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John Nash

“A Beautiful Mind ” By Andreina Zapata Childhood On June 13, 1928, John Forbes Nash was born in the small Appalachian city of Bluefield, West Virginia, the son of John Nash Sr., an electrical engineer, and Virginia Martin, a teacher. Virginia always had large dreams for her son pushing him to read at 4, learn Latin, and skip a grade at school. The first hint of John Nash’s math talent came in forth grade, when a teacher told Virginia that the boy couldn’t do the mathematics. Virginia laughed, well aware that her son was going down his own path to solve the simple problems. He was an avid reader of Compton's Picture Encyclopedia, Life Magazine, and Time magazine. Later he had a job at the Bluefield Daily Telegraph. At age 12, he was carrying out scientific experiments in his room at home. It was quite apparent at a young age that he didn't like working with other people, preferring to do things alone. He returned the social rejection of his classmates with practical jokes and intellectual superiority, believing their dances and sports to be a distraction from his experiments and studies. Martha, his younger sister, seems to have been a remarkably normal child, while Johnny seemed different from other children. She wrote later in life, "Johnny was always different. [My parents] knew he was different. And they knew he was bright. He always wanted to do things his way. Mother insisted I do things for him, that I include him in my friendships. ... but I wasn't too keen on showing off my somewhat odd brother."

Adolescence and Education In his adolescence, John only had two friends: Kirschner and Donald Reynolds. The first one died when was handling an explosive artifact invented for Nash. Donald was sent to a military school for what he did not treat with someone as odd as Nash. The Nash scientific talent was always evident. He had a Laboratory in his cellar where he made explosives, and animal experiments. In his autobiography, Nash notes that it was E.T. Bell's book Men of Mathematics in particular the essay on Fermat that first sparked an interest for him in mathematics. During war time, when other boys his age wanted to be soldiers, he was inventing secret codes. He attended classes at Bluefield College while still in high school. He later attended the Carnegie Institute of Technology (currently named Carnegie Mellon University) in Pittsburgh, Pennsylvania on a Westinghouse scholarship, where he studied first engineering and later chemistry before switching to mathematics. He received both his bachelor's degree and his master's degree in 1948 while at Carnegie. After graduation, Nash took a summer job in White Oak, Maryland working on a Navy research project being run by Clifford Ambrose Truesdell. From White Oak he went to Princeton University in Princeton, New Jersey, where he worked on his equilibrium theory. He earned a Ph.D. in 1950 with a dissertation on non-cooperative games. The thesis, which was written under the supervision of Albert W. Tucker, contained the definition and properties of what would later be called the Nash equilibrium.

Marriage At the Massachusetts Institute of Technology, he met Alicia Lopez-Harrison de Lardé, a physics student from El Salvador, whom he married in February 1957. Alicia admitted Nash to a mental hospital in 1959 for schizophrenia; their son John Charles Martin was born soon afterward but remained nameless for a year because she felt that John should have a say in the name. John Martin became a mathematician and, like his father, was later diagnosed with schizophrenia. Nash had another son, John David (b. June 19, 1953), with Eleanor Stier, but had little to do with the child or his mother. The couple divorced in 1963 and reunited in 1970, but in a nonromantic relationship that resembled that of two unrelated housemates. Alicia referred to him as her "boarder" and said they lived "like two distantly related individuals under one roof," according to Sylvia Nasar's 1998 biography of Nash, A Beautiful Mind. The couple renewed their relationship after Nash won the Nobel Prize in Economics in 1994. They remarried on June 1, 2001.

Nash Equilibrium

Now well-known-through-Hollywood, John Nash (1928-) won the 1994 Nobel Prize in the Economic Sciences with John Harsanyi and Reinhard Selten, "for their pioneering analysis of equilibria in the theory of non-cooperative---games."

Basic (Micro-Economics) Definition: A Nash Equilibrium is a set of mixed strategies for finite, non-cooperative games between two or more players whereby no player can improve his or her payoff by changing their strategy. Each player's strategy is an 'optimal' response (cf. optimality) based on the anticipated rational strategy of the other player(s) in the game.

Background: At Princeton, in a series of papers published from 1950-1953, "Equilibrium Points in N-Person Games," "Non-Cooperative Games," "The Bargaining Problem," and "Two Person Cooperative Games," Nash outlined a new paradigm for mathematical and economic thinkers with his pioneering use of Equilibrium Theory. He had been accepted to study in New Jersey from his native West Virginia on a Scholarship for (Pure) Mathematics, and worked briefly under the advising of Albert Einstein. Many of Nash's contemporaries refer to him as a (post)modern day 'genius' for his reformations to some of Adam Smith's views on Economics and when considering his more personal characteristics, including his unorthodox teaching and research procedures, and his past experiences with_schizophrenia.

The current (2003) home page of John F. Nash, Jr. at Princeton (Department of Mathematics) notes, "My current research interests include logic, game theory, and cosmology_and_gravitation."

Equilibrium Theory The Nash Theorem maintains its focus on rivalries with mutual gain; a perceptual focus of Nash's mathematical vision found in the light of Leon Walrus' General Equilibrium Theory (published 1874) and John von Neumann's and Oskar Morgenstern's theory of games (1944), now simply called Game Theory. Nash later established his own idea of dominant strategy equilibria through maximization solutions for zero-sum games. He did this with original mathematical techniques to demonstrate the existence of methods for finding a measurable equilibrium in a general class of non-cooperative games.

John Nash can be credited against astonishing odds with making a normative distinction between cooperative and non-cooperative games, and for using mathematical models to support and exemplify his research. But his contribution to theory has become (neo-Nash) a web of explanation(s) and justification(s) far beyond the original conceptions of the author, and has also progressed steadily into the social world; somewhere Nash himself may not have wanted it to go.

Incidentally (as if movies have no influence on science), the film "A Beautiful Mind" won the Oscar Award for Best Picture in 2001. The film was based (via Hollywood) on the life of John Nash; Russell Crowe was nominated for best Actor Oscar for playing the main character.

¡IMPORTANT !

This information only is an exercise to improve the learning about the English Language for the Practice II subject of Modern Languages Faculty of the Carabobo University. For this reason, I give excuses for any incorrect information that you can find about this famous mathematician. Andreina Zapata