Mathematician:John Willard Milnor

Mathematician

American mathematician best known for his work in differential topology.

Nationality

American

History

• Born: 20th February 1931, Orange, New Jersey, USA.
• 1949, 1950: Named a Putnam Fellow while at Princeton
• 1951: Graduated from Princeton
• 1962: Awarded Fields Medal
• 1967: Awarded National Medal of Science
• 1982: Awarded Leroy P. Steele Prize for Seminal Contribution to Research
• 1989: Awarded Wolf Prize in Mathematics
• 2004: Awarded Leroy P. Steele Prize for Mathematical Exposition
• 2011: Awarded Leroy P. Steele Prize for Lifetime Achievement

• 2011: Awarded Abel Prize for his "pioneering discoveries in topology, geometry and algebra"

Theorems, Definitions and Conjectures

• Fary-Milnor Theorem (proved independently of István Fáry)
• Milnor Conjecture (Algebraic K-Theory)
• Milnor Conjecture (Knot Theory)
• Milnor Conjecture (Manifolds)
• Milnor Fibration (also known as a Milnor Map)
• Milnor-Thurston Kneading Theory (with William Paul Thurston)
• Bott-Milnor-Kervaire 1,2,4,8 Theorem (with Raoul Bott and Michel André Kervaire)

• Disproved the Hauptvermutung

Results named for John Willard Milnor can be found here.

Publications

• 1950: On the Total Curvature of Knots
• 1953: An Axiomatic Approach to Measurable Utility (Econometrica Vol. 21: pp. 291 – 297) (with I.N. Herstein)  www.jstor.org/stable/1905540
• 1954: Isotopy of Links (doctoral thesis)
• 1956: On Manifolds Homeomorphic to the 7-Sphere
• 1959: Sommes de Variétés Différentiables et Structures Différentiables des Sphères
• 1959: Differentiable Structures on Spheres
• 1961: Two Complexes which are Homeomorphic but Combinatorially Distinct (in which he disproved the Hauptvermutung)
• 1963: Morse theory
• 1963: Groups of Homotopy Spheres (with Michel A. Kervaire)
• 1965: Lectures on the h-Cobordism Theorem
• 1965: Topology from the Differentiable Viewpoint (2nd edition 1997)
• 1968: Singular Points of Complex Hypersurfaces
• 1971: Introduction to Algebraic K-Theory
• 1973: Symmetric Bilinear Forms (with Dale Husemoller)
• 1974: Characteristic Classes (with James D. Stasheff)
• 1999: Dynamics in One Complex Variable

Sources

• John J. O'Connor and Edmund F. Robertson: "John Willard Milnor": MacTutor History of Mathematics archive

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Milnor, John Willard (1931-  )