John Milnor facts for kids
Quick facts for kids
John Willard Milnor
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Milnor at the Celebration of the 90th birthday of Beno Eckmann, Zürich
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| Born | February 20, 1931 |
| Nationality | American |
| Education | Princeton University (BA, MA, 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 areas like differential topology, which studies shapes and spaces, and dynamical systems, which looks at how things 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.
Contents
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.
College Years and Early Discoveries
As a student at Princeton University, Milnor showed great talent. He was named a Putnam Fellow in both 1949 and 1950. Even at just 19 years old, he proved an important idea known as the Fáry–Milnor theorem.
He earned his bachelor's degree in mathematics in 1951. His senior project was about "Link groups." He continued his studies at Princeton. In 1954, he received his Ph.D. in mathematics. His doctoral work was on "Isotopy of links." Both his senior project and his Ph.D. work were guided by his advisor, Ralph Fox.
Career Beginnings
After finishing his Ph.D., Milnor continued to work at Princeton. From 1970 to 1990, he was a professor at the Institute for Advanced Study. He also helped edit the Annals of Mathematics journal 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. He also served as Vice President of the AMS from 1976 to 1977.
Many students have learned from him, including Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. Siebenmann, and Michael Spivak. His wife, Dusa McDuff, is also a mathematics professor at Barnard College. She is known for her work in symplectic topology.
Key Mathematical Discoveries
John Milnor's research has changed how mathematicians understand shapes and spaces. He made many important discoveries.
Exotic Spheres
One of Milnor's most famous discoveries happened in 1956. He proved that there are 7-dimensional spheres that are "different" in a special way. These spheres look like regular spheres but have a unique "smoothness" to them. He called these "exotic spheres." This discovery started a whole new area of math called differential topology.
Milnor and another mathematician, Michel Kervaire, studied these exotic spheres. They found that a 7-dimensional sphere can have 15 different kinds of smoothness.
Understanding Singular Points
Milnor also studied special "singular points" on complex shapes. Imagine a point where a shape might pinch or cross itself. He developed a theory called the Milnor fibration to understand these points better. His 1968 book, Singular Points of Complex Hypersurfaces, helped this area of math grow a lot.
Disproving the Hauptvermutung
In 1961, Milnor showed that a long-held idea in math, called the Hauptvermutung, was not always true. He did this by showing two shapes that looked the same but were built differently.
Milnor Attractors
In 1984, Milnor introduced a new way to define an "attractor" in dynamical systems. An attractor is like a state or set of states that a system tends to evolve towards. His new definition included "unstable attractors." These are now known as Milnor attractors.
Work in Dynamics
Milnor has a strong interest in dynamics, especially how complex systems change over time. He looked at simple families of maps to understand how they behave. His work in this area has opened up many new ideas and problems for mathematicians to explore.
His other important contributions include ideas like microbundles, which are used in geometry, and work on algebraic K-theory, which connects algebra and geometry.
Awards and Recognition
John Milnor has received many top awards for his amazing contributions to mathematics.
In 1961, he became a member of the American Academy of Arts and Sciences. The next year, in 1962, he was awarded the Fields Medal. This is one of the most prestigious awards in mathematics, often called the "Nobel Prize of mathematics."
He was elected to the United States National Academy of Sciences in 1963. In 1965, he joined the American Philosophical Society. He also won the National Medal of Science in 1967.
Milnor has won the Lester R. Ford Award twice (in 1970 and 1984). He has also received the Leroy P. Steele Prize three times: for "Seminal Contribution to Research" (1982), for "Mathematical Exposition" (2004), and for "Lifetime Achievement" (2011).
In 1989, he was awarded the Wolf Prize in Mathematics. In 1991, Stony Brook University held a special event to celebrate his 60th birthday.
In 2011, Milnor received the Abel Prize. This award recognized his "pioneering discoveries in topology, geometry and algebra." When he heard the news, he 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
