By the time John Nash turned 30 in 1958, he was being hailed as a mathematical genius—a wunderkind who had made pioneering advances in the field of game theory. But in subsequent decades, a devastating struggle with schizophrenia hampered the mathematician’s career; although his ideas remained important, writes biographer Sylvia Nasar, “Nash, the man, was all but forgotten.”
Then, in 1994, Nash won the Nobel Prize in Economics. The recognition spurred “a long period of renewed activity and confidence” that coincided with an improvement in the newly minted laureate’s mental health, according to Princeton University. Now, the award that transformed Nash’s later life has sold for $735,000 at auction.
Engraved with Alfred Nobel’s profile and Nash’s name, the 18-karat gold prize sold at Christie’s Fine Printed Books & Manuscripts auction last week. As Charles Boothe reports for the Bluefield Daily Telegraph, proceeds will go to the John Nash Trust, while funds raised by the separate sale of Nash’s personal papers will benefit the National Alliance on Mental Illness. Per Christie’s, the trove of auctioned documents includes Nash’s 1951 doctoral thesis on game theory, a handwritten lecture he delivered at Princeton, and a note from a high school math teacher telling Nash he “will really go places” if he can manage to “organize [his] work.”
Today, Nash is perhaps best known as the subject of A Beautiful Mind, a 2001 biopic featuring Russell Crowe as the troubled mathematician. But during the mid-20th century, Nash was a bonafide academic celebrity in his own right. He discovered the idea that would lead to his Nobel Prize while still a university student, and his doctoral thesis, published in the Annals of Mathematics in 1951, “established the mathematical principles of game theory,” according to Encyclopedia Britannica.
Game theory is, in essence, a type of mathematics that looks at interactions between two or more “players” in scenarios with “set rules and outcomes.” In the words of the New York Times’ Kenneth Chang, the field focuses on “how to come up with a winning strategy in the game of life—especially when you do not know what your competitors are doing and the choices do not always look promising.” The core concept of game theory is the Nash equilibrium, which Chang broadly defines as “a stable state in which no player can gain advantage through a unilateral change of strategy assuming the others do not change what they are doing.”
A classic example of a Nash equilibrium is the “Prisoner’s Dilemma.” In this scenario, two criminal conspirators are arrested and held separately, each told that if they confess and testify against the other, they will be released without penalty. Their collaborator, meanwhile, will receive a 10-year jail sentence. “If both stay quiet, the prosecutors cannot prove the more serious charges and both would spend just a year behind bars for lesser crimes,” Chang writes. “If both confess, the prosecutors would not need their testimony, and both would get eight-year prison sentences.”
In theory, the smartest approach would be for both suspects to stay silent: This way, each is guaranteed a light sentence. But Nash’s equilibrium posits that both are likely to confess; the criminals can’t communicate, and refusing to confess only works as a strategy if both are on board. By confessing, each suspect can either win their freedom or spend eight years in prison. Remaining quiet, meanwhile, will result in a sentence of either one year or 10.
Game theory is mainly used in economics, but its principles apply to a range of settings, including nuclear strategy, which Christie’s notes was a matter of dire concern during the 1950s.
In an essay written upon receiving the Nobel Prize, Nash, who died in a car crash in 2015, described the “mental disturbances” that began plaguing him in 1959. Admitting he had “spent times of the order of five to eight months in hospitals in New Jersey, always on an involuntary basis and always attempting a legal argument for release,” he also spoke of recovery and a future he felt was laden with promise.
“Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements,” he wrote. “However, I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future.”