John Milnor

34.1k total citations · 14 hit papers
111 papers, 17.6k citations indexed

About

John Milnor is a scholar working on Geometry and Topology, Mathematical Physics and Applied Mathematics. According to data from OpenAlex, John Milnor has authored 111 papers receiving a total of 17.6k indexed citations (citations by other indexed papers that have themselves been cited), including 56 papers in Geometry and Topology, 48 papers in Mathematical Physics and 18 papers in Applied Mathematics. Recurrent topics in John Milnor's work include Homotopy and Cohomology in Algebraic Topology (27 papers), Geometric and Algebraic Topology (19 papers) and Mathematics and Applications (17 papers). John Milnor is often cited by papers focused on Homotopy and Cohomology in Algebraic Topology (27 papers), Geometric and Algebraic Topology (19 papers) and Mathematics and Applications (17 papers). John Milnor collaborates with scholars based in United States, Chile and France. John Milnor's co-authors include Edgar H. Brown, John C. Moore, James Stasheff, Michel Kervaire, Dale Husemöller, I. N. Herstein, Hyman Bass, Jean-Pierre Serre, Shmuel Friedland and Lloyd S. Shapley and has published in prestigious journals such as Nature, Proceedings of the National Academy of Sciences and Econometrica.

In The Last Decade

John Milnor

109 papers receiving 13.5k citations

Hit Papers

Singular points of complex hypersurfaces 1951 2026 1976 2001 1968 1967 1963 1965 1971 400 800 1.2k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Singular points of complex hypersurfaces
    1968 1.3k citations John Milnor Medical Entomology and Zoology profile →
  2. Topology from the Differentiable Viewpoint.
    1967 867 citations John Milnor et al. American Mathematical Monthly profile →
  3. Morse Theory. (AM-51)
    1963 840 citations John Milnor Princeton University Press eBooks profile →
  4. On the Structure of Hopf Algebras
    1965 832 citations John Milnor et al. Annals of Mathematics profile →
  5. Introduction to algebraic K-theory
    1971 747 citations John Milnor profile →
  6. Curvatures of left invariant metrics on lie groups
    1976 711 citations John Milnor Advances in Mathematics profile →
  7. Characteristic Classes. (AM-76)
    1974 648 citations John Milnor et al. Princeton University Press eBooks profile →
  8. On the concept of attractor
    1985 595 citations John Milnor Communications in Mathematical Physics profile →
  9. Dynamics in One Complex Variable
    2000 538 citations John Milnor Medical Entomology and Zoology profile →
  10. Symmetric Bilinear Forms
    1973 538 citations John Milnor et al. profile →
  11. Lectures on the H-Cobordism Theorem
    1965 520 citations John Milnor Princeton University Press eBooks profile →
  12. Groups of Homotopy Spheres: I
    1963 493 citations John Milnor et al. Annals of Mathematics profile →
  13. An Axiomatic Approach to Measurable Utility
    1953 417 citations John Milnor et al. profile →
  14. Games Against Nature
    1951 209 citations John Milnor profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
John Milnor United States 58 10.6k 9.2k 3.3k 3.2k 2.5k 111 17.6k
Walter Rudin United States 37 4.0k 0.4× 7.2k 0.8× 9.3k 2.8× 2.1k 0.7× 4.6k 1.8× 183 24.2k
Sergey Fomin United States 32 4.2k 0.4× 3.3k 0.4× 1.1k 0.3× 2.5k 0.8× 1.7k 0.6× 73 9.7k
Serge Lang United States 43 4.7k 0.4× 3.0k 0.3× 1.4k 0.4× 2.3k 0.7× 1.7k 0.7× 169 8.1k
Vladimir I. Arnold Russia 48 4.1k 0.4× 3.1k 0.3× 2.3k 0.7× 825 0.3× 1.3k 0.5× 200 13.0k
Victor Guillemin United States 40 3.9k 0.4× 4.3k 0.5× 2.1k 0.6× 1.3k 0.4× 733 0.3× 174 7.8k
Jonathan M. Borwein Canada 57 2.9k 0.3× 2.6k 0.3× 2.8k 0.8× 2.3k 0.7× 7.2k 2.8× 457 15.3k
Edwin Hewitt United States 30 2.6k 0.2× 4.7k 0.5× 2.9k 0.9× 1.8k 0.6× 1.7k 0.7× 105 8.7k
Wilhelm Magnus United States 20 1.8k 0.2× 1.8k 0.2× 1.2k 0.4× 735 0.2× 1.0k 0.4× 42 8.0k
Richard P. Stanley United States 52 6.4k 0.6× 3.1k 0.3× 762 0.2× 6.6k 2.1× 4.4k 1.7× 196 14.9k
Elias M. Stein United States 40 2.0k 0.2× 11.1k 1.2× 18.0k 5.4× 490 0.2× 4.0k 1.6× 96 23.5k

Countries citing papers authored by John Milnor

Since Specialization
Citations

This map shows the geographic impact of John Milnor's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by John Milnor with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites John Milnor more than expected).

