Editing John Milnor

{{Short description|American mathematician (born 1931)}}
{{For|those of a similar name|John Milner (disambiguation)}}
{{Use mdy dates|date=November 2022}}
{{Infobox scientist
| name              = John Willard Milnor
| image             = John Milnor.jpg
| image_size        = 220px
| caption           = Milnor at the Celebration of the 90th birthday of [[Beno Eckmann]], Zürich
| birth_date        = {{birth date and age|1931|02|20}}
| birth_place       = [[Orange, New Jersey]]
| death_date        = 
| death_place       = 
| nationality       = American
| field             = Mathematics
| work_institution  = [[Princeton University]], [[State University of New York at Stony Brook|Stony Brook University]]
| education         = [[Princeton University]] ([[Bachelor of Arts|BA]], [[Master of Arts|MA]], [[Doctor of Philosophy|PhD]])
| thesis_title      = Isotopy of Links
| thesis_url        = https://search.worldcat.org/title/176565421
| thesis_year       = 1954
| doctoral_advisor  = [[Ralph Fox]]
| doctoral_students = [[Tadatoshi Akiba]] <br/> [[Jon Folkman]] <br/>[[John N. Mather|John Mather]]<br/>[[Laurent C. Siebenmann]]<br/>[[Michael Spivak]]
| known_for         = [[Exotic sphere]]s<br />[[Fáry–Milnor theorem]]<br />[[Hauptvermutung]]<br />[[Milnor K-theory]]<br />[[Microbundle]]<br /> [[Milnor Map]], [[Milnor number]] and [[Milnor fibration]] in the theory of complex hypersurface singularities, part of [[singularity theory]] and [[algebraic geometry]]<br />[[Milnor–Thurston kneading theory]]<br />[[Plumbing (mathematics)|Plumbing]]<br />[[Milnor–Wood inequality]]<br />[[Surgery theory]]<br />[[Rokhlin's theorem|Kervaire-Milnor theorem]]<br />[[Spectral geometry|Isospectral Non-Isometric compact Riemannian manifolds]]<br />[[Švarc–Milnor lemma]]
| spouse            = [[Dusa McDuff]]
| prizes            = [[Putnam Fellow]] (1949, 1950)<br/> [[Sloan Fellowship]] (1955)<br/> [[Fields Medal]] (1962)<br/> [[National Medal of Science]] (1967)<br/> [[Leroy P. Steele Prize]] (1982, 2004, 2011)<br/> [[Wolf Prize in Mathematics|Wolf Prize]] (1989)<br/> [[Abel Prize]] (2011)<br/> [[Lomonosov Gold Medal]] (2020)
| religion          = 
| footnotes         = 
}}

'''John Willard Milnor''' (born February 20, 1931) 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 [[Leroy P. Steele Prize|Steele prizes]].

