Rakesh Vohra of the Game Theory Society reports that not only was John Nash returning from the airport after returning from Norway to receive the Abel Prize in mathematics, its equivalent of the Nobel (the Fields medal is the equivalent of the John Bates Clark award, given for those under 40), which he got for his embedding theorem, which he always viewed as more important than his Nobel prize winning game theory equilibrium, which he considered to be mathematically trivial, despite its wide applicability in economics and other disciplines, but it has only recently been revealed that he had a third major intellectual breakthrough that has only become public since 2012 when the National Security Agency declassified a letter Nash initially wrote in 1950 to its predecessor, the NSA not becoming officially organized until 1952.

In this letter Nash proposed a form of possible encryption used decades later by the NSA based on computational complexity theory, particularly the distinction between N, or polynomial length programs, and NP, or exponential length programs, relative to the key. While declaring this to be a true distinction, he foresaw the later problem that it might be impossible to prove, and so far it has not been, becoming the greatest unsolved problem of computational complexity theory. Nevertheless Nash used this as the key to hardening encryption code systems, with his thoughts on this far ahead of any of the thinking at that time, although it took those he wrote to a long time to realize it and follow up on his advice.

This makes me understand a bit more a famous incident in 1958 reported in Sylvia Nasar's book, A Beautiful Mind, although it did not turn up in the movie version. A. Adrian Albert, chair of the math department at the University of Chicago, then one of the top in the world, offered Nash a position, with him then in the MIT department. He turned down the offer on the grounds that he was expecting to shortly be appointed "Emperor of Antactica." In fact, this was one of the first signs of his developing mental illness, although at the time Albert dismissed this as mere eccentricity, which many brilliant mathematicians exhibit.

What makes this new report from Vohra interesing in light of this is that this secret letter may have been the key to Albert's invitation. The reason for this was a little known fact even now, that during World War II Adrian Albert was almost certainly the top cryptanalyst in the US, with some of his work remaining classified for decades as well. Under the circumstances, it is highly likely that Albert was one of the few people who was privy to Nash's letter at the time and understood its significance. I have no confirmation of this, but the facts about Albert are fairly clear if one googles him properly, with his role in these matters in the US publicly, but not widely, known (

I provide a link to his Wiki entry, which is both sparse and contains at least one mistake). He remains a relatively obscure mathematician, but one , whose importance far outweighs his reputation.

Update: So, there is more about the Albert-Nash link that I have been thinking about, with a further speculation completely unprovable regarding why it was this year that Nash (with Nirenberg) got the Abel Prize. First let me note that Abel's work is closely linked to that of Albert, with Abelian groups being a central focus of Albert's study and linked to the algebraic forms he used in his cryptanalytic (or cryptographic) work. I also suspect that while officially Nash received the prize for his embedding theorem, the revelation of his letter on computational complexity to the NSA (sent in 1955, closer to the year Albert made his job offer to Nash, with that even more evidence that the secret letter was crucial to that rejected job offer), The revelation of this letter may well have provided a tipping point for finally giving the award to Nash, although he had almost certainly been on the list for a long time for the embedding theorem, as he himself considered it his most important work, at least in his public comments, having kept quiet about this letter until its public revelation.

The further wiggle on this is the appearance and success during the past year of the movie about fellow cryptanalyst, Alan Turing, The Imitation Game. Again, I do not know, but my speculation is that this could not have hurt. Both Nash and Turing were the prime subjects of popular movies that depicted both their sufferings and their classified work, although in the movie about Nash it did not show his most serious classified work, but rather depicted it as the central part of his fantasy, and his fantasies did involve matters of international peace and war, with himself both the victim of red-tie wearing communist agents as well as thinking he was an international messianic figure who would achieve world peace between the superpowers. Indeed, the matter of his thinking he would become the Emperor of Antarctica, the ostensible reason he rejected Adrian Albert's job offer, was tied to such fantasies, 1958 being the Internatinal Geophysical Year of Antarctica, when the US and the USSR and 10 other nations signed a treaty to mutually manage Antarctica.

This matter of the letter was not in Sylvia Nasar's book, but he did work for RAND, although probably not on this openly, with most of his more known work there being on game theory, with him becoming upset there by the Dresher-Flood experiments on the repeated prisoner's dilemma showing agents not using the Nash equilibrium but cooperating a lot in the experiments, including even the very rationalistic, Armen Alchian. This upset him so much that it would lead him to abandon game theory work, leaving the naming of the prisoner's dilemma game to his major professor, the late Albert W. Tucker. But, in the end , the more fantastical version in the movie may have been closer to reality, with his close link to the also suffering and highly secret Alan Turing possibly a key to his eventual receipt of this prestigious award, clearly the culmination of his life. It was indeed "going out at the top" that happened in this particular case of a husband-wife death, for better or worse (with their schizophrenic son, Johnny, the clear victim of this situation)..

Further update: The error that I am aware of in Adrian Albert's Wiki entry is the claim that in 1961-62, he was the first director of the Communications Research Division of the Institute for Defense Analysis, located in John von Neumann Hall on the Princeton campus, an NSA front research group. He was the second such director, not the first. (One can find a discussion of Princeton's IDA/CRD unit, no longer on the campus, in James Bamford's seminal book on the NSA,

*The Puzzle Palace.)*
Barkley Rosser