Their divorce in 1963 came amid a nine-year series of hospitalizations that began in 1961.
After his discharge in 1970, she felt he would be better off boarding in a room of the house she’d moved to in Princeton Junction than in an institution or on his own.
The game cannot end in a draw, and this fact is highly non-trivial: as shown neatly in these notes it is equivalent Brouwer’s Fixed-Point Theorem, which was later instrumental to Nash’s great work on two-player non-zero-sum games.
Hex was originally invented in 1942 by the Danish polymath Piet Hein.
They married in early 1957 and shortly began raising a family.
The rapid phase of Nash’s descent in early 1959 was “like a tornado.” One must marvel at how she coped in the 1960s with his condition, raising their son, and finding computer-related work near Cambridge and later Princeton.
It was the lead story on for part of this afternoon.
Many stories continue to emerge, among which we mention the NY Times (longer obit), Princeton, a local Princeton site, and appreciations by Peter Woit of Columbia and by Frederic Friedel of Chess Base GMBH. Alicia’s life was one of boldness and courage from the day she emigrated with her family from El Salvador in 1944.
If the first player loses at this game, it’s because he’s made a mistake, but nobody knows what the perfect strategy is.” For board sizes above , Nash’s words are still true, even with the computing might and sophisticated algorithms exerted in this 2013 paper by Jakub Pawlewicz and Ryan Hayward.
The nub was proved in 1976 by Shimon Even and Bob Tarjan: deciding who stands to win a given Hex position on an board is -complete.
White and Black alternate placing stones of their color, with White trying to form a path connecting the north and south borders, Black east-west.
The corner squares count as border for either player.
Nash conceived it independently from an angle that leaps out at us from this account by his fellow Princeton graduate student David Gale, as quoted in Sylvia Nasar’s biography “Gale!