Tell me a bio of John Forbes Nash Jr..

Include key facts about their life, career, achievements, and impact.

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John Forbes Nash Jr. was a renowned American mathematician, economist, and philosopher. He was born on June 13, 1928, in Bluefield, West Virginia, to John Forbes Nash Sr. and Margaret Virginia Martin Nash. Nash's early life was marked by a strong interest in mathematics, which was encouraged by his parents.

**Education and Career:**

Nash attended Carnegie Institute of Technology (now Carnegie Mellon University), where he earned his Bachelor's degree in mathematics in 1948. He then moved to Princeton University, where he earned his Ph.D. in mathematics in 1950. Nash's Ph.D. thesis, "Non-Cooperative Games," introduced the concept of Nash equilibrium, a fundamental idea in game theory.

**Achievements:**

Nash's work in game theory revolutionized the field of economics and mathematics. His most notable contribution is the Nash equilibrium, which describes a stable state in a game where no player can improve their outcome by unilaterally changing their strategy. This concept has far-reaching implications in economics, politics, and social sciences.

**Awards and Recognition:**

Nash's work earned him numerous awards and recognition, including:

1. **John von Neumann Theory Prize** (1996) for his contributions to game theory and economics.
2. **Nobel Memorial Prize in Economic Sciences** (1994) for his work on game theory, along with John Harsanyi and Reinhard Selten.
3. **National Medal of Science** (1978) for his contributions to mathematics and economics.

**Personal Life and Struggles:**

Nash's personal life was marked by struggles with mental health. He was diagnosed with paranoid schizophrenia in the late 1950s and spent several years in and out of hospitals. Despite his struggles, Nash continued to work on mathematics and economics, often in isolation.

**A Beautiful Mind:**

The book "A Beautiful Mind" by Sylvia Nasar, published in 1998, tells the story of Nash's life, including his struggles with mental health and his contributions to mathematics and economics. The book was adapted into a film in 2001, starring Russell Crowe as Nash.

**Legacy:**

John Nash's legacy extends far beyond his mathematical contributions. His work has influenced fields such as economics, politics, and social sciences. His story has also inspired countless people to pursue careers in mathematics and economics, despite the challenges they may face.

Nash passed away on May 23, 2015, at the age of 86, leaving behind a legacy of groundbreaking work and a testament to the power of human resilience.
John Forbes Nash Jr. was an American mathematician and economist born on June 13, 1928, in Bluefield, West Virginia. He is best known for his work on game theory, differential geometry, and partial differential equations.

**Early Life and Education**

John Nash was the son of a physician and grew up in a family that valued education. He showed a keen interest in mathematics from an early age and entered Carnegie Institute of Technology (now Carnegie Mellon University) in 1945, where he studied mathematics. He later transferred to Princeton University, where he earned his undergraduate degree in 1948 and his Ph.D. in 1950 under the supervision of Albert W. Tucker.

**Career**

Nash's career as a mathematician and economist spanned over six decades. He made significant contributions to several fields, including:

1. **Game Theory**: Nash's most notable work is the development of the Nash equilibrium, a fundamental concept in game theory that describes the stable state of a game, where no player can improve their outcome by unilaterally changing their strategy.
2. **Differential Geometry**: Nash's work on differential geometry included the development of Nash manifolds, which are used to describe the geometry of curved spaces.
3. **Partial Differential Equations**: Nash made significant contributions to the study of partial differential equations, including the development of the Nash-Moser theorem.

**Achievements**

Nash's achievements include:

1. **Prix Nobel d'Economie** (1994) for his work on game theory, which he shared with John Harsanyi and Reinhard Selten.
2. **John von Neumann Theory Prize** (1978) for his work on game theory and economics.
3. **American Mathematical Society's Steele Prize** (1968) for his work on differential geometry.

**Challenges and Mental Health**

Nash struggled with mental health issues throughout his life, including paranoid schizophrenia. His condition began to manifest in the early 1950s, and he was hospitalized several times for treatment. Despite these challenges, Nash continued to work on his mathematics and made significant contributions to his field.

**Legacy**

John Nash's work has had a profound impact on economics, game theory, and mathematics. His contributions have influenced fields such as economics, political science, and computer science. The movie "A Beautiful Mind" (2001), directed by Ron Howard and starring Russell Crowe as Nash, helped to raise awareness about Nash's life and work.

**Personal Life**

Nash married Alicia Lardé Lovelace in 1957, and they had one son, John Charles Martin Nash, who died in 1985. Alicia Nash was a strong support for John throughout his struggles with mental health and was instrumental in helping him to achieve his goals.

John Nash passed away on May 23, 2015, at the age of 86. His legacy continues to inspire mathematicians, economists, and scientists around the world.