Edward Nelson was born on May 4, 1932, in Decatur, Georgia. He is a professor in the Mathematics Department at Princeton University. He is known for his work on mathematical physics and mathematical logic. In mathematical logic, he is noted especially for his internal set theory. Nelson received his Ph.D. in 1955 from the University of Chicago, where he worked with Irving Segal. He was a member of the Institute for Advanced Study from 1956–1959. He has held a position at Princeton University from 1959 to the present, attaining the rank of professor there in 1964.
Nelson has made contributions to the theory of infinite dimensional group representations, the mathematical treatment of quantum field theory, the use of stochastic processes in quantum mechanics, and the reformulation of probability theory in terms of non-standard analysis.
For many years he worked on mathematical physics and probability theory, and still has a residual interest in these fields, particularly in possible extensions of stochastic mechanics to field theory.
In recent years he has been working on mathematical logic and the foundations of mathematics. One of his goals is to extend IST (Internal Set Theory—a version of a portion of Abraham Robinson's nonstandard analysis) in a natural way to include external functions and sets, in a way that provides an external function with specified properties unless there is a finitary obstacle to its existence. Other work centers on fragments of arithmetic, studying the divide between those theories interpretable in Raphael Robinson's Arithmetic and those that are not; computational complexity, including the problem of whether P is equal to NP or not; and automated proof checking.