# Mathematician:John Willard Milnor

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## 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- )