Life part 2

In 1948, in Nash's application to Princeton’s mathematics department, Nash's advisor and former Carnegie Tech professor R.J. Duffin wrote a letter of recommendation consisting of a single sentence: ¨This man is a genius¨. Though accepted by Harvard University, which had been his first choice because of what he perceived to be the institution's greater prestige and superior mathematics faculty, he was aggressively pursued by then chairman of the mathematics department at Princeton University, Solomon Lefschetz, whose offer of the John S. Kennedy fellowship was enough to convince him that Harvard valued him less. Thus, from White Oak he went to Princeton Univeristy, where he worked on his equilibrium theory (Nash equilibrium). He earned a doctorate in 1950 with a dissertation on non-cooperative games.The thesis, which was written under the supervision of Albert W. Tusker, contained the definition and properties of what would later be called the "Nash equilibrium". These studies led to four articles:

• ¨Equilibriun Points In N-Person Games¨, Proceedings Of The National Academy Of Sciences (1950),

• "The Bargaining Problem", Econometrica (1950)
• "Two-person Cooperative Games", Econometrica (1953)
• "Non-cooperative Games", Annals of Mathematics (1951)

Nash also did important work in the area of algebraic geometry:

• "Real algebraic manifolds", Annals of Mathematics.

His most famous work in pure mathematics was the Nash embedding theorem, which showed that any abstract Riemannian manifold can be isometrically realized as a submanifold of Euclideam space. He also made contributions to the theory of nonlinear parabolic partial differential equations.