, paper 68
70. ^ Atiyah 1988c, papers 61, 62, 63
71. ^ Atiyah 1988c, p. 3
72. ^ Atiyah 1988c, paper 65
73. ^ Atiyah 1988c, paper 73
74. ^ Atiyah 1988a, paper 15
75. ^ Atiyah 1988c, paper 74
76. ^ Atiyah 1988c, paper 76
77. ^ Atiyah, Bott & Patodi 1973
78. ^ Atiyah 1988d, papers 80–83
79. ^ Atiyah 1988d, papers 84, 85, 86
80. ^ Atiyah 1976
81. ^ Atiyah & Schmid 1977
82. ^ Atiyah 1988d, paper 91
83. ^ Atiyah 1988d, papers 92, 93
84. ^ Atiyah 1988e.
85. ^ Atiyah 1988e, papers 94, 97
86. ^ Atiyah 1988e, paper 95
87. ^ Atiyah 1988e, paper 96
88. ^ Atiyah 1988e, paper 99
89. ^ Atiyah 1988a, paper 19, p. 13
90. ^ Atiyah 1988e, paper 112
91. ^ Atiyah 1988e, paper 101
92. ^ Atiyah 1988e, paper 102
93. ^ Boyer et al. 1993
94. ^ Harder & Narasimhan 1975
95. ^ Atiyah 1988e, papers 104–105
96. ^ Atiyah 1988e, paper 106
97. ^ Atiyah 1988e, paper 108
98. ^ Atiyah 1988e, paper 109
99. ^ Atiyah 1988e, paper 110
100. ^ Atiyah 1988e, paper 124
101. ^ Atiyah 1988e, papers 115, 116
102. ^ Atiyah & Hitchin 1988
103. ^ Atiyah 1988e, paper 118
104. ^ Atiyah 1988e, paper 117
105. ^ Atiyah 1988e, papers 119, 120, 121
106. ^ Michael Atiyah 2004
107. ^ Atiyah 2007
108. ^ Atiyah 2004, paper 127
109. ^ Atiyah 2004, paper 132
110. ^ Atiyah 1990
111. ^ Atiyah 2004, paper 139
112. ^ Atiyah 2004, papers 141, 142
113. ^ Atiyah 2004, papers 163, 164, 165, 166, 167, 168
114. ^ Atiyah 1988a, paper 19, p. 19
115. ^ Atiyah 2004, paper 169
116. ^ Atiyah 2004, paper 170
117. ^ Atiyah 2004, paper 172
118. ^ Atiyah 2004, paper 173
119. arXiv:1610.09366 [math.DG
     ].
120. ^ What is the current understanding regarding complex structures on the 6-sphere? (MathOverflow), retrieved 24 September 2018
121. ^ Atiyah's May 2018 paper on the 6-sphere (MathOverflow), retrieved 24 September 2018
122. ^ "Skepticism surrounds renowned mathematician's attempted proof of 160-year-old hypothesis". Science | AAAS. 24 September 2018. Archived from the original on 26 September 2018. Retrieved 26 September 2018.
123. ^ "Riemann hypothesis likely remains unsolved despite claimed proof". Archived from the original on 24 September 2018. Retrieved 24 September 2018.
124. ^ Fields medal citation: Cartan, Henri (1968), "L'oeuvre de Michael F. Atiyah", Proceedings of International Conference of Mathematicians (Moscow, 1966), Izdatyel'stvo Mir, Moscow, pp. 9–14
125. ^ "2004: Sir Michael Francis Atiyah and Isadore M. Singer". www.abelprize.no. Retrieved 22 August 2022.
126. ^ Royal archive winners 1989–1950, archived from the original on 9 June 2008, retrieved 14 August 2008
127. ^ Sir Michael Atiyah FRS, Newton institute, archived from the original on 31 May 2008, retrieved 14 August 2008
128. ^ Copley archive winners 1989–1900, archived from the original on 9 June 2008, retrieved 14 August 2008
129. ^ "Benjamin Franklin Medal for Distinguished Achievement in the Sciences Recipients". American Philosophical Society. Archived from the original on 24 September 2012. Retrieved 27 November 2011.
130. ^ Jawaharlal Nehru Birth Centenary Medal, archived from the original on 10 July 2012, retrieved 14 August 2008
131. ^ 2008 President's medal, retrieved 14 August 2008
132. ^ La Grande Medaille, archived from the original on 1 August 2010, retrieved 25 January 2011
133. ^ Legion d'honneur, archived from the original on 24 September 2011, retrieved 11 September 2011
134. ^ "Book of Members, 1780-2010: Chapter A" (PDF). American Academy of Arts and Sciences. Archived (PDF) from the original on 10 May 2011. Retrieved 27 April 2011.
135. ^ List of Fellows of the American Mathematical Society Archived 5 August 2013 at the Wayback Machine, retrieved 3 November 2012.
136. ^ "Heriot-Watt University Edinburgh: Honorary Graduates". www1.hw.ac.uk. Archived from the original on 18 April 2016. Retrieved 4 April 2016.
137. ^ Honorary Doctorates, Charles University in Prague, retrieved 4 May 2018
138. ^ The Michael Atiyah building, archived from the original on 9 February 2009, retrieved 14 August 2008
139. ^ American University of Beirut establishes the Michael Atiyah Chair in Mathematical Sciences, archived from the original on 3 April 2008, retrieved 14 August 2008
140. ^ "Michael Atiyah 1929-2019". University of Oxford Mathematical Institute. 11 January 2019. Archived from the original on 11 January 2019. Retrieved 11 January 2019.
141. ^ "A tribute to former President of the Royal Society Sir Michael Atiyah OM FRS (1929 - 2019)". The Royal Society. 11 January 2019. Archived from the original on 11 January 2019. Retrieved 11 January 2019.