==Early life and career==
Milnor was born on February 20, 1931, in [[Orange, New Jersey]].<ref>Staff. [https://library.ias.edu/files/pdfs/hs/cos.pdf#page=35 ''A COMMUNITY OF SCHOLARS: The Institute for Advanced Study Faculty and Members 1930–1980''] {{Webarchive|url=https://web.archive.org/web/20111124234612/http://library.ias.edu/files/pdfs/hs/cos.pdf#page=35 |date=November 24, 2011 }}, p.&nbsp;35. [[Institute for Advanced Study]], 1980. Accessed November 24, 2015. "Milnor, John Willard M, Topology Born 1931 Orange, NJ."</ref> His father was J. Willard Milnor, an  engineer,<ref>{{Cite web |title=John Milnor - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Milnor/ |access-date=2023-03-27 |website=Maths History |language=en}}</ref> and his mother was Emily Cox Milnor.<ref>{{cite book|author1=Helge Holden|author2=Ragni Piene|title=The Abel Prize 2008–2012|url=https://books.google.com/books?id=tEprnQEACAAJ|date=February 3, 2014|publisher=Springer Berlin Heidelberg|isbn=978-3-642-39448-5|pages=353–360}}</ref><ref>{{cite book|author=Allen G. Debus|title=World Who's who in Science: A Biographical Dictionary of Notable Scientists from Antiquity to the Present|url=https://books.google.com/books?id=CZNNAQAAIAAJ|year=1968|publisher=Marquis-Who's Who|page=1187}}</ref> As an undergraduate at [[Princeton University]] he was named a [[William Lowell Putnam Mathematical Competition|Putnam Fellow]] in 1949 and 1950<ref name="MMA">{{cite web |title=Putnam Competition Individual and Team Winners |url=http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners |publisher=[[Mathematical Association of America]] |access-date=December 10, 2021 |archive-date=March 12, 2014 |archive-url=https://web.archive.org/web/20140312205244/http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners |url-status=dead }}</ref> and also proved the [[Fáry–Milnor theorem]] when he was only 19 years old. Milnor graduated with an A.B. in mathematics in 1951 after completing a senior thesis, titled "Link groups", under the supervision of [[Ralph Fox]].<ref>{{Cite book|last=Milnor|first=John W.|url=https://catalog.princeton.edu/catalog/4122388|title=Link groups|date=1951|publisher=Princeton, NJ: Department of Mathematics|language=en}}</ref> He remained at Princeton to pursue graduate studies and received his Ph.D. in mathematics in 1954 after completing a doctoral dissertation, titled "Isotopy of links", also under the supervision of Fox.<ref>{{Cite book|last=Milnor|first=John W.|url=https://catalog.princeton.edu/catalog/1682505|title=Isotopy of links|date=1954|publisher=Princeton, NJ: Department of Mathematics|language=en}}</ref> His dissertation concerned [[link group]]s (a generalization of the classical knot group) and their associated link structure, classifying [[Brunnian link]]s up to link-homotopy and introduced new invariants of it, called [[Milnor invariants]]. Upon completing his doctorate, he went on to work at Princeton. He was a professor at the [[Institute for Advanced Study]] from 1970 to 1990.

He was an editor of the ''[[Annals of Mathematics]]'' for a number of years after 1962. He has written a number of books which are famous for their clarity, presentation, and an inspiration for the research by many mathematicians in their areas even after many decades since their publication. He served as Vice President of the [[American Mathematical Society|AMS]] in 1976–77 period.

His students have included [[Tadatoshi Akiba]], [[Jon Folkman]], [[John Mather (mathematician)|John Mather]], [[Laurent C. Siebenmann]], [[Michael Spivak]], and Jonathan Sondow. His wife, [[Dusa McDuff]], is a professor of mathematics at [[Barnard College]] and is known for her work in [[symplectic topology]].

==Research==
One of Milnor's best-known works is his proof in 1956 of the existence of [[Seven-dimensional space|7-dimensional]] [[Hypersphere|spheres]] with nonstandard differentiable structure, which marked the beginning of a new field – differential topology. He coined the term [[exotic sphere]], referring to any ''n''-sphere with nonstandard differential structure. Kervaire and Milnor initiated the systematic study of exotic spheres by [[Kervaire–Milnor group]]s, showing in particular that the 7-sphere has 15 distinct [[differentiable structure]]s (28 if one considers orientation).

[[Egbert Brieskorn]] found simple algebraic equations for 28 complex hypersurfaces in complex 5-space such that their intersection with a small sphere of dimension 9 around a [[Singular point of a curve|singular point]] is diffeomorphic to these exotic spheres. Subsequently, Milnor worked on the [[topology]] of isolated [[Singular point of a curve|singular points]] of complex hypersurfaces in general, developing the theory of the [[Milnor fibration]] whose fiber has the [[homotopy]] type of a bouquet of ''μ'' spheres where ''μ'' is known as the [[Milnor number]]. Milnor's 1968 book on his theory, ''Singular Points of Complex Hypersurfaces'', inspired the growth of a huge and rich research area that continues to mature to this day.

