John Nash: The Life of a Mathematical Genius and Nobel Laureate

John Nash was a brilliant mathematician who made significant contributions to game theory, differential geometry, and partial differential equations. He was awarded the Nobel Prize in Economics in 1994 for his work on game theory.

A Beautiful Mind: The Life of Mathematical Genius and Novel Laureate John Nash

by Sylvia Nasar

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Language	:	English
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Nash was born in Bluefield, West Virginia, on June 13, 1928. He showed an early aptitude for mathematics and went on to study at Carnegie Mellon University and Princeton University. At Princeton, he completed his doctoral dissertation under the supervision of John von Neumann, one of the most influential mathematicians of the 20th century.

Nash's early work focused on game theory, a branch of mathematics that studies strategic interactions between rational agents. In his seminal paper, "Non-Cooperative Games," Nash proved the existence of Nash equilibria, which are sets of strategies for the players of a game that are stable in the sense that no player can unilaterally improve their outcome by changing their strategy. This work had a profound impact on economics, political science, and other fields that study strategic behavior.

In the early 1950s, Nash began to work on differential geometry, a branch of mathematics that studies the geometry of smooth surfaces. He made significant contributions to the theory of isometric embeddings, which are mappings between two Riemannian manifolds that preserve the distance between points. This work had applications in physics, engineering, and computer graphics.

In the late 1950s, Nash began to work on partial differential equations, a branch of mathematics that studies equations involving functions of several variables. He made significant contributions to the theory of elliptic partial differential equations, which are equations that arise in a wide variety of applications, including fluid dynamics, heat transfer, and elasticity.

Nash's career was interrupted by a period of mental illness. In the early 1960s, he was diagnosed with schizophrenia and spent several years in and out of mental hospitals. During this time, he was unable to work on mathematics. However, in the early 1990s, Nash began to recover from his illness. He returned to teaching and research and eventually won the Nobel Prize in Economics in 1994 for his work on game theory.

Nash's life was marked by both triumph and tragedy. He made brilliant contributions to mathematics, but he also struggled with mental illness. However, he never gave up on his work or his life. He is an inspiration to all who face challenges in their lives.

Nash died in a car accident in 2015. He was 86 years old.

Legacy

John Nash's legacy is immense. His work on game theory, differential geometry, and partial differential equations has had a profound impact on a wide range of fields, including economics, political science, physics, engineering, and computer graphics.

Nash was also a gifted teacher and mentor. He inspired generations of students and helped to shape the future of mathematics.

Nash's story is an inspiration to all who face challenges in their lives. He showed that it is possible to overcome adversity and achieve great things.

Awards and honors

• Nobel Prize in Economics (1994)
• John von Neumann Theory Prize (1978)
• Abel Prize (2015)
• Member of the National Academy of Sciences
• Member of the American Academy of Arts and Sciences
• Doctor of Science degrees from Carnegie Mellon University, Princeton University, and Harvard University

Books and movies

Nash's life has been the subject of several books and movies, including:

• A Beautiful Mind (book by Sylvia Nasar, 1998)
• A Beautiful Mind (movie directed by Ron Howard, 2001)
• Nash Equilibrium (book by Ken Binmore, 2007)

Further reading

• Nobel Prize biography
• AMS obituary
• New York Times obituary

A Beautiful Mind: The Life of Mathematical Genius and Novel Laureate John Nash

by Sylvia Nasar

4.5 out of 5

Language	:	English
File size	:	18084 KB
Text-to-Speech	:	Enabled
Enhanced typesetting	:	Enabled
X-Ray	:	Enabled
Word Wise	:	Enabled
Print length	:	465 pages
Screen Reader	:	Supported

FREE