Opinion 144: "Dear Sirs: Nash is a mathematical genius": True, But even more Importantly, John Nash was a True Visionary, who realized that using computers offers "another route to knowledge, rather than mere ideas''

By Doron Zeilberger

Written: May 25, 2015

I just read the New York Times, deservedly long, obituary by Erica Goode, of John Nash, where it said (p. A16, lines 5-9)

"A one-sentence letter written in support of his application to Princeton's doctoral program in math, said simply, 'This man is a genius'".

Few people know that this "one-sentence recommendation letter" was written by John Nash's Carnegie Tech undergraduate mentor, Richard J. Duffin, and the original wording was "Dear Sirs: Nash is a mathematical genius". [ quoted in: line N, page xviii, `Constructive approachs to mathematical models', (C.V. Coffman and G.J. Fix, eds., a volume in honor of R.J. Duffin, Acad. Press, 1979) ]

We all know that Duffin's assessment was more than true, but there are many "geniuses" around. John Nash was not just a genius, but a true visionary. He fully understood the impact of the computer on the future of mathematics, and I was delighted when I heard him say, in the "public lecture" at the 2002 Beijing ICM, (Aug. 21, 2002)

"Nowadays we can do computer experiments using Mathematica, and even solve a system of 42 equations. This offers another route to knowledge, rather than mere ideas''

And he did not only talk, but actually did, in his later years, a pioneering research (that one day would get the recognition that it deserves) in computerized Game Theory, in The agencies method for modeling coalitions and cooperation in games , assisted by then students, Alex Kontorovich, Sebastian Luhmer, and Atul Pokharel, using the computer algebra system Mathematica, and he commented that their work (using Mathematica) was "particularly important".

Let me now share few personal reminiscences. Those who watched the movie probably remember the fictional seminar talk that Russel Crowe, playing John Nash, delivered, after which he was told that he is going to be awarded the Nobel Prize. In real life the talk was given by my good friend and collaborator, the late Herbert S. Wilf, on Oct.10, 1994, in the Institute for Advanced Study's "Combinatorics and Complexity seminar", entitled "Recent Progress in the WZ Theory of Automated Finding and Proving of Identities" as told by Harold W. Kuhn, in the Preface (p. vii) to "The Essential John Nash" [ ed. by H. W. Kuhn and S. Nasar, Princeton University Press, 2002].

In 2005, Drew Sills and I wanted to invite him to give a talk at our Experimental Mathematics Seminar. Drew tried to email and phone him, but both bounced, because the "boxes" were full. Then Drew wrote him snail-mail, never expecting to hear back from him. And indeed, Drew did not hear from him for a few weeks. One day, quite by accident, he checked his "other email account", that he never uses, but for some reason was the one listed in the directory, that John Nash must have gotten from the internet, saying that he would be glad to accept the invitation to talk at our seminar.

This talk (see here) was the most well-attended talk ever, with Standing Room Only, and was also beautiful and lucid, describing "Experimental Game Theory" using Mathematica (mentioned above). Accompanied by Nash was his son, also called John, who got his math PhD from Rutgers twenty years earlier.

Here is the picture from that memorable dinner.

Let me conclude with a quote that I particularly liked from his Autobiography, written for the Nobel committee, and reproduced in the "Essential John Nash".

"So at the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However, this is not entirerly a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos" [my emphasis] .

So geniuses and visionaries, and even the rest of us, mere mortals, should sometimes take "irrationality breaks", but, if possible, not lasting decades.

Rest in Peace, dear John, I will miss bumping into you in the Princeton "dinky".

Added July 14, 2015: Read feedback by Drew Sills.
Opinions of Doron Zeilberger