John Willard Milnor (b. February 20, 1931) is a mathematician known for his work in differential topology and K-theory and his influential books, which are widely considered to be examples of fine mathematical writing. He won the Fields Medal in 1962. As of 2005, John Milnor is a distinguished professor at the State University of New York at Stony Brook with his wife Dusa McDuff. February 20 is the 51st day of the year in the Gregorian Calendar. ... 1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, K-theory is, firstly, an extraordinary cohomology theory which consists of topological K-theory. ... The Fields Medal is a prize awarded to up to four mathematicians not over forty years of age at each International Congress of the International Mathematical Union (therefore once every four years). ... The State University of New York at Stony Brook (SUNYSB), also commonly referred to as Stony Brook University (SBU), is a public research university located in Stony Brook, New York (about 65 miles east of Manhattan, New York). ... Dusa McDuff is an English mathematician whose first work was in the field of von Neumann algebras but has most recently made fundamental and wide-ranging contributions to symplectic geometry, especially in connection with Gromovs pseudo-holomorphic curves. ...

As an undergraduate at Princeton University he was named a Putnam Fellow in 1949 and 1950 and also proved the Fary-Milnor theorem. He continued on to graduate school at Princeton and wrote his thesis, entitled isotopy of links, which concerned link groups (a generalization of the classical knot group) and their associated link structure. His advisor was Ralph Fox. Upon completing his doctorate he went on to work at Princeton. Princeton University is a coeducational private university located on an extensive campus in and around suburban Princeton, New Jersey. ... The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools. ... 1949 (MCMXLIX) was a common year starting on Saturday (the link is to a full 1949 calendar). ... 1950 (MCML) was a common year starting on Sunday (link will take you to calendar). ... In mathematics, the Fary-Milnor theorem in knot theory states that for any knot C in , if the total curvature then C is an unknot, where is the curvature (it is possible for an unknotted curve to have large total curvature). ... An illustration of a homotopy between the two bold paths In topology, two continuous functions from one topological space to another are called homotopic (Greek homeos = identical and topos = place) if one can be continuously deformed into the other, such a deformation being called a homotopy between the two functions. ... The Borromean rings, a link with three components each equivalent to the unknot. ... Ralph H. Fox was an American mathematician. ...

In 1962 Milnor was awarded the Fields Medal for his work in differential topology. He later went on to win the National Medal of Science (1967), the Leroy P Steele Prize for Seminal Contribution to Research (1982), the Wolf Prize in Mathematics (1989), and the Leroy P Steele Prize for Mathematical Exposition (2004). 1962 (MCMLXII) was a common year starting on Monday (the link is to a full 1962 calendar). ... The Fields Medal is a prize awarded to up to four mathematicians not over forty years of age at each International Congress of the International Mathematical Union (therefore once every four years). ... National Medal of Science The National Medal of Science, also called the Presidential Medal of Science, is an honor given by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social... 1967 (MCMLXVII) was a common year starting on Sunday of the Gregorian calendar (the link is to a full 1967 calendar). ... The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. ... 1982 (MCMLXXXII) was a common year starting on Friday of the Gregorian calendar. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ... 1989 (MCMLXXXIX) was a common year starting on Sunday of the Gregorian calendar. ... The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. ... 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ...

He has been editor of the Annals of Mathematics since 1962. His books include Topology from the Differentiable Viewpoint, Morse Theory, Characteristic Classes (with Stasheff), Lectures on the h-Cobordism Theorem, Dynamics in One Complex Variable, and Singular Points of Complex Hypersurfaces. The Annals of Mathematics (ISSN 0003-486X), often just called Annals, is a bimonthly mathematics research journal published by Princeton University and the Institute for Advanced Study. ... 1962 (MCMLXII) was a common year starting on Monday (the link is to a full 1962 calendar). ...

His most celebrated single result is his proof of the existence of 7-dimensional spheres with nonstandard differential structure. Later with Kervaire, he showed that the 7-sphere has 15 differentiable structures (28 if you consider orientation). An n-sphere with nonstandard differential structure is called an exotic sphere, a term coined by Milnor. In topology, an atlas describes how a complicated space is glued together from simpler pieces. ... In mathematics, an exotic sphere is a differential manifold M, such that from a topological point of view M is a sphere, but not from the point of view of its differential structure. ...

His students have included Michael Spivak, John Mather, and Tadatoshi Akiba. Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. ... John Mather is a mathematician at Princeton University known for his work on Hamiltonian dynamics, descended from Atherton Mather, a cousin of Cotton Mather. ... Tadatoshi Akiba (秋葉 忠利 Akiba Tadatoshi, born November 3, 1942 in Arakawa, Tokyo) is mayor of the city of Hiroshima, Japan. ...

External links

• Mathematics Genealogy Project page for Milnor (includes link to a biography).