John Milnor | Academic Influence

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John Milnor

Mathematics

#42

World Rank

#128

Historical Rank

#13

USA Rank

Differential Topology

#1

World Rank

#1

Historical Rank

#1

USA Rank

Topology

#3

World Rank

#8

Historical Rank

#2

USA Rank

Algebraic Topology

#5

World Rank

#8

Historical Rank

#3

USA Rank

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Mathematics

John Milnor's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Princeton University

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Why Is John Milnor Influential?

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According to Wikipedia, John Willard Milnor is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and the only mathematician to have won the Fields Medal, the Wolf Prize, the Abel Prize and all three Steele prizes.

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John Milnor's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Singular points of complex hypersurfaces (1968) (2630)
Dynamics in one complex variable (2000) (1635)
On the Structure of Hopf Algebras (1965) (1527)
Topology from the differentiable viewpoint (1965) (1430)
Curvatures of left invariant metrics on lie groups (1976) (1327)
Lectures on the h-cobordism theorem (1965) (1008)
On the concept of attractor (1985) (908)
Introduction to algebraic K-theory (1971) (798)
On iterated maps of the interval (1988) (754)
AN AXIOMATIC APPROACH TO MEASURABLE UTILITY (1953) (701)
A note on curvature and fundamental group (1968) (615)
Characteristic Classes. (AM-76) (1974) (609)
Solution of the congruence subgroup problem for SLn (n ≥ 3) and Sp2n (n ≥ 2) (1967) (579)
On Manifolds Homeomorphic to the 7-Sphere (1956) (552)
Construction of Universal Bundles, II (1956) (538)
On the Betti numbers of real varieties (1964) (522)
Dynamics in One Complex Variable: Introductory Lectures (1990) (469)
On spaces having the homotopy type of a CW-complex (1959) (440)
On the existence of a connection with curvature zero (1958) (407)
THE STEENROD ALGEBRA AND ITS DUAL1 (1958) (400)
Dynamical properties of plane polynomial automorphisms (1989) (392)
WHITEHEAD TORSION BY (2007) (339)
EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS. (1964) (334)
Hyperbolic geometry: The first 150 years (1982) (323)
ON THE TOTAL CURVATURE OF KNOTS (1950) (320)
Geometry and Dynamics of Quadratic Rational Maps (1993) (305)
Growth of finitely generated solvable groups (1968) (302)
A Unique Decomposition Theorem for 3-Manifolds (1962) (298)
Singular Points of Complex Hypersurfaces. (AM-61), Volume 61 (1969) (295)
Groups of Homotopy Spheres, I (2015) (295)
On fundamental groups of complete affinely flat manifolds (1977) (293)
AlgebraicK-theory and quadratic forms (1970) (288)
On axiomatic homology theory. (1962) (275)
On the parallelizability of the spheres (1958) (274)
THE GEOMETRIC REALIZATION OF A SEMI-SIMPLICIAL COMPLEX (1957) (274)
GROUPS WHICH ACT ON Su WITHOUT FIXED POINTS. (1957) (267)
Games Against Nature (1951) (240)
A DUALITY THEOREM FOR REIDEMEISTER TORSION (1962) (240)
Singularities of 2-spheres in 4-space and cobordism of knots (1966) (227)
Isolated singularities defined by weighted homogeneous polynomials (1970) (227)
On the Cobordism Ring Ω ∗ and a Complex Analogue, Part I (1960) (225)
ON THE 3-DIMENSIONAL BRIESKORN MANIFOLDS M(p,q,r) (1975) (224)
Construction of Universal Bundles, I (2010) (213)
Construction of Universal Bundles, I (2010) (213)
Algebraic K-Theory and Quadratic Forms (2005) (207)
Values of Large Games II: Oceanic Games (1978) (205)
Two Complexes Which are Homeomorphic But Combinatorially Distinct (1961) (166)
Periodic Orbits, Externals Rays and the Mandelbrot Set: An Expository Account (1999) (164)
On isometries of inner product spaces (1969) (161)
