# 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.

American

## History

• Born: 20th February 1931, Orange, New Jersey, USA.
• 1949, 1950: Named a Putnam Fellow while at 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

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. Hersteinwww.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