Introduction to John Forbes Nash Jr.
Let me introduce you to John Forbes Nash Jr., an American mathematician born in 1928 in West Virginia. He made groundbreaking contributions to differential geometry and partial differential equations, and he's best known for developing the Nash Equilibrium, a key concept in game theory illustrated by examples like the prisoner's dilemma. Nash shared the 1994 Nobel Prize in Economics with two others for laying the mathematical foundations of game theory, and he passed away in a car crash in 2015.
Early Life and Education
You should know that Nash was born in Bluefield, West Virginia, and pursued mathematics at the Carnegie Institute of Technology before earning his doctorate from Princeton University at just 22 years old. It was during his time at Princeton that he started developing his equilibrium theory. He later worked at MIT and the RAND Corporation. In 1959, Nash was diagnosed with paranoid schizophrenia, which disrupted his career for over two decades. By the early 1970s, treatment helped him improve enough to teach again at Princeton, where he spent the last 20 years of his life as a senior research mathematician. He earned the nickname 'Phantom of Fine Hall' for his nocturnal habit of covering blackboards with complex equations. Tragically, in 2015, Nash and his wife Alicia died in a taxi crash in New Jersey at ages 86 and 82, respectively, while returning from Norway where he had received the Abel Prize.
Notable Accomplishments and Deeds
Nash is credited with several pivotal mathematical theories that solidified his reputation. These include the Nash-Moser inverse function theorem, the Nash-De Giorgi theorem, and the Nash embedding theorems, which the Norwegian Academy of Science and Letters described as among the most original results in 20th-century geometric analysis. In a reflective speech, Nash acknowledged the improbability of further achievements at age 66 after a 25-year gap due to his illness, yet he expressed hope for future contributions through ongoing research.
Awards
As I mentioned, Nash received the 1994 Nobel Prize in Economics alongside John C. Harsanyi and Reinhard Selten for their pioneering work on equilibria in non-cooperative games. He also won the 2015 Abel Prize, Norway's prestigious mathematics award given by the Norwegian Academy of Science and Letters in honor of Niels Henrik Abel, recognizing extraordinary mathematical milestones.
Legacy
Nash's work left a lasting impact on mathematics, particularly through concepts like the Nash embedding theorem. He distinguished between cooperative games, where players share objectives, and non-cooperative games involving individual competition. While not a household name, his life story, including his genius and mental health struggles, was captured in the 2001 Academy Award-winning film A Beautiful Mind, starring Russell Crowe and based on Sylvia Nasar's 1998 biography.
Key Takeaways
- John Forbes Nash Jr. was born in 1928 and pioneered differential geometry and partial differential equations.
- He developed the Nash Equilibrium and won the 1994 Nobel Prize in Economics and the 2015 Abel Prize.
- Nash battled paranoid schizophrenia but returned to academia at Princeton.
- He died in a 2015 car crash in New Jersey.
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