Remarks on Iterated Cubic Maps (1990) (145)
On Lattès Maps (2004) (140)
Fixed points of polynomial maps. Part II. Fixed point portraits (1993) (135)
On the Entropy Geometry of Cellular Automata (1988) (129)
Lectures on characteristic classes (1957) (129)
Analytic Proofs of the “Hairy Ball Theorem” and the Brouwer Fixed Point Theorem (1978) (114)
The Mandelbrot Set, Theme and Variations: Local connectivity of Julia sets: expository lectures (2000) (113)
Remarks Concerning Spin Manifolds (1965) (111)
The Steenrod Algebra and Its Dual (2010) (110)
Some Consequences of a Theorem of Bott (1958) (104)
The Fibonacci unimodal map (1991) (101)
On the Stiefel-Whitney numbers of complex manifolds and of spin manifolds (1965) (99)
On the concept of attractor: Correction and remarks (1985) (97)
Microbundles: Part I (1964) (97)
On polylogarithms, Hurwitz zeta functions, and the Kubert identities (1983) (94)
ON 2-SPHERES IN 4-MANIFOLDS. (1961) (93)
Pasting Together Julia Sets: A Worked Out Example of Mating (2004) (92)
DIFFERENTIABLE STRUCTURES ON SPHERES. (1959) (87)
Some Experimental n-Person Games (1952) (84)
On Entropy and Monotonicity for Real Cubic Maps (1998) (84)
On Rational Maps with Two Critical Points (1997) (82)
Differentiable manifolds which are homotopy spheres (1959) (80)
Advanced Problems: 5600-5609 (1968) (75)
Fubini Foiled: Katok’s Paradoxical Example in Measure Theory (1997) (74)
Introduction to Algebraic K-Theory. (AM-72), Volume 72 (1972) (73)
On the Geometry of the Kepler Problem (1983) (73)
Towards the Poincaré Conjecture and the Classification of 3-Manifolds, Volume 50, Number 10 (2003) (72)
On total curvatures of closed space curves (1953) (62)
Cubic Polynomial Maps with Periodic Critical Orbit, Part I (2009) (58)
AN EXAMPLE OF ANOMALOUS SINGULAR HOMOLOGY (1962) (56)
A Problem in Cartography (1969) (51)
Prospects in Mathematics (1971) (46)
SEMI-CHARACTERISTICS AND COBORDISM (1969) (45)
BERNOULLI NUMBERS, HOMOTOPY GROUPS, A N D A THEOREM OF ROHLIN (2010) (44)
On the immersion ofn-manifolds in (n+1)-space (1956) (42)
On Latt\`es Maps (2004) (40)
Some curious involutions of spheres (1964) (40)
Hyperbolic components in spaces of polynomial maps (1992) (39)
On characteristic classes for spherical fibre spaces (1968) (39)
Local connectivity of Julia sets: expository lectures (1992) (39)
Algebraic Topology – A Student's Guide: On the construction FK (1972) (37)
On Deciding Whether a Surface is Parabolic or Hyperbolic (1977) (36)
Characteristic Classes. (Am-76), Volume 76 (1962) (36)
SYMMETRIC INNER PRODUCTS IN CHARACTERISTIC 2 (1972) (36)
Two remarks on fiber homotopy type. (1960) (36)
On the homology of Lie groups made discrete (1983) (34)
Schwarzian Derivatives and Cylinder Maps (2006) (32)
Topological methods in modern mathematics : a Symposium in Honor of John Milnor's Sixtieth Birthday (1993) (30)
Differential Topology Forty-six Years Later (2011) (30)
Directional Entropies of Cellular Automaton-Maps (1986) (30)
Hyperbolic Components (2012) (30)
A nobel prize for John Nash (1995) (29)
Collected Papers of John Milnor (2009) (27)
A Monotonicity Conjecture for Real Cubic Maps (1993) (23)
Antipode preserving cubic maps: the Fjord theorem (2015) (22)
Review: Norman Steenrod, The topology of fibre bundles (1958) (21)
Non-expansive Hénon maps (1988) (21)
Classification of ( n - 1 )-connected 2n-dimensional manifolds and the discovery of exotic spheres (2000) (19)
On Games of Survival (1956) (18)
Dynamics in One Complex Variable. (AM-160): Third Edition. (AM-160) (2011) (17)
On the whitehead homomorphism $J$ (1958) (17)
Novikov Conjectures, Index Theorems and Rigidity: On the Steenrod homology theory (first distributed 1961) (1995) (16)
Villous tumor of rectum and a portion of the sigmoid flexure causing severe electrolyte imbalance (1959) (15)
Elliptic Curves as Attractors in ℙ2 Part 1: Dynamics (2007) (13)
