Mathematician:John Willard Milnor

Mathematician

American mathematician best known for his work in differential topology.

Fields Medal

John Willard Milnor was awarded a Fields Medal in $\text {1962}$ at the International Congress of Mathematicians in Stockholm, Sweden:

Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology.

Wolf Prize

John Willard Milnor was awarded a Wolf Prize for Mathematics in $\text {1989}$:

For ingenious and highly original discoveries in geometry, which have opened important new vistas in topology from the algebraic, combinatorial, and differentiable viewpoint.

Abel Prize

John Willard Milnor was awarded an Abel Prize in $\text {2011}$:

For pioneering discoveries in topology, geometry, and algebra.

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): Milnor, John Willard (1931-  )