Numeric Jungle

A Beautiful Mind

book cover

  • Nash’s Princeton Math PhD thesis on non-cooperative game theory (Nash equilibrium) only has 29 pages, which won him the Nobel Memorial Prize in Economics decades later. He met John von Neumann @Princeton and von Neumann may inspire Nash. However, Nash was skeptical about von Neumann stealing his ideas and stopped speaking with von Neumann.

  • He was an arrogant young man in the graduate school, he once fought with Serge Lang (later a UChicago algebraist published a famous Algebra book) by suggesting Lang to date with his advisor’s daughter.

  • His game theory was somewhat disappointed to his undergraduate advisor (who wrote “He is a mathematical genius” in Nash’s recommendation letter) and other mathematicians since they believe Nash can contribute more in pure math with his talent. At this time, Nash shifted his interests to geometry, differential equations.

  • Being a professor in a top math department was Nash’s goal after PhD, staying in the academia can protect him from the Vietnam War enlistment. He was very stressful about the enlistment and asked for helps from his bosses in school & RAND.

  • In NYU Courant Institute, Nash started to work on partial differential equations (PDE) with Nirenberg and other analysts. With almost no background in mathematical analysis, Nash was able to rediscover many important theorems and inequalities with his own approach. Nash rarely reads books or papers, he tackled hard problems directly and discussed his findings and questions with other top mathematicians, including Lars Hörmander. Although Nash enjoyed the time in Courant, he chose MIT due to the high cost of living in NYC.

  • Ill-temperated and arrogant Nash did not have good relationships with many professors at MIT. A prof once challenged him to solve the embedding theorem (every Riemannian manifold can be embedded in a higher dimensional Euclidean space with distances preserved). Nash claimed he can prove the theorem within a week. Then after a year, he published the paper on Nash’s embedding theorem and won him more respects.

  • After a few productive years, Nash claimed he proved the Riemann hypothesis and he started a series of lectures @Columbia. However, most of his attempts were proposed before and turned out to be false; and he started to have symptoms of schizophrenia during the lectures.

  • Paranoid schizophrenia and inappropriate treatments destroyed Nash in his 30s-60s. Nash suffered greatly in the psychiatric hospitals and insulin shock therapy - a popular risky treatment in the 1960s. He escaped from the hospital several times; he went to France, Eastern Europe and tried to abandon his US citizenship unsuccessfully. While he was paranoid, his classmates John Milnor and Eugenio Calabi already became famous mathematicians.

  • Alicia, Nash’s wife, took great effort to support of Nash and their child, John Charles Nash (who is also schizophrenic). After graduated from MIT, she gave up going to grad school, many good career opportunities; she commuted 4 hours a day in order to take care of Nash. When their child just born, she left their child to her mom and traveled to France since Nash was going there relentlessly. She is definitely a hero behind Nash(s) and mental health care awareness.