Arithmetic of Unicritical Polynomial Maps (2012) (13)
On Real and Complex Cubic Curves (2016) (12)
Fifty Years Ago: Topology of Manifolds in the 50's and 60's (2006) (12)
Laminations and foliations in dynamics, geometry and topology : proceedings of the conference on laminations and foliations in dynamics, geometry and topology, May 18-24, 1998, SUNY at Stony Brook (2001) (11)
Morse Theory. (Am-51), Volume 51 (1963) (11)
Conformal dynamics problem list (1990) (10)
On the relationship between differentiable and combinatorial manifolds (1956) (10)
Most knots are wild (1964) (10)
Remarks on quadratic rational maps (1992) (8)
16. Sums of Positional Games (1953) (7)
Errata for ``Cubic polynomial maps with periodic critical orbit, Part II (2010) (6)
Problems in holomorphic dynamics (1992) (5)
2. Vector Bundles (1974) (5)
Topology through the centuries: Low dimensional manifolds (2015) (5)
John Forbes Nash Jr. (1928–2015) (2016) (4)
Microbundles differentiable structures (1961) (4)
CW Complex (2009) (3)
The W. Thurston algorithm applied to real polynomial maps (2020) (3)
THE WORK OF M. H. FREEDMAN (1997) (2)
ON THE WHITEHEAD HOMOMORPHISM / BY (2007) (2)
3. The Game of Hex (2002) (2)
Introduction to Exotic Spheres [reprinted from Collected Papers of John Milnor, III, 2007] (2015) (2)
The Mathematical Work of the 1998 Fields (1998) (2)
On bicritical rational maps (1997) (2)
Appendix C: Connections, Curvature, and Characteristic Classes (1974) (2)
Princeton in Trouble (1973) (1)
The Characteristics of a Vector Field on the Two-Sphere (1953) (1)
The W. Thurston Algorithm for Real Quadratic Rational Maps (2020) (1)
The Kervaire–Milnor correspondence 1958–1961 (2015) (1)
On Antipode Preserving Cubic Maps , ( Draft of Feb . 15 , 2015 ) (2015) (1)
Group actions, divisors, and plane curves (2018) (1)
PART II. A RAPID COURSE IN RIEMANNIAN GEOMETRY (1963) (1)
Using the Fatou Set to Study the Julia Set (2000) (1)
1. ON GAMES OP SURVIVAL (1958) (1)
ﬁbered spaces in 3 -manifolds (2020) (1)
3. The Whitehead Group K1Λ (1972) (0)
17. The Oriented Cobordism Ring Ω (1974) (0)
Section 3. Elementary Cobordisms (1965) (0)
Second Abel Conference A Mathematical Celebration of John Milnor (2011) (0)
18. Thom Spaces and Transversality (1974) (0)
Problems on Local Connectivity. 1 (1992) (0)
Appendix G. Parameter Spaces (2011) (0)
Appendix C. Rotations, Continued Fractions, and Rational Approximation (2011) (0)
§ 10. THE CLASSICAL CASE: CURVES IN C2 (1969) (0)
Appendix E. Branched Coverings and Orbifolds (2011) (0)
PART III. THE CALCULUS OF VARIATIONS APPLIED TO GEODESICS (1963) (0)
Inner Product Spaces over a Field (1973) (0)
Appendix A. Theorems from Classical Analysis (2011) (0)
§4. Stiefel-Whitney Classes (1974) (0)
6. A Cell Structure for Grassmann Manifolds (1974) (0)
4. THE FIBRATION THEOREM (1969) (0)
10. The Thom Isomorphism Theorem (1974) (0)
Dynamical systems (1953-2000) (2012) (0)
Complex systems : the role of mathematics (2000) (0)
DIFFERENTIAL TOPOLOGY 46 YEARS LATER (2011) (0)
Appendix H. Computer Graphics and Effective Computation (2011) (0)
1. Smooth Manifolds (1974) (0)
spheres (2020) (0)
Sections 8. Elimination of Critical Points of Index 0 end 1 (1965) (0)
3. Constructing New Vector Bundles Out of Old (1974) (0)
16. Chern Numbers and Pontrjagin Numbers (1974) (0)
The mathematical works of J.H.C. Whitehead (1965) (0)
13. More about Dedekind Domains (1972) (0)
PART I. NON-DEGENERATE SMOOTH FUNCTIONS ON A MANIFOLD (1963) (0)
7. THE MIDDLE BETTI NUMBER OF THE FIBER (1969) (0)
Periodic Points: Global Theory (2000) (0)
FROM THE DIFFERENTIABLE VIEWPOINT By (2013) (0)
Appendix. Continuous Steinberg Symbols (1972) (0)
Section 6. A Stronger Cancellation Theorem (1965) (0)
BOOKS, 1963–1974 (2021) (0)
6. THE CASE OF AN ISOLATED CRITICAL POINT (1969) (0)