In 1961 Milnor disproved the [[Hauptvermutung]] by illustrating two [[simplicial complex]]es that are [[Homeomorphism|homeomorphic]] but [[Combinatorial topology|combinatorially]] distinct, using the concept of [[analytic torsion|Reidemeister torsion]].<ref>{{cite book
 | last = Ranicki | first = A. A.
 | editor1-last = Ranicki | editor1-first = A. A.
 | editor2-last = Casson | editor2-first = A. J.
 | editor3-last = Sullivan | editor3-first = D. P.
 | editor4-last = Armstrong | editor4-first = M. A.
 | editor5-last = Rourke | editor5-first = C. P.
 | editor6-last = Cooke | editor6-first = G. E.
 | contribution = On the Hauptvermutung
 | doi = 10.1007/978-94-017-3343-4_1
 | isbn = 0-7923-4174-0
 | mr = 1434101
 | pages = 3–31
 | publisher = Kluwer Academic Publishers, Dordrecht
 | series = {{mvar|K}}-Monographs in Mathematics
 | title = The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds
 | volume = 1
 | year = 1996}} See pp. 3-4</ref>

In 1984 Milnor introduced a definition of [[attractor]].<ref>{{Cite journal|last=Milnor|first=John|date=1985|title=On the concept of attractor|url=https://projecteuclid.org/euclid.cmp/1103942677|journal=Communications in Mathematical Physics|language=EN|volume=99|issue=2|pages=177–195|issn=0010-3616|doi=10.1007/BF01212280|bibcode=1985CMaPh..99..177M|s2cid=120688149}}</ref>  The objects generalize standard attractors, include so-called unstable attractors and are now known as Milnor attractors.

Milnor's current interest is dynamics, especially holomorphic dynamics. His work in dynamics is summarized by Peter Makienko in his review of ''Topological Methods in Modern Mathematics'':

<blockquote>It is evident now that low-dimensional dynamics, to a large extent initiated by Milnor's work, is a fundamental part of general dynamical systems theory. Milnor cast his eye on dynamical systems theory in the mid-1970s. By that time the Smale program in dynamics had been completed. Milnor's approach was to start over from the very beginning, looking at the simplest nontrivial families of maps. The first choice, one-dimensional dynamics, became the subject of his joint paper with [[William Thurston|Thurston]]. Even the case of a unimodal map, that is, one with a single critical point, turns out to be extremely rich. This work may be compared with [[Henri Poincaré|Poincaré's]] work on [[Diffeomorphism#Topology|circle diffeomorphisms]], which 100 years before had inaugurated the qualitative theory of dynamical systems. Milnor's work has opened several new directions in this field, and has given us many basic concepts, challenging problems and nice theorems.<ref name="John Milnor's Sixtieth Birthday Symposium">{{cite book |author-last=Lyubich | author-first=Mikhail |chapter=Back to the origin: Milnor’s program in dynamics | editor-last=Goldberg | editor-first=Lisa R. | editor-last2=Phillips | editor-first2=Anthony Valiant | title=Topological Methods in Modern Mathematics: A Symposium in Honor of John Milnor's Sixtieth Birthday | publisher=Publish or Perish | date=1993 | isbn=0-914098-26-8 | pages=85–92}}</ref> </blockquote>

His other significant contributions include [[microbundle]]s, influencing the usage of [[Hopf algebra]]s, theory of [[quadratic forms]] and the related area of [[bilinear form|symmetric bilinear forms]], higher [[algebraic K-theory]], [[game theory]], and three-dimensional [[Lie group]]s.

==Awards and honors==
Milnor was elected as a member of the [[American Academy of Arts and Sciences]] in 1961.<ref>{{Cite web|title=John Willard Milnor|url=https://www.amacad.org/person/john-willard-milnor|website=American Academy of Arts & Sciences|language=en|access-date=May 31, 2020}}</ref> In 1962 Milnor was awarded the [[Fields Medal]] for his work in differential topology. He was elected to the United States [[National Academy of Sciences]] in 1963 and the [[American Philosophical Society]] 1965.<ref>{{Cite web |title=John W. Milnor |url=http://www.nasonline.org/member-directory/members/52491.html |access-date=October 6, 2022 |website=www.nasonline.org}}</ref><ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=John+Milnor&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=October 6, 2022 |website=search.amphilsoc.org}}</ref> He later went on to win the [[National Medal of Science]] (1967), the [[Lester R. Ford Award]] in 1970<ref>{{cite journal|author=Milnor, John|title=A problem in cartography|journal=Amer. Math. Monthly|volume=76|issue=10|year=1969|pages=1101–1112|url=http://www.maa.org/programs/maa-awards/writing-awards/a-problem-in-cartography|doi=10.2307/2317182|jstor=2317182}}</ref> and again in 1984,<ref>{{cite journal|author=Milnor, John|title=On the geometry of the Kepler problem|journal=Amer. Math. Monthly|volume=90|issue=6|year=1983|pages=353–365|url=http://www.maa.org/programs/maa-awards/writing-awards/on-the-geometry-of-the-kepler-problem|doi=10.2307/2975570|jstor=2975570}}</ref> the [[Leroy P. Steele Prize]] for "Seminal Contribution to Research" (1982), the [[Wolf Prize]] in Mathematics (1989), the [[Leroy P. Steele Prize]] for Mathematical Exposition (2004), and the [[Leroy P. Steele Prize]] for Lifetime Achievement (2011). In 1991 a symposium was held at Stony Brook University in celebration of his 60th birthday.<ref>{{citation|title=Topological methods in modern mathematics| series=Proceedings of the symposium in honor of John Milnor's sixtieth birthday held at the State University of New York, Stony Brook, New York, June 14–21, 1991|editor1-first=Lisa R.|editor1-last=Goldberg|editor2-first=Anthony V.|editor2-last=Phillips|publisher=[[Publish-or-Perish Press]]| location=Houston, TX|year=1993|isbn=978-0-914098-26-3}}</ref>

