Reflection Paper on a Beautiful Mind
A Beautiful Mind is a story based on the life of the famous mathematician John Forbes Nash, Jr. His contributions to mathematics are outstanding. When he was an undergraduate, he proved Brouwer's fixed point theorem. He then broke one of Riemann's most perplexing mathematical problems and became famous for the Nash Solution. Game Theory from then on, Nash provided breakthrough after breakthrough in mathematics. In 1958 John Forbes Nash was described as being 'the most promising young mathematician in the world'. John solved problems in mathematics that many mathematicians deemed not solvable. On the threshold of such a promising and outstanding career, he then went on to suffer through three decades of a devastating form of paranoid schizophrenia. He lost his teaching professions and his job. He refused all medical treatment and spent years in and out of delusional states. Remarkably, in 1994 John won the Nobel Prize in Economic Science for his work on Game Theory, he was only 21 when he wrote his paper.
The story of John Forbes Nash Jr. is definitely connected with Logic, as he is a mathematician. In his breaking of many perplexing mathematical problems, he used logic. And in producing his famous Game theory, logical systems were used. Among the important properties that logical systems can have:
Consistency, which means that no theorem of the system contradicts another.
Validity, which means that the system's rules of proof will never allow a false inference from true premises. A logical system has the property of soundness when the logical system has the property of validity and only uses premises that prove true (or, in the case of axioms, are true by definition).
Completeness, which means that if a theorem is true, it can be proven.
Soundness, which means that the premises are true and the argument is valid. In one of the scenes in the movie, where Nash was in a bar with friends, the use of logic was very evident. While Nash and his friends
The story of John Forbes Nash Jr. is definitely connected with Logic, as he is a mathematician. In his breaking of many perplexing mathematical problems, he used logic. And in producing his famous Game theory, logical systems were used. Among the important properties that logical systems can have:
Consistency, which means that no theorem of the system contradicts another.
Validity, which means that the system's rules of proof will never allow a false inference from true premises. A logical system has the property of soundness when the logical system has the property of validity and only uses premises that prove true (or, in the case of axioms, are true by definition).
Completeness, which means that if a theorem is true, it can be proven.
Soundness, which means that the premises are true and the argument is valid. In one of the scenes in the movie, where Nash was in a bar with friends, the use of logic was very evident. While Nash and his friends