(posted May 24, 2015 by Rakesh Vohra)
On Saturday May 23rd, 2015, a taxi bearing John Forbes Nash and Alicia Larde went out of control and hit a guard rail. Both were thrown from the vehicle and met their deaths. Nash was 86 and Larde was 82. Nash is survived by two sons, John Charles Martin Nash and John David Stier.
Nash is known to the wider world because of his struggles with schizophrenia in his youth, and Larde for the care and support she gave him. This was described in Sylvia Nasar’s biography and popularized in a movie with Russell Crowe playing Nash and Jennifer Connelly playing Larde. With the passage of time it appeared that his schizophrenia faded. Nash once remarked that the voices in his head never went away. Rather, he had chosen to ignore them.
Nash was part of that remarkable cohort that passed through Princeton’s Fine Hall in the 1950s. Shapley, Shubik, Tucker, Kuhn, names now familiar in our mouths as household words. Nash himself will be remembered for three things. The first is Nash equilibrium. Legend has it that von Neuman was unhappy with the concept because it gave up on the idea of finding a notion of value for non-zero-sum games. Nevertheless, it stuck as members of this society well know. To say more would be to gild a lilly that needs it not. For this contribution Nash was honored with the 1994 Nobel memorial prize in Economics.
The second is the Nash embedding theorem. It shows that every Riemannian manifold can be isometrically embedded into some Euclidean space. For this contribution, Nash was awarded the 2015 Abel prize. In fact, Nash and Larde were in Norway fours days prior to their deaths for the Abel prize award ceremony, and on their way home from the airport when the accident happened.
Third is his anticipation by at least a decade the notion of computational complexity and trapdoor functions in cryptography. These ideas are outlined in a handwritten letter by Nash to the U.S. National Security Agency in 1955. This letter was declassified in 2012. A succinct summary can be found here as well as a link to a copy of the letters themselves.
In the period after the award of the Nobel, Nash was much concerned with the notion of `ideal money.’ The underlying question was formulated in 1903 by Charles Conant as follows: “Can a better form of standard money be devised than silver and gold? Is a more equitable means attainable of conducting exchanges than by the use of coined money?” Nash’s views on the subject can be found here and are interesting to read in light of current discussions about bitcoin and other alternatives to money.
It should not be forgotten, but probably will, that Nash developed the board game Hex (also invented independently by Piet Hein). It is an example of a connection game played on a board of equal length and width where the game spaces are hexagonal. The players play at perpendicular angles to each other, and the goal of each is to connect from his side to the opposite side.
Further obituaries: New York Times, Guardian, BBC World Service.