Milnor was awarded the 2011 [[Abel Prize]],<ref>{{cite web |author= |title=2011: John Milnor |url=https://abelprize.no/abel-prize-laureates/2011 |archive-url= |archive-date= |access-date=August 22, 2022 |website=Abelprisen (Abel Prize) website}}</ref> for his "pioneering discoveries in topology, geometry and algebra."<ref name=hindu>{{cite news|last=Ramachandran|first=R.|title=Abel Prize awarded to John Willard Milnor|url=http://www.thehindu.com/sci-tech/science/article1565424.ece|access-date=March 24, 2011|newspaper=The Hindu|date=March 24, 2011}}</ref> Reacting to the award, Milnor told the ''[[New Scientist]]'' "It feels very good," adding that "[o]ne is always surprised by a call at 6 o'clock in the morning."<ref>{{cite news|last=Aron|first=Jacob|title=Exotic sphere discoverer wins mathematical 'Nobel'|url=https://www.newscientist.com/article/dn20281-exotic-sphere-discoverer-wins-mathematical-nobel.html|access-date=March 24, 2011|newspaper=New Scientist|date=March 23, 2011}}</ref>

In 2013 he became a [[fellow]] of the [[American Mathematical Society]], for "contributions to differential topology, geometric topology, algebraic topology, algebra, and dynamical systems".<ref>[https://www.ams.org/profession/ams-fellows/new-fellows 2014 Class of the Fellows of the AMS], [[American Mathematical Society]], retrieved November 4, 2013.</ref>

In 2020 he received the [[Lomonosov Gold Medal]] of the Russian Academy of Sciences.<ref>[http://www.ras.ru/about/awards/awdlist.aspx?awdid=1 Lomonosov Gold Medal 2020].</ref>

