# Michael Atiyah

#218

Most Influential Person Now

British mathematician

## Michael Atiyah's AcademicInfluence.com Rankings

Michael Atiyahmathematics Degrees

Mathematics

#9

World Rank

#53

Historical Rank

Algebraic Geometry

#8

World Rank

#9

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Topology

#5

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#10

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Measure Theory

#63

World Rank

#105

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Mathematics

## Why Is Michael Atiyah Influential?

(Suggest an Edit or Addition)According to Wikipedia, Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.

## Michael Atiyah's Published Works

### Published Works

- Introduction to commutative algebra (1969) (4267)
- The Yang-Mills equations over Riemann surfaces (1983) (2150)
- Spectral asymmetry and Riemannian Geometry. I (1973) (1897)
- Self-duality in four-dimensional Riemannian geometry (1978) (1477)
- Construction of Instantons (1978) (1325)
- The moment map and equivariant cohomology (1984) (1191)
- Vector Bundles Over an Elliptic Curve (1957) (951)
- Convexity and Commuting Hamiltonians (1982) (945)
- The Index of elliptic operators. 3. (1968) (937)
- The Index of Elliptic Operators: IV (1971) (907)
- The Index of elliptic operators. 1 (1968) (898)
- Complex analytic connections in fibre bundles (1957) (897)
- The Geometry and Dynamics of Magnetic Monopoles (1988) (877)
- A Lefschetz Fixed Point Formula for Elliptic Complexes: I (1967) (643)
- On the heat equation and the index theorem (1973) (634)
- Vector bundles and homogeneous spaces (1961) (589)
- Elliptic operators, discrete groups and von Neumann algebras (1976) (574)
- The index of elliptic operators on compact manifolds (1963) (573)
- THE INDEX OF ELLIPTIC OPERATORS (1997) (573)
- Seminar on the Atiyah-Singer Index Theorem. (1968) (541)
- The Index of Elliptic Operators: II (1968) (492)
- Spectral asymmetry and Riemannian geometry. II (1975) (476)
- A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications (1968) (444)
- Topological quantum field theories (1988) (424)
- Instantons and algebraic geometry (1977) (422)
- Equivariant $K$-theory and completion (1969) (416)
- M-Theory Dynamics On A Manifold Of G_2 Holonomy (2001) (395)
- K -THEORY AND REALITY (1966) (381)
- Characters and cohomology of finite groups (1961) (379)
- Dirac operators coupled to vector potentials. (1984) (353)
- Riemann surfaces and spin structures (1971) (352)
- Resolution of Singularities and Division of Distributions (1970) (347)
- Index theory for skew-adjoint fredholm operators (1969) (333)
- The Index of elliptic operators. 5. (1971) (329)
- Elliptic operators and compact groups (1974) (320)
- Twisted K-theory (2004) (292)
- Lacunas for hyperbolic differential operators with constant coefficients I (1970) (267)
- Spectral asymmetry and Riemannian geometry. III (1976) (266)
- An M theory flop as a large N duality (2000) (248)
- On the Krull-Schmidt theorem with application to sheaves (1956) (242)
- BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS (1968) (236)
- Spin-manifolds and group actions (1970) (225)
- The Geometry and Physics of Knots (1990) (213)
- Group representations, λ-rings and the J-homomorphism (1969) (207)
- Topological aspects of Yang-Mills theory (1978) (206)
- Low energy scattering of non-Abelian monopoles (1985) (206)
- Skyrmions from instantons (1989) (202)
