John Milnor facts for kids

Quick facts for kids John Willard Milnor
Milnor at the Celebration of the 90th birthday of Beno Eckmann, Zürich
Born	(1931-02-20) February 20, 1931 (age 94) Orange, New Jersey
Nationality	American
Alma mater	Princeton University (AB, PhD)
Known for	Exotic spheres Fáry–Milnor theorem Hauptvermutung Milnor K-theory Microbundle Milnor Map, Milnor number and Milnor fibration in the theory of complex hypersurface singularities, part of singularity theory and algebraic geometry Milnor–Thurston kneading theory Plumbing Milnor–Wood inequality Surgery theory Kervaire-Milnor theorem Isospectral Non-Isometric compact Riemannian manifolds Švarc–Milnor lemma
Spouse(s)	Dusa McDuff
Awards	Putnam Fellow (1949, 1950) Sloan Fellowship (1955) Fields Medal (1962) National Medal of Science (1967) Leroy P. Steele Prize (1982, 2004, 2011) Wolf Prize (1989) Abel Prize (2011) Lomonosov Gold Medal (2020)
Scientific career
Fields	Mathematics
Institutions	Princeton University, Stony Brook University
Thesis	Isotopy of Links (1954)
Doctoral advisor	Ralph Fox
Doctoral students	Tadatoshi Akiba Jon Folkman John Mather Laurent C. Siebenmann Michael Spivak

John Willard Milnor (born February 20, 1931) is an American mathematician. He is famous for his important work in different areas of mathematics. These include differential topology (the study of smooth shapes), algebraic K-theory (a part of algebra), and dynamical systems (how systems change over time).

Milnor is a respected professor at Stony Brook University. He is the only mathematician to have won the Fields Medal, the Wolf Prize, the Abel Prize, and all three Steele prizes. These are some of the highest honors in mathematics.

Early Life and Education

John Milnor was born on February 20, 1931, in Orange, New Jersey. His father, J. Willard Milnor, was an engineer. His mother was Emily Cox Milnor.

Milnor showed great talent for math from a young age. While studying at Princeton University, he won the Putnam Fellow award in both 1949 and 1950. When he was only 19 years old, he proved an important idea known as the Fáry–Milnor theorem.

He earned his first degree in mathematics in 1951. His senior project was about "Link groups." He then continued his studies at Princeton. In 1954, he received his Ph.D. (doctorate) in mathematics. His Ph.D. paper, "Isotopy of links," was also guided by his teacher, Ralph Fox. This paper looked at how different "links" (like tangled loops) can be classified.

A Career in Mathematics

After finishing his Ph.D., Milnor continued to work at Princeton University. From 1970 to 1990, he was a professor at the Institute for Advanced Study. This is a famous place where top researchers work.

He also helped edit the Annals of Mathematics for many years. Milnor has written several math books. These books are known for being very clear and easy to understand. They have inspired many other mathematicians to do their own research. He also served as Vice President of the AMS from 1976 to 1977.

Many students have learned from Milnor. Some of his notable students include Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. Siebenmann, and Michael Spivak. His wife, Dusa McDuff, is also a mathematics professor. She teaches at Barnard College and is known for her work in symplectic topology.

Important Discoveries

One of Milnor's most famous discoveries happened in 1956. He proved that there are 7-dimensional spheres that have unusual smooth structures. This discovery helped start a whole new area of math called differential topology.

He created the term "exotic sphere" for any n-sphere with a non-standard smooth structure. Milnor and another mathematician, Kervaire, studied these exotic spheres. They showed that the 7-sphere, for example, has 15 different smooth structures.

Milnor also worked on the topology of singular points in complex shapes. He developed the idea of the Milnor fibration. His 1968 book, Singular Points of Complex Hypersurfaces, led to a lot of new research in this field.

In 1961, Milnor showed that a long-held idea called the Hauptvermutung was false. He did this by showing two shapes that looked the same but were different in a specific mathematical way.

In 1984, Milnor came up with a new way to define an "attractor" in dynamical systems. These are now called Milnor attractors. They help explain how systems settle into certain patterns over time.

Milnor's current work focuses on dynamics, especially how complex systems change. His work has opened up many new directions in this field. He has given mathematicians many basic ideas, challenging problems, and interesting theorems.

He has also made important contributions to other areas of math. These include microbundles, Hopf algebras, quadratic forms, game theory, and three-dimensional Lie groups.

Awards and Recognition

Milnor has received many awards for his amazing work in mathematics. In 1961, he became a member of the American Academy of Arts and Sciences. In 1962, he won the Fields Medal, which is often called the "Nobel Prize of mathematics."

He was elected to the United States National Academy of Sciences in 1963. He also became a member of the American Philosophical Society in 1965. Other major awards include:

• National Medal of Science (1967)
• Lester R. Ford Award (1970 and 1984)
• Leroy P. Steele Prize for "Seminal Contribution to Research" (1982)
• Wolf Prize in Mathematics (1989)
• Leroy P. Steele Prize for Mathematical Exposition (2004)
• Leroy P. Steele Prize for Lifetime Achievement (2011)

In 1991, a special event was held at Stony Brook University to celebrate his 60th birthday.

In 2011, Milnor was awarded the Abel Prize. This prize recognized his "pioneering discoveries in topology, geometry and algebra." When he heard about the award, Milnor said he was "very surprised."

In 2013, he became a fellow of the American Mathematical Society. This was for his many contributions to different areas of mathematics. In 2020, he received the Lomonosov Gold Medal from the Russian Academy of Sciences.

See also

In Spanish: John Milnor para niños

• List of things named after John Milnor
• Orbit portrait
• Microbundle