Fields of papers citing papers by John Milnor

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by John Milnor. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by John Milnor. The network helps show where John Milnor may publish in the future.

Co-authorship network of co-authors of John Milnor

This figure shows the co-authorship network connecting the top 25 collaborators of John Milnor. A scholar is included among the top collaborators of John Milnor based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with John Milnor. John Milnor is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Milnor, John. (2011). Differential Topology Forty-six Years Later. Notices of the American Mathematical Society. 58(6). 804–809. 9 indexed citations
2.
Kiwi, Jan, et al.. (2010). Cubic polynomial maps with periodic critical orbit, Part II: Escape regions. Conformal Geometry and Dynamics of the American Mathematical Society. 14(4). 68–112. 15 indexed citations
3.
Milnor, John. (1988). On the Entropy Geometry of Cellular Automata.. Complex Systems. 2. 2516–2516. 56 indexed citations
4.
Milnor, John. (1988). Non-expansive Hénon maps. Advances in Mathematics. 69(1). 109–114. 15 indexed citations
5.
Milnor, John. (1985). On the concept of attractor: Correction and remarks. Communications in Mathematical Physics. 102(3). 517–519. 68 indexed citations
6.
Milnor, John. (1983). On the homology of Lie groups made discrete. Commentarii Mathematici Helvetici. 58(1). 72–85. 37 indexed citations
7.
Milnor, John. (1982). Hyperbolic geometry: The first 150 years. Bulletin of the American Mathematical Society. 6(1). 9–24. 138 indexed citations
8.
Milnor, John. (1978). Analytic Proofs of the "Hairy Ball Theorem" and the Brouwer Fixed Point Theorem. American Mathematical Monthly. 85(7). 521–521. 35 indexed citations
9.
Milnor, John. (1977). On fundamental groups of complete affinely flat manifolds. Advances in Mathematics. 25(2). 178–187. 176 indexed citations
10.
Milnor, John. (1969). Singular Points of Complex Hypersurfaces. (AM-61). Princeton University Press eBooks. 282 indexed citations
11.
Milnor, John. (1969). A Problem in Cartography. American Mathematical Monthly. 76(10). 1101–1101. 9 indexed citations
12.
Milnor, John. (1968). Growth of finitely generated solvable groups. Journal of Differential Geometry. 2(4). 141 indexed citations
13.
Kiehl, Reinhardt, J. M. Boardman, Hyman Bass, et al.. (1967). Die De Rham Kohomologie algebraischer Mannigfaltigkeiten über einem bewerteten Körper (p.5 à 20) . Singularities of differentiable maps (p.21 à 57) . Solution of the congruence subgroup problem for SLn (n≧3) and Sp2n (n≧2) (p.59 à 137) . Algebraic equations for nonsmoothable 8-manifolds. 53 indexed citations
14.
Fox, Ralph H. & John Milnor. (1966). Singularities of 2-spheres in 4-space and cobordism of knots. Osaka Journal of Mathematics. 3(2). 257–267. 100 indexed citations
15.
Milnor, John. (1965). Lectures on the H-Cobordism Theorem. Princeton University Press eBooks. 520 indexed citations breakdown →
16.
Milnor, John. (1965). On the Stiefel-Whitney numbers of complex manifolds and of spin manifolds. Topology. 3(3). 223–230. 59 indexed citations
17.
Hirsch, Morris W. & John Milnor. (1964). Some curious involutions of spheres. Bulletin of the American Mathematical Society. 70(3). 372–378. 21 indexed citations
18.
Milnor, John. (1959). On Spaces Having the Homotopy Type of a CW-Complex. Transactions of the American Mathematical Society. 90(2). 272–272. 143 indexed citations
19.
Milnor, John. (1956). On the relationship between differentiable and combinatorial manifolds. Medical Entomology and Zoology. 5 indexed citations
20.
Milnor, John. (1953). The Characteristics of a Vector Field on the Two-Sphere. Annals of Mathematics. 58(2). 253–253. 2 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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