- Analytic cycles on complex manifolds (1962) (202)
- The geometry and physics of knots: Frontmatter (1990) (202)
- Riemann-Roch theorems for differentiable manifolds (1959) (201)
- Mathematics: Frontiers and Perspectives (2000) (187)
- The experience of mathematical beauty and its neural correlates (2014) (168)
- A geometric construction of the discrete series for semisimple Lie groups (1977) (156)
- POWER OPERATIONS IN K -THEORY (1966) (151)
- On framings of 3-manifolds (1990) (149)
- On equivariant Euler characteristics (1989) (148)
- Instantons in two and four dimensions (1984) (144)
- On analytic surfaces with double points (1958) (143)
- Topological Lagrangians and cohomology (1990) (142)
- The logarithm of the dedekind η-function (1987) (138)
- Twisted K-theory and cohomology (2005) (127)
- Sir Michael Atiyah : a great mathematician of the twentieth century (1999) (125)
- The Index Problem for Manifolds with Boundary (1994) (123)
- Bordism and Cobordism (1961) (115)
- SYMMETRIES OF ISLAMIC GEOMETRICAL PATTERNS (1994) (113)
- On the heat equation and the index theorem (1973) (112)
- Lie theory and geometry : in honor of Bertram Kostant (1997) (111)
- Circular symmetry and stationary phase approximation (1981) (110)
- New invariants of 3 and 4 dimensional manifolds (1987) (105)
- A geometric construction of the discrete series for semisimple Lie groups (1977) (95)
- Vector Fields on Manifolds (2013) (93)
- K -THEORY AND THE HOPF INVARIANT (1966) (93)
- Vector bundles and the Künneth formula (1962) (90)
- On the periodicity theorem for complex vector bundles (1964) (89)
- A Lefschetz fixed point formula for elliptic differential operators (1966) (85)
- Geometry and kinematics of two Skyrmions (1993) (85)
- Deformations of instantons. (1977) (85)
- THE GEOMETRY AND DYNAMICS OF MAGNETIC MONOPOLES. M.B. PORTER LECTURES (1988) (82)
- Geometry and physics (1996) (81)
- Angular momentum, convex Polyhedra and Algebraic Geometry (1983) (81)
- Polyhedra in Physics, Chemistry and Geometry (2003) (79)
- Introduction to the Problem of Minimal Models in the Theory of Algebraic Surfaces (1960) (79)
- Eta invariants, signature defects of cusps, and values of L-functions (1983) (78)
- Complex Fibre Bundles and Ruled Surfaces (1955) (76)
- The geometry of point particles (2001) (73)
- Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (73)
- Integrals of the Second Kind on an Algebraic Variety (1955) (71)
- Notes on the Lefschetz fixed point theorem for elliptic complexes (1964) (70)
- The Riemann–Roch theorem for analytic embeddings (1962) (66)
- Twistor theory at fifty: from contour integrals to twistor strings (2017) (65)
- Mathematics in the 20th century (2001) (61)
- Low-energy scattering of non-Abelian magnetic monopoles (1985) (60)
- Vector bundles on projective 3-space (1976) (58)
- The Nature of Mathematical Proof (2005) (57)
- Vector fields with finite singularities (1972) (56)
- What is supersymmetry? (1986) (53)
- The signature of fibre-bundles (2015) (53)
- Curvature, cones and characteristic numbers (2012) (52)
- Immersions and embeddings of manifolds (1962) (50)
- The Unity of Mathematics (1978) (46)
- Geometric models of matter (2011) (44)
- Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (43)
- On the K-theory of compact lie groups (1965) (42)
- Compact lie groups and the stable homotopy of spheres (1974) (42)
- Representation Theory of Lie Groups (1980) (41)
- Projective planes, Severi varieties and spheres (2002) (41)
