John Nash

The life of John Nash

Timeline 1928Born on 13 June in Bluefield, West Virginia, in the United States. 1945Enters the Carnegie Institute of Technology, in Pittsburgh, to study chemical engineering. Switches to mathematics. 1948Arrives at Princeton. Invents the game his colleagues call “Nash”, known today as Hex. 1950Defends the thesis “Non-cooperative games”, with the Nash equilibrium. Publishes “The bargaining problem”. 1951Becomes an instructor at MIT. 1956Publishes the isometric embedding theorem. 1957Marries Alicia Lardé, a physics student at MIT. 1958Publishes the result on the regularity of parabolic equations. 1959First psychiatric hospitalisation. Three decades of illness begin. 1994Receives the Nobel Prize in Economics, with John Harsanyi and Reinhard Selten. 2001Remarries Alicia. The film A Beautiful Mind is released. 2015Receives the Abel Prize, with Louis Nirenberg. Dies in a car crash on 23 May, together with Alicia. ◀ Previous Follow the journey Next ▶ 1928–1945 BluefieldHe grows up in a railway and coal town. He reads Men of Mathematics and proves Fermat’s little theorem by himself. 1945–1948 PittsburghAt the Carnegie Institute of Technology he swaps chemical engineering for mathematics and has the bargaining idea. 1948–1951 PrincetonHe invents Hex and defends his 28-page thesis with the Nash equilibrium. 1951–1959 MITA professor at MIT. He proves the embedding theorem and the result on parabolic equations. In 1959 his illness begins. 1970–2015 PrincetonHe wanders the corridors as “the phantom of Fine Hall” and recovers at the end of the 1980s. 1994 StockholmHe receives the Nobel Prize in Economics, with John Harsanyi and Reinhard Selten. 2015 OsloHe receives the Abel Prize, with Louis Nirenberg. On the way home, on 23 May, he and Alicia die in a taxi crash in New Jersey. Enable JavaScript to see the map. The stages are listed below. John Nash’s places, from Bluefield to Princeton, and the journeys to receive the Nobel and the Abel. Map: © OpenStreetMap contributors

October 14, 2026 Read

The game of Hex: why the first player wins

In 1948, in the common room of the Princeton mathematics building, where professors and students played chess and Go in the afternoons, John Nash presented a new game. The board is a rhombus covered with hexagonal cells, like a honeycomb. Two players, red and blue, take turns placing pieces, one at a time, on empty cells. The pieces never move. Red wants to form a chain of red pieces joining the top edge to the bottom one; blue, a blue chain joining the left edge to the right one.

October 14, 2026 Read

The Nash equilibrium: nobody does better alone

An equilibrium point is an n-tuple such that each player’s mixed strategy maximizes his payoff if the strategies of the others are held fixed. — John Nash, Proceedings of the National Academy of Sciences (1950) In 1944 John von Neumann and the economist Oskar Morgenstern published Theory of Games and Economic Behavior, a huge book that turned strategic decisions into mathematics: card games, wars, markets. Von Neumann’s great result applied to two-player zero-sum games, in which what one wins the other loses, like chess or poker. But most of life is not like that: in a trade deal, a negotiation or traffic, both sides can win together, or lose together.

October 14, 2026 Read

Mixed strategies: the penalty kick and odds and evens

Every finite game has an equilibrium point. — John Nash, Non-Cooperative Games, doctoral thesis (1950) Some games have no equilibrium at all if each player picks a fixed move. The simplest is odds and evens. Ana calls “evens”, Bruno calls “odds”, and each shows one or two fingers. If the sum is even, Ana wins a point; if it is odd, Bruno wins. Reducing each choice to “one” or “two” fingers, the payoffs are:

October 14, 2026 Read

The Nash bargaining solution

A new treatment is presented of a classical economic problem, one which occurs in many forms, as bargaining, bilateral monopoly, etc. — John Nash, The Bargaining Problem (1950) In 1948, still an undergraduate at the Carnegie Institute of Technology, Nash took a course in international economics, the only economics course of his life. He came out of it with a question: when two people negotiate, how do they share the gains from a deal? Economists thought the answer depended on each side’s psychology, skill and bluffing, and that there was nothing to say in general. Nash showed that, if the deal must satisfy a few reasonable requirements, there is only one possible answer. The paper, written before he arrived at Princeton, was published in 1950 in the journal Econometrica.

October 14, 2026 Read

Crumpling without stretching: the embedding theorem

Take a sheet of paper. You can roll it into a cylinder without tearing or stretching it: distances measured on the sheet, with a flexible ruler, stay the same. But you cannot wrap a ball with it without making folds. The sheet and the sphere have different intrinsic geometries, and Gauss proved in 1827 that this difference, the curvature, does not change when the surface is bent without stretching. In the nineteenth century Bernhard Riemann had an even bolder idea: to describe a surface, or a space of any dimension, by its internal measurements alone, without drawing it anywhere. All it takes is a rule, the metric, that says how to measure the length of any curve. This is how general relativity describes spacetime: from inside, without a larger space around it.

October 14, 2026 Read

The heat equation and the regularity of De Giorgi and Nash

In 1900, at the International Congress of Mathematicians in Paris, David Hilbert presented a list of 23 problems that, in his view, would guide twentieth-century mathematics. Problem 19 asked, in simple terms: are the solutions of the “well-behaved” problems of the calculus of variations always smooth functions? Half a century later, the question was still open for an important class of equations. In 1956 Nash heard about it from a colleague and decided to attack it.

October 14, 2026 Read

The legacy of John Nash

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. However I am still making the effort. — John Nash, autobiographical note for the Nobel Foundation (1994) John Nash is the only person to have received both the Nobel Prize and the Abel Prize, the two highest honours in economics and in mathematics. The two halves of his work seem to have nothing in common: one is about human decisions, the other about surfaces and equations. What unites them is the style: attacking problems everyone thought impossible with ideas nobody had had.

October 14, 2026 Read

Image credits

Photographs and images All come from Wikimedia Commons. We use the thumbnails provided by Commons, unedited. Portrait of John Nash, photo by Peter Badge: source page · CC BY-SA 3.0. John Nash in 2006, in Cologne, photo by Elke Wetzig: source page · CC BY-SA 3.0. Isometric embedding of the flat torus, Hevea project, uploaded by Romainbehar: source page · CC0. Blog figures The cover, the Hex board and the graph of the product of gains in bargaining are original illustrations, with versions in each language of the site. The board shows an invented game, in which red has completed its chain.

October 14, 2026 Read