Background
Milnor was born on February 20, 1931, in the City of Orange, New Jersey, to John Willard and Emily (Cox) Milnor.
Zürich, Germany
Milnor at the Celebration of the 90th birthday of Beno Eckmann, Zürich
Princeton, NJ 08544, United States
Milnor published his first paper, “On the Total Curvature of Knots,” in 1950 while he was an undergraduate at Princeton University. It has been said that Milnor mistook an unsolved conjecture written on the board for the homework assignment, and his simple yet ingenious solution was the catalyst for this paper. He received his Bachelor of Arts degree in 1951 and continued his doctoral work at Princeton. In 1954 Milnor received his Ph.D. under the direction of Ralph Fox, a mathematician known as the dean of American knot theorists.
Princeton, NJ 08544, United States
Milnor published his first paper, “On the Total Curvature of Knots,” in 1950 while he was an undergraduate at Princeton University. It has been said that Milnor mistook an unsolved conjecture written on the board for the homework assignment, and his simple yet ingenious solution was the catalyst for this paper. He received his Bachelor of Arts degree in 1951 and continued his doctoral work at Princeton. In 1954 Milnor received his Ph.D. under the direction of Ralph Fox, a mathematician known as the dean of American knot theorists.
(The theory of characteristic classes provides a meeting g...)
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory.
https://www.amazon.com/gp/product/0691081220/ref=dbs_a_def_rwt_hsch_vapi_taft_p1_i1
1974
(This elegant book by distinguished mathematician John Mil...)
This elegant book by distinguished mathematician John Milnor provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.
https://www.amazon.com/Topology-Differentiable-Viewpoint-Willard-Milnor/dp/0691048339/ref=sr_1_2?keywords=John+Milnor&qid=1580728956&sr=8-2
1997
(This volume studies the dynamics of iterated holomorphic ...)
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing.
https://www.amazon.com/gp/product/0691124884/ref=dbs_a_def_rwt_hsch_vapi_taft_p1_i2
mathematician professor author
Milnor was born on February 20, 1931, in the City of Orange, New Jersey, to John Willard and Emily (Cox) Milnor.
Milnor published his first paper, “On the Total Curvature of Knots,” in 1950 while he was an undergraduate at Princeton University. It has been said that Milnor mistook an unsolved conjecture written on the board for the homework assignment, and his simple yet ingenious solution was the catalyst for this paper. He received his Bachelor of Arts degree in 1951 and continued his doctoral work at Princeton. In 1954 Milnor received his Ph.D. under the direction of Ralph Fox, a mathematician known as the dean of American knot theorists.
In 1955 Milnor was the Higgins Lecturer at Princeton and he quickly moved through the ranks of assistant, associate, and full professor. In 1962 Princeton appointed him the Henry Putnam University Professor of mathematics.
Milnor was a visiting professor at the University of California at Berkeley during the academic year 1959-1960, and at the University of California at Los Angeles in 1967-1968. He spent two years as professor of mathematics at the Massachusetts Institute of Technology, and then returned to Princeton in 1970 as professor at the Institute for Advanced Study.
At around that time, Milnor became interested in the use of computer graphics to experiment with the new field of dynamical systems. Although he did not begin to publish his work in this area until 1985, he was nevertheless influential through preprints of his work in progress and his collaboration with other mathematicians.
In addition to receiving the 1962 Fields Medal, Milnor was elected to the National Academy of Science in 1963, and has been awarded the National Medal of Science in 1967, the Steele Prize of the American Mathematical Society in 1982, and the Wolf Prize in 1989.
In 1989 Milnor accepted the position of director at the newly formed Institute for Mathematical Sciences at the State University of New York at Stony Brook. In June of 1991, the Institute and the Mathematics Department at Stony Brook organized a conference in honor of Milnor’s sixtieth birthday. The proceedings of the conference contain summaries of Milnor’s work and its influence on geometry, topology, mathematical physics, algebraic geometry, dynamical systems, and others. The participation by 220 mathematicians (including one hundred graduate students) from around the world testifies to Milnor’s lasting influence on these many branches of mathematics.
Milnor contributed to algebraic geometry on singular points of complex hypersurfaces, and in 1961 he showed that the Hauptvermutung (German: “main conjecture”), a principal conjecture in the theory of manifolds concerning triangulations of n-dimensional manifolds, which had been an open question since 1908, is not true for complexes in dimensions greater than 3. Beginning in the 1970s, he worked on complex dynamics.
Milnor was noted as an influential teacher, particularly through his books on the Morse theory and the h-cobordism theorem, which are universally regarded as models of mathematical exposition. His publications include Differential Topology (1958), Morse Theory (1963), Topology from the Differentiable Viewpoint (1965), and Dynamics in One Complex Variable (1999). His Collected Papers were published in five volumes from 1994 to 2010.
Milnor is considered one of the leading topologists in the second half of the twentieth century. In 1956 he astounded the mathematical world with the first example of manifolds that are distinct when considered in the context of calculus, but are equivalent when viewed geometrically. He was awarded the Fields Medal in 1962 for his work in differential topology and the Abel Prize in 2011 for his work in topology, geometry, and algebra.
(The theory of characteristic classes provides a meeting g...)
1974(This volume studies the dynamics of iterated holomorphic ...)
(This elegant book by distinguished mathematician John Mil...)
1997Milnor’s primary work concerned the study of manifolds. These spaces arise in topology - a branch of mathematics related to geometry - and are the analogs of curves and surfaces. Near any point, a coordinate system can be introduced so that the immediate neighborhood of the point looks like ordinary Euclidean space (although it may be of any finite dimension). The coordinate systems for various points can be different but must fit together in a continuous fashion. A smooth manifold results if corners and other sharp folds are prohibited, which can be related to conditions from calculus. In 1956 Milnor published the paper “On Manifolds Homeomorphic to the 7-Sphere,” which presented the first example of a pair of manifolds that are equivalent from the continuous point of view (homeomorphic), but distinct as smooth manifolds when calculus considerations are introduced. Over the next ten years, he studied these “exotic” spheres and found a way to combine them.
Milnor has always been recognized as a master of using current algebraic techniques to analyze complex geometrical objects. In addition to his mathematical innovations, he was known for the clarity of his lectures.
Graduate students would frequently volunteer to write up their notes from Milnor’s courses. They would work with him through countless revisions, each time making further improvements over the previous draft. By means of the resulting mimeographed documents, Milnor’s ability to organize new and complicated fields of mathematics was influential far beyond his immediate students.
Quotes from others about the person
As Lisa Goldberg and Anthony Phillips state in Topological Methods in Modern Mathematics, “When Milnor speaks, you understand.”
Milnor married Brigitte Weber on January 5, 1954. They had three children, Stefan, Daniel, and Gabrielle. His wife now is Dusa McDuff, a professor of mathematics at Barnard College.