- Convexity and Loop Groups (1983) (41)
- Eigenvalues of the dirac operator (1985) (41)
- Algebraic topology and operators in Hilbert space (1969) (41)
- Configurations of points (2001) (39)
- On complex Stiefel manifolds (1960) (38)
- Mathematics for physics (1983) (37)
- The Art of Mathematics (2009) (36)
- Bott Periodicity and the Parallelizability of the spheres (1961) (35)
- The geometry of classical particles (2002) (34)
- Quantum theory and geometry (1995) (34)
- Nahm’s equations, configuration spaces and flag manifolds (2001) (34)
- K-Theory Past and Present (2000) (33)
- Skyrmions, instantons, mass and curvature (2004) (30)
- Special Article Mathematics in the 20th Century (2002) (30)
- Lacunas for hyperbolic differential operators with constant coefficients. II (1973) (29)
- Idempotency: List of Participants (1998) (29)
- Bakerian Lecture, 1975: Global geometry (1976) (28)
- A Variant of K-theory: K_{+-} (2003) (23)
- NEW INVARIANTS OF THREE-DIMENSIONAL AND FOUR-DIMENSIONAL MANIFOLDS (1987) (22)
- EXPONENTIAL ISOMORPHISMS FOR λ-RINGS (1971) (19)
- Pulling the strings (2005) (18)
- MAGNETIC MONOPOLES AND THE YANG-BAXTER EQUATIONS (1991) (18)
- DUALITY IN MATHEMATICS AND PHYSICS (2008) (17)
- Fields Medallists' Lectures (1997) (17)
- Topological quantum field theory (2003) (17)
- Topological quantum field theory (2003) (17)
- An interview with Michael Atiyah (1984) (14)
- Algebraic topology and elliptic operators (2010) (14)
- Complex geometry of nuclei and atoms (2016) (14)
- The Jones-Witten invariants of knots (1990) (14)
- Yang-Mills and bundles over algebraic curves (1981) (13)
- Time evolution in a geometric model of a particle (2014) (13)
- Paul Dirac: The Man and his Work (1998) (12)
- A Shifted View of Fundamental Physics (2010) (12)
- How research is carried out (1974) (12)
- Quantum physics and the topology of knots (1995) (12)
- Paul Dirac: The Dirac equation and geometry (1998) (12)
- Geometric Models of Helium (2017) (11)
- Anomalies and index theory (1984) (10)
- Invariant differential operators and eigenspace representations (1980) (9)
- The Non-Existent Complex 6-Sphere (2016) (9)
- Surveys in Differential Geometry VIII, Papers in Honor of Calabi, Lawson, Siu and Uhlenbeck (2003) (9)
- A survey of K-theory (1977) (8)
- Signature defects of cusps and values of L-functions (1984) (8)
- Maslov optimization theory: topological aspect (1998) (8)
- X-THEORY AND REALITY (1966) (8)
- The Encoding of Temporally Irregular and Regular Visual Patterns in the Human Brain (2008) (8)
- Quantum field theory and low dimensional geometry (1990) (7)
- Monopoles and Yang-Baxter equations (1995) (7)
- Anyons in geometric models of matter (2016) (7)
- The Harish-Chandra character (1980) (7)
- On the Work of Edward Witten (1997) (6)
- Mathematics in the twentieth century (2000) (6)
- The Role of Algebraic Topology in Mathematics (1966) (6)
- The impact of Thom’s cobordism theory (2004) (6)
- Green's functions for selfdual four manifolds (1981) (6)
- THE WORK OF SIMON DONALDSON (1997) (6)
- Lecture 1: Transversally elliptic operators (1974) (6)
- Equivariant Cohomology and Representations of the Symmetric Group (2000) (6)
- THE FINE STRUCTURE CONSTANT (2018) (6)
- Differential analysis : papers presented at the Bombay Colloquium, 1964 (1964) (6)
- М. Вернь Formal equivariant Â class, splines and multiplicities of the index of transversally elliptic operators (2018) (5)
- Abstracts of additional presentations made at the Royal Society Discussion Meeting ‘The nature of mathematical proof’ (2005) (5)