==Publications==
===Books===
*{{cite book
  |last= Milnor
  |first= John W.
  |others= Notes by [[Michael Spivak|M. Spivak]] and R. Wells
  |title= Morse theory
  |series= Annals of Mathematics Studies, No. 51
  |publisher=  [[Princeton University Press]]
  |location= Princeton, NJ
  |year= 1963
  |isbn= 0-691-08008-9
   }}<ref>{{cite journal|author=Kuiper, N. H.|author-link=Nicolaas Kuiper|title=Review: ''Morse theory'', by John Milnor|journal=Bull. Amer. Math. Soc.|year=1965|volume=71|issue=1|pages=136–137|doi=10.1090/s0002-9904-1965-11251-4|doi-access=free}}</ref>
*{{cite book
  |last= Milnor
  |first= John W.
  |others= Notes by [[Larry Siebenmann|L. Siebenmann]] and J. Sondow
  |author-mask= 2
  |title= Lectures on the h-cobordism theorem
  |publisher= Princeton University Press
  |location= Princeton, NJ
  |year= 1965
  |isbn= 0-691-07996-X
  |oclc= 58324
   }}
*{{cite book
  |last= Milnor
  |first= John W.
  |author-mask= 2
  |title= Singular points of complex hypersurfaces
  |series= Annals of Mathematics Studies, No. 61
  |publisher= Princeton, NJ: Princeton University Press; Tokyo: University of Tokyo Press
  |year= 1968
  |isbn= 0-691-08065-8
   }}
*{{cite book
  |last= Milnor
  |first= John W.
  |author-mask= 2
  |title= Introduction to algebraic K-theory
  |series= Annals of Mathematics Studies, No. 72
  |publisher= Princeton University Press
  |location= Princeton, NJ
  |year= 1971
  |isbn= 978-0-691-08101-4
   }}
*{{cite book
  |last1= Husemoller |author-link1=Dale Husemoller
  |first1= Dale
  |last2= Milnor
  |first2= John W.
  |title= Symmetric bilinear forms
  |publisher= Springer-Verlag
  |location= New York, NY
  |year= 1973
  |isbn= 978-0-387-06009-5
   }}
*{{cite book
  |last= Milnor
  |first= John W.
  |author2=Stasheff, James D. |author-link2=Jim Stasheff
  |title= Characteristic classes
  |series= Annals of Mathematics Studies, No. 76
  |publisher= Princeton, NJ: Princeton University Press; Tokyo: University of Tokyo Press
  |year= 1974
  |isbn= 0-691-08122-0
   }}<ref>{{cite journal|author=Spanier, E. H.|author-link=Edwin Spanier|title=Review: ''Characteristic classes'', by John Milnor and James D. Stasheff|journal=Bull. Amer. Math. Soc.|year=1975|volume=81|issue=5|pages=862–866|doi=10.1090/s0002-9904-1975-13864-x|doi-access=free}}</ref>
*{{cite book
  |last= Milnor
  |first= John W.
  |title=Topology from the differentiable viewpoint
  |series= Princeton Landmarks in Mathematics
  |publisher= Princeton University Press
  |location= Princeton, NJ
  |year= 1997
  |orig-year= 1965
  |isbn= 0-691-04833-9
   }}
*{{cite book
  |last= Milnor
  |first= John W.
  |author-mask= 2
  |title= Dynamics in one complex variable
  |publisher= Vieweg
  |location= Wiesbaden, Germany
  |year= 1999
  |isbn= 3-528-13130-6
   }}{{cite book|title=3rd edn|year=2006}}<ref>{{cite journal|author=Hubbard, John|author-link=John H. Hubbard|title=Review: ''Dynamics in one complex variable'', by John Milnor|journal=Bull. Amer. Math. Soc. (N.S.)|year=2001|volume=38|issue=4|pages=495–498|doi=10.1090/s0273-0979-01-00918-1|doi-access=free}}</ref>

===Journal articles===
*{{Cite journal
  |first= John W.
  |last= Milnor
  |title= On manifolds homeomorphic to the 7-sphere
  |journal= [[Annals of Mathematics]]
  |volume= 64
  |year= 1956
  |issue= 2
  |pages= 399–405
  |mr= 0082103
  |doi= 10.2307/1969983
  |publisher= Princeton University Press
  |jstor=1969983
   |s2cid= 18780087
 }}
*{{Cite journal
  |first= John W.
  |last= Milnor
  |author-mask= 2
  |title= Sommes de variétés différentiables et structures différentiables des sphères
  |journal= [[Bulletin de la Société Mathématique de France]]
  |volume= 87
  |year= 1959
  |pages= 439–444
  |mr= 0117744
  |publisher= [[Société Mathématique de France]]
  |doi= 10.24033/bsmf.1538
 |doi-access= free
  }}
*{{Cite journal
  |first= John W.
  |last= Milnor
  |author-mask= 2
  |title= Differentiable structures on spheres
  |journal= [[American Journal of Mathematics]]
  |volume= 81
  |year= 1959b
  |issue= 4
  |pages= 962–972
  |mr= 0110107
  |doi= 10.2307/2372998
  |publisher= [[Johns Hopkins University Press]]
  |jstor=2372998
   }}
*{{Cite journal
  |first= John W.
  |last= Milnor
  |author-mask= 2
  |jstor= 1970299
  |title= Two complexes which are homeomorphic but combinatorially distinct
  |journal= Annals of Mathematics
  |volume= 74
  |year= 1961
  |issue= 2
  |pages= 575–590
  |mr= 133127
  |doi= 10.2307/1970299
  |publisher= Princeton University Press
  }}
*{{Cite journal
  |first= John
  |last= Milnor
  |author-mask= 2
  |title= On the concept of attractor
  |journal= Communications in Mathematical Physics
  |volume= 99
  |year= 1984
  |issue= 2
  |pages= 177–195
  |mr = 0790735
  |doi= 10.1007/BF01212280
  |publisher= Springer Press
  |bibcode= 1985CMaPh..99..177M
 |s2cid= 120688149
 }}
*{{cite journal| first1 = Michel A. | last1 = Kervaire | author-link1 = Michel Kervaire | first2 = John W. | last2 = Milnor | author-link2 = John Milnor | url = http://www.uni-math.gwdg.de/schick/publ/Groups%20of%20homotopy%20spheres%20I.pdf | title = Groups of homotopy spheres: I | journal = Annals of Mathematics | publisher = Princeton University Press | volume = 77 | year = 1963 | issue = 3 | pages = 504–537 | doi = 10.2307/1970128| jstor = 1970128| mr = 0148075}}
*{{Cite journal|first=John W.|last= Milnor |title=Differential topology forty-six years later|journal= [[Notices of the American Mathematical Society]] |volume=58|year=2011|issue= 6 |pages=804–809|url=https://www.ams.org/notices/201106/rtx110600804p.pdf}}

