Edward Nelson
Edward Nelson ( born May 4, 1932 in Decatur, Georgia) is an American mathematician who deals with analysis, mathematical physics, probability theory and logic.
Life and work
Nelson studied at the University of Chicago, where in 1953 he took his master's degree and received his doctorate in 1955. 1956 to 1959 and in 1973/74 he was at the Institute for Advanced Study. After that he went to Princeton University, where he was an assistant professor in 1959, associate professor in 1962 and professor in 1964.
The early work of Nelson dealt with infinite-dimensional representations of groups, mathematical quantum field theory and stochastic processes in the foundations of quantum mechanics, presented in his book Dynamical theories of Brownian motion that also deals with physical aspects. Its stochastic mechanics as an interpretation of quantum mechanics, he gave in the 1980s to
Nelson is known for its Internal Set Theory, a version of Abraham Robinson's nonstandard analysis, in which the axioms of set theory are supplemented. He was also involved in the reformulation of the theory of probability in the context of nonstandard analysis. His other interests include complexity theory (including the P- NP problem ).
He is a member of the American Academy of Arts and Sciences since 1997 and of the National Academy of Sciences. Nelson is an honorary doctorate from the University of Strasbourg. In 1995 he received the Leroy P. Steele Prize. In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver ( Markov fields ).
Writings
- Dynamical Theory of Brownian Motion. Princeton University Press 1967
- Topics in Dynamics 1: flows. Princeton University Press 1969
- Tensor analysis. Princeton University Press 1967
- Quantum Fluctuations. Princeton University Press, 1985
- Predicative Arithmetic. Princeton University Press, 1986
- Radically elementary probability theory. Annals of Mathematical Studies, Princeton 1987