- The Influence of Computers and Informatics on Mathematics and its Teaching: Mathematics and the Computer Revolution (1986) (4)
- A note on the tangents of a twisted cubic (1952) (4)
- Michael Atiyah collected works (2004) (4)
- The Social Responsibility of Scientists (1999) (4)
- Introduction To Commutative Algebra, Student Economy Edition (2015) (4)
- Commentary on the article of manin (1985) (4)
- What is Geometry? The 1982 Presidential Address (1982) (4)
- Mathematics: Art and science (2005) (4)
- Einstein and Geometry (2007) (4)
- John Arthur Todd (1998) (4)
- William Vallance Douglas Hodge (1977) (3)
- Science for evil: the scientist's dilemma (1999) (3)
- Edinburgh Lectures on Geometry, Analysis and Physics (2010) (3)
- A Nuclear-Weapon-Free World: Steps Along the Way (2000) (3)
- The Relativistic Geometry and Dynamics of Electrons (2018) (3)
- Reflections on geometry and physics (1993) (3)
- Mathematics and the computer revolution (2016) (2)
- Hyperbolic differential equations and algebraic geometry (1968) (2)
- THE GROTHENDIECK RING IN GEOMETRY AND TOPOLOGY (2010) (2)
- Address of the President, Sir Michael Atiyah, O. M., given at the Anniversary Meeting on 30 November 1994 (1995) (2)
- Understanding the 6-Dimensional Sphere (2018) (2)
- Address of the President, Sir Michael Atiyah, given at the Anniversary meeting on 29 November 1991 (1992) (2)
- Classical Groups and Classical Differential Operators on Manifolds (2010) (2)
- APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY (1965) (2)
- Representation theory of Lie groups : proceedings of the SRC/LMS Research Symposium on Representations of Lie Groups, Oxford, 28 June-15 July 1977 (1979) (2)
- Eighty Years On (2011) (2)
- The Interaction between Geometry and Physics (2006) (2)
- Paul Dirac: Paul Dirac: aspects of his life and work (1998) (2)
- A Community of Scholars: Impressions of the Institute for Advanced Study (2011) (2)
- Scalar curvature, flat Borromean rings, and the 3-body problem (2017) (2)
- Vector Bundles on Algebraic Varieties: Papers presented at the Bombay Colloquium 1984 (1987) (2)
- Benjamin Franklin and the Edinburgh Enlightenment1 (2006) (2)
- William Vallance Douglas Hodge, 17 June 1903 - 7 July 1975 (1976) (1)
- Riemann's Influence in Geometry, Analysis and Number Theory (2007) (1)
- Geometry of Low-dimensional Manifolds: Representations of braid groups (1991) (1)
- Congurations of points (2010) (1)
- COMPLEX ANALYTIC CONNECTIONS IN FIBRE (2010) (1)
- The Hirzebruch Signature Theorem for Conical Metrics (2016) (1)
- Friedrich Hirzebruch (1927--2012) (2014) (1)
- Raoul Harry Bott, FRS, 1923–2005 (2010) (1)
- Anniversary Address by the President of the Royal Society: Sir Michael Atiyah (1996) (1)
- Note on Involutions (1977) (1)
- GEOMETRY AND ANALYSIS Papers dedicated to the memory of V. K. Patodi (1984) (1)
- The millennium prize promblems : Clay Mathematics Institute Millennium Meeting, Collège de France, Paris, May 24-25, 2000 (2002) (1)
- Real and Complex Geometry in Four Dimensions (1980) (1)
- The geometry and physics of knots: History and background (1990) (1)
- Geometry and Physics: Where Are We Going? (2021) (1)
- Remarks on Morse Theory (1980) (1)
- Integral geometry and representation theory (1980) (1)
- ISLAMIC PATTERNS AND THEIR SYMMETRIES (1994) (1)
- Computing and the cultures of proving. Dicussion (2005) (1)
- THE WORK OF SERGE NOVIKOV (1997) (1)