===Lecture notes===
*{{cite book| first1 = John Willard | last1 = Milnor  | first2 = James Raymond | last2= Munkres | author-link2= James Munkres | contribution = Lectures on Differential Topology | title = Collected papers of John Milnor, Volume 4 | editor-first = John Willard | editor-last = Milnor | publisher = American Mathematical Society | pages = 145–176 | year = 2007| isbn = 978-0-8218-4230-0 | contribution-url = https://books.google.com/books?id=PrZANUa0dtgC&pg=PA145 }}

==See also==
{{Portal|Biographies|Mathematics}}
* [[List of things named after John Milnor]]
* [[Orbit portrait]]
* [[Microbundle]]

==References==
{{reflist|30em}}

==External links==
{{wikiquote}}
* {{MacTutor Biography|id=Milnor}}
* [http://www.math.sunysb.edu/~jack/ Home page at SUNYSB]
* [http://owpdb.mfo.de/detail?photoID=9831 Photo]
* [http://www.maths.ed.ac.uk/~aar/exotic.htm Exotic spheres home page]
* [https://web.archive.org/web/20120119102126/http://www.abelprisen.no/en/multimedia/2011/index.html The Abel Prize 2011 – video ]
* {{Cite journal | last1 = Raussen | first1 = Martin | last2 = Skau | first2 = Christian |date=March 2012 | title = Interview with John Milnor | journal = [[Notices of the American Mathematical Society]] | volume = 59  | issue = 3 | pages = 400–408 | url = https://www.ams.org/notices/201203/rtx120300400p.pdf  | doi=10.1090/noti803| doi-access = free }}
* {{cite web|title=Seminar Videos, IMS Video Collection|website=Institute for Mathematical Sciences, Stony Brook University|url=http://www.math.stonybrook.edu/ims-video-collection}} (40 links from 1965 to May 2021, with 9 videos from Milnor's seminars)

{{Fields medalists}}
{{Wolf Prize in Mathematics}}
{{Abel Prize laureates}}
{{Winners of the National Medal of Science|math-stat-comp}}

{{Authority control}}

{{DEFAULTSORT:Milnor, John}}
[[Category:1931 births]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Abel Prize laureates]]
[[Category:Fields Medalists]]
[[Category:Institute for Advanced Study faculty]]
[[Category:Living people]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Foreign members of the Russian Academy of Sciences]]
[[Category:National Medal of Science laureates]]
[[Category:People from Orange, New Jersey]]
[[Category:Princeton University alumni]]
[[Category:Princeton University faculty]]
[[Category:Putnam Fellows]]
[[Category:Stony Brook University faculty]]
[[Category:American topologists]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Dynamical systems theorists]]
[[Category:American geometers]]
[[Category:Sloan Research Fellows]]
[[Category:Members of the American Philosophical Society]]
[[Category:Reeves family]]