John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems.

[6] He remained at Princeton to pursue graduate studies and received his Ph.D. in mathematics in 1954 after completing a doctoral dissertation, titled "Isotopy of links", also under the supervision of Fox.

He has written a number of books which are famous for their clarity, presentation, and an inspiration for the research by many mathematicians in their areas even after many decades since their publication.

His students have included Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. Siebenmann, Michael Spivak, and Jonathan Sondow.

Kervaire and Milnor initiated the systematic study of exotic spheres by Kervaire–Milnor groups, showing in particular that the 7-sphere has 15 distinct differentiable structures (28 if one considers orientation).

Milnor's 1968 book on his theory, Singular Points of Complex Hypersurfaces, inspired the growth of a huge and rich research area that continues to mature to this day.

In 1961 Milnor disproved the Hauptvermutung by illustrating two simplicial complexes that are homeomorphic but combinatorially distinct, using the concept of Reidemeister torsion.

Milnor's work has opened several new directions in this field, and has given us many basic concepts, challenging problems and nice theorems.

"[18] Reacting to the award, Milnor told the New Scientist "It feels very good," adding that "[o]ne is always surprised by a call at 6 o'clock in the morning.