Symmetric Inner Product Spaces over Z (1973) (0)
§11. Matsumoto’s Computation of K2 of a Field (1972) (0)
15. Power Norm Residue Symbols (1972) (0)
Homotopy, homology and manifolds (2009) (0)
PART IV. APPLICATIONS TO LIE GROUPS AND SYMMETRIC SPACES (1963) (0)
12. Proof of Matsumoto’s Theorem (1972) (0)
4. The Exact Sequence Associated with an Ideal (1972) (0)
3. THE CURVE SELECTION LEMMA (1969) (0)
Appendix D. Two or More Complex Variables (2011) (0)
§7. The Cohomology Ring H*(Gn; Z/2) (1974) (0)
20. Combinatorial Pontrjagin Classes (1974) (0)
Appendix B. Length-Area-Modulus Inequalities (2011) (0)
APPENDIX. THE HOMOTOPY TYPE OF A MONOTONE UNION (1963) (0)
Integral , Closed , Kovalevskaya Monoids for a Composite Ideal (2012) (0)
THE WORK OF J. H. C. WHITEHEAD (1962) (0)
Section 9. The h-Cobordism Theorem end Some Applications (1965) (0)
This note will present strange but quite elementary proofs of two classical theorems of topology (2016) (0)
15. Pontrjagin Classes (1974) (0)
5. THE TOPOLOGY OF THE FIBERAND OF K (1969) (0)
The Mathematical Work of Curt McMullen (2007) (0)
11. Computations in a Smooth Manifold (1974) (0)
Section 7. cancellation of Critical Points in the Middle Dimensions (1965) (0)
§8. Existence of Stiefel-Whitney Classes (1974) (0)
On t he Entropy Geometry of C ellular Automata (2006) (0)
Smooth Cubic Curves over ${\mathbb C}$ and ${\mathbb R}$ (2016) (0)
2. ELEMENTARY FACTS ABOUT REAL OR COMPLEX ALGEBRAIC SETS (1969) (0)
5. Grassmann Manifolds and Universal Bundles (1974) (0)
16. Number Fields (1972) (0)
Appendix B: Bernoulli Numbers (1974) (0)
LECTLTHES ON TEE h-COBORDISM THEOREM (1965) (0)
2 . Constructing Projective Modules (1972) (0)
19. Multiplicative Sequences and the Signature Theorem (1974) (0)
1. Projective Modules and K0Λ (1972) (0)
Local Fixed Point Theory (2000) (0)
Appendix F. No Wandering Fatou Components (2011) (0)
13. Complex Vector Bundles and Complex Manifolds (1974) (0)
Topological Manifolds and Smooth Manifolds [reprinted from Proc. Internat. Congr. Math. (Stockholm 1962)] (2015) (0)
Appendix A: Singular Homology and Cohomology (1974) (0)
The fundamental group (2009) (0)
14. Chern Classes (1974) (0)
Seven days: 25?31 March 2011 (2011) (0)
9. Oriented Bundles and the Euler Class (1974) (0)
6. Extending the Exact Sequences (1972) (0)
2006 Fields Medals Awarded, Volume 53, Number 9 (2006) (0)
14. The Transfer Homomorphism (1972) (0)
Section 5. A Cancellation Theorem (1965) (0)
9. Computations in the Steinberg Group (1972) (0)
Discrete Valuations and Dedekind Domains (1973) (0)
ON ITERATED CUBIC MAPS (0)
10. Computation of K2Z (1972) (0)
8. IS K A TOPOLOGICAL SPHERE (1969) (0)
7. The Case of a Commutative Banach Algebra (1972) (0)
ALGEBRAIC TOPOLOGY AT THE STEKLOV MATHEMATICAL INSTITUTE OF THE ACADEMY OF SCIENCES OF THE USSR (2008) (0)
APPENDIX B. THE MULTIPLICITY OF AN ISOLATED SOLUTION OF ANALYTIC EQUATIONS (1969) (0)
§8. The Product K1Λ ⊗ K1Λ → K2Λ (1972) (0)
11. A FIBRATION THEOREM FOR REAL SINGULARITIES (1969) (0)
Structure of the Fatou Set (2000) (0)
APPENDIX A. WHITNEY’S FINITENESS THEOREM FOR ALGEBRAIC SETS (1969) (0)
The Stony Brook Reviews : Gene Therapy and Chemoselective Vector Modification Research highlights : Poliovirus : A Promising Candidate for Oncolytic Treatment Graphene (2012) (0)
Section 1. The Cobordism Category (1965) (0)
5. Steinberg Groups and the Functor K2 (1972) (0)
Section 2. Morse Functions (1965) (0)
Iterated Holomorphic Maps (2000) (0)
Elliptic Curves as Attractors in ${\mathbb P}^2$ Part 1: Dynamics (2006) (0)
Prospects in Mathematics. (AM-70) (1972) (0)
9. BRIESKORN VARIETIES AND WEIGHTED HOMOGENEOUS POLYNOMIALS (1969) (0)
Dynamical systems (1984-2012) (2014) (0)
Preface and Guide to the Literature (1972) (0)
Section 4. Rearrangement of CobordlBms (1965) (0)

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