John Nash

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:

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

his work on the embedding problem

and his work on real algebraic manifolds

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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About Edward Dunne

I am the Executive Editor of Mathematical Reviews. Previously, I was an editor for the AMS Book Program for 17 years. Before working for the AMS, I had an academic career working at Rice University, Oxford University, and Oklahoma State University. In 1990-91, I worked for Springer-Verlag in Heidelberg. My Ph.D. is from Harvard. I received a world-class liberal arts education as an undergraduate at Santa Clara University.
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1 Response to John Nash

  1. Avatar Deane Yang says:

    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

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