As many of you may have heard by now, John Nash died in a car crash while traveling home from Norway where he had just received the Abel Prize. Here is the obituary in the *New York Times*. Most people are aware of Nash’s work on non-cooperative games, for which he won the Nobel Prize:

**MR0043432****(13,261g)**Nash, John Non-cooperative games.*Ann. of Math. (2)***54,**(1951). 286–295**MR0035977****(12,40a)**Nash, John F., Jr. The bargaining problem.*Econometrica***18,**(1950). 155–162.

Within mathematics, he is equally known for his work on differential equations, such as

**MR0100158****(20 #6592)**Nash, J. Continuity of solutions of parabolic and elliptic equations.*Amer. J. Math.***80**1958 931–954,

his work on the embedding problem

**MR0075639****(17,782b)**Nash, John The imbedding problem for Riemannian manifolds.*Ann. of Math. (2)***63**(1956), 20–63**MR0065993****(16,515e)**Nash, John C1 isometric imbeddings.*Ann. of Math. (2)***60,**(1954). 383–396,

and his work on real algebraic manifolds

**MR0050928****(14,403b)**Nash, John Real algebraic manifolds.*Ann. of Math. (2)***56,**(1952). 405–421.

The embedding theorem depended heavily on what is now known as the Nash-Moser Inverse Function Theorem. Richard Hamilton gave an excellent presentation of that work in the *Bulletin of the American Mathematical Society.*

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Until recently, Nash’s paper on C1 isometric embeddings, as well as Kuiper’s improvement, was viewed by most as only a geometric oddity. However, the techniques developed in the paper have been used recently by De Lellis and Székelyhidi to make significant new progress in the apparently totally unrelated Onsager conjecture on weak solutions to Euler’s equation for fluid flow. See, for example,

MR3254331 Reviewed

De Lellis, Camillo(CH-ZRCH); Székelyhidi, László, Jr.(D-LEIP-IM)

Dissipative Euler flows and Onsager’s conjecture. (English summary)

J. Eur. Math. Soc. (JEMS) 16 (2014), no. 7, 1467–1505.

Slides from a talk on this topic can be found here:

http://www.math.ucr.edu/~fluidspde/Slides/Buckmaster.pdf