Editing Michael Atiyah (section)

===Collaborations===
[[File:Mathematical Institute, University of Oxford.jpg|thumb|right|The old [[The Mathematical Institute, University of Oxford|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 [[Raoul Bott]] on the [[Atiyah–Bott fixed-point theorem]] and many other topics, with [[Isadore M. Singer]] on the [[Atiyah–Singer index theorem]], and with [[Friedrich Hirzebruch]] on topological K-theory,<ref>{{harvnb|Atiyah|2004|p=9}}</ref> all of whom he met at the [[Institute for Advanced Study]] in Princeton in 1955.<ref>{{harvnb|Atiyah|1988a|p=2}}</ref> His other collaborators included; [[J. Frank Adams]] ([[Hopf invariant]] problem), Jürgen Berndt (projective planes), Roger Bielawski (Berry–Robbins problem), Howard Donnelly ([[L-function]]s), [[Vladimir Drinfeld|Vladimir G. Drinfeld]] (instantons), Johan L. Dupont (singularities of [[vector field]]s), [[Lars Gårding]] ([[Hyperbolic partial differential equation|hyperbolic differential equation]]s), [[Nigel Hitchin|Nigel J. Hitchin]] (monopoles), [[William V. D. Hodge]] (Integrals of the second kind), [[Michael Hopkins (mathematician)|Michael Hopkins]] ([[K-theory]]), [[Lisa Jeffrey]] (topological Lagrangians), John D. S. Jones (Yang–Mills theory), [[Juan Maldacena]] (M-theory), [[Yuri I. Manin]] (instantons), [[Nick Manton|Nick S. Manton]] (Skyrmions), [[Vijay Kumar Patodi|Vijay K. Patodi]] (spectral asymmetry), A. N. Pressley (convexity), [[Elmer Rees]] (vector bundles), [[Wilfried Schmid]] (discrete series representations), [[Graeme Segal]] ([[K-theory|equivariant K-theory]]), Alexander Shapiro<ref>{{MathGenealogy|name=Alexander Shapiro|id=41807}}</ref> (Clifford algebras), L. Smith (homotopy groups of spheres), [[Paul Sutcliffe]] (polyhedra), [[David O. Tall]] (lambda rings), [[J. A. Todd|John A. Todd]] ([[Stiefel manifold]]s), [[Cumrun Vafa]] (M-theory), [[Richard S. Ward]] (instantons) and [[Edward Witten]] (M-theory, topological quantum field theories).<ref>{{harvnb|Atiyah|2004|pp=xi-xxv}}</ref>

His later research on [[gauge field theories]], particularly [[Yang–Mills]] theory, stimulated important interactions between [[geometry]] and [[theoretical physics|physics]], most notably in the work of Edward Witten.<ref>{{Cite web |url=http://www.sns.ias.edu/ckfinder/userfiles/files/ComemorativeLecturePopular%281%29.pdf |title=Edward Witten – Adventures in physics and math |access-date=30 October 2016 |archive-url=https://web.archive.org/web/20160823223743/http://www.sns.ias.edu/ckfinder/userfiles/files/ComemorativeLecturePopular(1).pdf |archive-date=23 August 2016 |url-status=live  }}</ref>

{{quote box
|align=right
|width=33%
|quote=If you attack a mathematical problem directly, very often you come to a dead end, nothing you do seems to work and you feel that if only you could peer round the corner there might be an easy solution. There is nothing like having somebody else beside you, because he can usually peer round the corner.
|source=Michael Atiyah<ref>{{harvnb|Atiyah|1988a|loc = paper 12, p. 233}}</ref>
}}
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,
[[Peter Kronheimer]] 1986,
[[Ruth Lawrence]] 1989,
[[George Lusztig]] 1971,
[[Jack Morava]] 1968,
Michael Murray 1983,
Peter Newstead 1966,
[[Ian R. Porteous]] 1961,
[[John Roe (mathematician)|John Roe]] 1985,
Brian Sanderson	1963,
[[Rolph Ludwig Edward Schwarzenberger|Rolph Schwarzenberger]] 1960,
Graeme Segal 1967,
David Tall 1966,
and Graham White 1982.<ref name="genealogy"/>

Other contemporary mathematicians who influenced Atiyah include [[Roger Penrose]], [[Lars Hörmander]], [[Alain Connes]] and [[Jean-Michel Bismut]].<ref>{{harvnb|Atiyah|2004|p=10}}</ref> Atiyah said that the mathematician he most admired was [[Hermann Weyl]],<ref>{{harvnb|Atiyah|1988a|p=307}}</ref> and that his favourite mathematicians from before the 20th century were [[Bernhard Riemann]] and [[William Rowan Hamilton]].<ref>{{citation |url= http://www.superstringtheory.com/people/atiyah.html |title= Interview with Michael Atiyah |publisher= superstringtheory.com |access-date= 14 August 2008 |archive-url= https://web.archive.org/web/20080914135040/http://www.superstringtheory.com/people/atiyah.html |archive-date= 14 September 2008 |url-status= live }}</ref>

The seven volumes of Atiyah's collected papers include most of his work, except for his commutative algebra textbook;<ref>{{harvnb|Atiyah|Macdonald|1969}}</ref> the first five volumes are divided thematically and the sixth and seventh arranged by date.