- K-theory : lectures by M. F. Atiyah; Notes by D. W. Anderson (1967) (1)
- Geometry and analysis of Shimizu L-functions. (1982) (1)
- The challenge of computer mathematics. Discussion (2005) (1)
- The Israeli-Palestinian Science Organization (2007) (1)
- The geometry and physics of knots: The infinite-dimensional case (1990) (1)
- Erratum to the Paper: A Geometric Construction of the Discrete Series for Semisimple Lie Groups (1980) (1)
- The European Mathematical Society (1991) (1)
- Raoul Harry Bott. 24 September 1923 — 20 December 2005 (2007) (1)
- Acte d'investidura dorctor honoris causa del Professor sir Michael Francis Atiyah (2008) (0)
- Paul Dirac: The monopole (1998) (0)
- Paul Dirac: Antimatter (1998) (0)
- CHAPTER 10. Some Inequalities (1988) (0)
- Book Review: Lectures on mechanics (1994) (0)
- Lecture 6: The operators \bar \partial ^ \pm for G = S1 (1974) (0)
- Lecture 4: The naturality of the index and the localization theorem (1974) (0)
- A UK Academy of Medicine? (1996) (0)
- PRM volume 122 issue 1-2 Cover and Front matter (1992) (0)
- THE GATEWAY FROM ISLAMIC PATTERNS TO INVARIANCE AND GROUPS (1994) (0)
- Lecture 10: Applications (1974) (0)
- Algebraic Topology – A Student's Guide: Characters and cohomology of finite groups (1972) (0)
- 2006 Fields Medals Awarded, Volume 53, Number 9 (2006) (0)
- Thoughts of a Mathematician (2008) (0)
- CHAPTER 1. The Monopole Equations (1988) (0)
- O ct 2 00 2 Lagrangian surfaces with circular ellipse of curvature in complex space forms (2008) (0)
- Lecture 7: Toral actions with finite isotropy groups (1974) (0)
- A problem in Euclidean Geometry (2013) (0)
- Anyon Networks from Geometric Models of Matter (2021) (0)
- Biodiversity A Joint Statement (1992) (0)
- Józef Rotblat: My Friend (2007) (0)
- The Heidelberg Laureate Forum on the moving frontier between mathematics and computer science (2017) (0)
- Quantum Field Theory and Low-Dimensional Geometry (Common Trends in Mathematics and Quantum Field Theories) (1991) (0)
- The Riemann Hypothesis (2018) (0)
- CHAPTER 7. The 2-monopole Space (1988) (0)
- Invitation to Physicists (1991) (0)
- MANIFOLDS OF PIECEWISE LINEAR MAPS AND A RELATED NORMED LINEAR SPACE (2007) (0)
- Address of the President, Sir Michael Atiyah, O. M., given at the Anniversary Meeting on 30 November 1993 (1994) (0)
- The Feynman integral formulation (1990) (0)
- Working with Raoul Bott: From geometry to physics (2010) (0)
- CHAPTER 15. Comparisons with KdV Solitons (1988) (0)
- Rings and Ideals (2018) (0)
- Viii. Final Perspectives Viii.6 Advice to a Young Mathematician (2008) (0)
- John Arthur Todd, 23 August 1908 - 22 December 1994 (1996) (0)
- William Leonard Edge (2018) (0)
- VI.90 William Vallance Douglas Hodge (2010) (0)
- The mysteries of space (1992) (0)
- Non-abelian moduli spaces (1990) (0)
- CHAPTER 9. The Anti-self-dual Einstein Equations (1988) (0)
- CHAPTER 2. Geometry of the Monopole Spaces (1988) (0)
- if-THEORY AND THE HOPF INVARIANT (2005) (0)
- New Developments in the Theory of Knots; The Geometry and Physics of Knots; The Geometry of Four‐Manifolds (1992) (0)
- 100 Years of Mathematics. (2000) (0)
- Todd function as weak analytic function (2019) (0)
- Rings and Modules of Fraction (2018) (0)
- msp MATHEMATICS AND CULTURE : GEOMETRY IN OXFORD 1960 – 1990 (2012) (0)
- What is a proof? Discussion (2005) (0)
- MILLENNIUM LECTURE - CAIRO, 15 JANUARY 2000 (2001) (0)
- Lessons from the Scottish Enlightenment (2011) (0)