Sources

• Boyer, Charles P.;
  MR 1217348
• Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004), Compact Complex Surfaces, Berlin: Springer, p. 334,
  ISBN 978-3-540-00832-3
• Gel'fand, Israel M. (1960), "On elliptic equations", Russ. Math. Surv., 15 (3): 113–123,
  ISBN 0-387-13619-3
  . On page 120 Gel'fand suggests that the index of an elliptic operator should be expressible in terms of topological data.
• Harder, G.; Narasimhan, M. S. (1975), "On the cohomology groups of moduli spaces of vector bundles on curves",
  S2CID 117851906, archived from the original
  on 5 March 2016, retrieved 30 September 2013
• Matsuki, Kenji (2002), Introduction to the Mori program, Universitext, Berlin, New York:
  MR 1875410
• Palais, Richard S. (1965), Seminar on the Atiyah–Singer Index Theorem, Annals of Mathematics Studies, vol. 57, S.l.: Princeton Univ Press,
  ISBN 978-0-691-08031-4
  . This describes the original proof of the index theorem. (Atiyah and Singer never published their original proof themselves, but only improved versions of it.)
• S2CID 55847918
  .
• Yau, Shing-Tung; Chan, Raymond H., eds. (1999), "Sir Michael Atiyah: a great mathematician of the twentieth century", Asian J. Math., 3 (1), International Press: 1–332,
  MR 1701915, archived from the original
  on 8 August 2008.
• Yau, Shing-Tung, ed. (2005), The Founders of Index Theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer, International Press, p. 358,
  ISBN 978-1-57146-120-9, archived from the original
  on 7 February 2006.

External links

• Michael Atiyah tells his life story at Web of Stories
• The celebrations of Michael Atiyah's 80th birthday in Edinburgh, 20-24 April 2009
• Mathematical descendants of Michael Atiyah
• "Sir Michael Atiyah on math, physics and fun", superstringtheory.com, Official Superstring theory web site], retrieved 14 August 2008
• Atiyah, Michael, Beauty in Mathematics (video, 3m14s), retrieved 14 August 2008
• Atiyah, Michael, The nature of space (Online lecture), retrieved 14 August 2008
• Batra, Amba (8 November 2003), Maths guru with Einstein's dream prefers chalk to mouse. (Interview with Atiyah.), Delhi newsline, archived from the original on 8 February 2009, retrieved 14 August 2008
• Michael Atiyah at the Mathematics Genealogy Project
• Halim, Hala (1998), "Michael Atiyah:Euclid and Victoria", Al-Ahram Weekly On-line, no. 391, archived from the original on 16 August 2004, retrieved 26 August 2008
• Meek, James (21 April 2004), "Interview with Michael Atiyah", The Guardian, London, retrieved 14 August 2008
• Sir Michael Atiyah FRS, Isaac Newton Institute, retrieved 14 August 2008
• "Atiyah and Singer receive 2004 Abel prize" (PDF), Notices of the American Mathematical Society, 51 (6): 650–651, 2006, retrieved 14 August 2008
• Raussen, Martin; Skau, Christian (24 May 2004), Interview with Michael Atiyah and Isadore Singer, retrieved 14 August 2008
• Photos of Michael Francis Atiyah, Oberwolfach photo collection, retrieved 14 August 2008
• Wade, Mike (21 April 2009), Maths and the bomb: Sir Michael Atiyah at 80, London: Timesonline, retrieved 12 May 2010
• List of works of Michael Atiyah from
  Celebratio Mathematica
• Connes, Alain; Kouneiher, Joseph (2019). "Sir Michael Atiyah, a Knight Mathematician : A tribute to Michael Atiyah, an inspiration and a friend". Notices of the American Mathematical Society. 66 (10): 1660–1685.
  S2CID 204743755
  .
• Portraits of Michael Atiyah at the National Portrait Gallery, London

Professional and academic associations
Preceded by George Porter	57th President of the Royal Society 1990–1995	Succeeded by Sir Aaron Klug
Preceded by Lord Sutherland of Houndwood	42nd President of the Royal Society of Edinburgh 2005–2008	Succeeded by David Wilson, Baron Wilson of Tillyorn
Academic offices
Preceded by Sir Andrew Huxley	35th Master of Trinity College, Cambridge 1990–1997	Succeeded by Amartya Sen
Preceded by The Lord Porter of Luddenham	4th Chancellor of the University of Leicester 1995–2005	Succeeded by Sir Peter Williams
Awards and achievements
Preceded by Robin Hill	Copley Medal 1988	Succeeded by César Milstein