- Dirac operators coupled to vector potentials: (elliptic operators/index theory/characteristic classes/anomalies/gauge fields) (1989) (0)
- CHAPTER 11. The Metric on M02 (1988) (0)
- CHAPTER 14. Particle Scattering (1988) (0)
- CLASSIFICATION,IDENTIFICATION AND CONSTRUCTION OF THE SEVENTEEN TYPES OF TWO-DIMENSIONAL PERIODIC PATTERNS (1994) (0)
- Professor S.-T. Yau at 70 (2019) (0)
- PRM volume 116 issue 3-4 Cover and Front matter (1990) (0)
- CHAPTER 16. Background Material (1988) (0)
- Jo Rotblat: Man With a Cause (2007) (0)
- The Royal Society of Edinburgh Two-day Conference organised (2015) (0)
- Woods Hole (Commentary on [124]) (2017) (0)
- TWISTED K-THEORY OLD AND NEW 3 General plan of the paper (2007) (0)
- Discrete Valuation Rings and Dedekind Domains (2018) (0)
- A Geometer Explores the Universe (2012) (0)
- Physics and mathematics of strings: Proceedings of a Royal Society Discussion Meeting, held on 8 and 9 December 1988 (1989) (0)
- J ul 2 00 4 Twisted K-theory (0)
- THE MATHEMATICAL HERITAGE OF HENRI POINCARÉ (Proceedings of Symposia in Pure Mathematics, 39) (1985) (0)
- The Logarithm of the Dedekind q-Function (2004) (0)
- SCIENCE AND THE MILITARY : Warfare (2003) (0)
- CHAPTER 13. Geodesics on M02 (1988) (0)
- Lecture 9: The cohomology formula (1974) (0)
- CONFORMAL COMPACTIFICATIONS AND THEIR TOPOLOGY Objekttyp (2019) (0)
- The Impact of Physics on Geometry (1988) (0)
- CHAPTER 6. Particles and Symmetric Products (1988) (0)
- CHAPTER 5. The Twistor Description (1988) (0)
- Anyons in geometric models of matter (2017) (0)
- Early papers : general papers (1988) (0)
- Lacunas of hyperbolic differential equationes(講演記録) (1970) (0)
- ISLAMIC PATTERNSAND THEIR GEOMETRICAL STRUCTURES (1994) (0)
- Surveys in Differential Geometry XV A Shifted View of Fundamental Physics (2011) (0)
- The geometry and physics of knots: Final comments (1990) (0)
- Lecture 2: The index of transversally elliptic operators (1974) (0)
- M. Hervé, Several Complex Variables: Local Theory (Oxford University Press, 1963), 26s. 6d. (1964) (0)
- Address of the President, Sir Michael Atiyah, O. M., given at the Anniversary Meeting on 30 November 1992 (1993) (0)
- EQUIVARIANT K-TΉEORY AND COMPLETION (2008) (0)
- Geometry Topology and Physics (1988) (0)
- Some applications of topological methods in algebraic geometry (1955) (0)
- CHAPTER 3. Metric of Monopole Spaces (1988) (0)
- A Community of Scholars (2017) (0)
- Lecture 3: The excision and multiplicative properties (1974) (0)
- Mathematics and the real world (1998) (0)
- ARITHMETIC PHYSICS – ABEL LECTURE (2019) (0)
- K-Theory and the Jones Polynomial (2018) (0)
- LECTURES ON DIFFERENTIAL GEOMETRY (1966) (0)
- PRM volume 115 issue 1-2 Cover and Front matter (1990) (0)
- Lecture 5: The index homomorphism for G = S1 (1974) (0)
- IN PRAISE OF PATTERN, SYMMETRY, UNITY & ISLAMIC ART (1994) (0)
- New developments in the theory and application of solitons : proceedings of a Royal Society Discussion Meeting held on 1 and 2 November, 1984 (1985) (0)
- Time evolution in a geometric model of a particle (2015) (0)
- CHAPTER 4. Hyperkahler Property of the Metric (1988) (0)
- CHAPTER 8. Spectral Radii and the Conformal Structure (1988) (0)
- POWER OPERATIONS IN Z-THEORY (2005) (0)
- Collected papers of V. K. Patodi (1996) (0)
- The Relativistic Geometry and Dynamics of Electrons (2018) (0)
- CHAPTER 12. Detailed Properties of the Metric (1988) (0)

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Michael Atiyah is affiliated with the following schools: