# Frases de John Forbes Nash

## John Forbes Nash

**Data de nascimento:** 13. Junho 1928**Data de falecimento:** 23. Maio 2015

John Forbes Nash Jr. foi um matemático norte-americano que trabalhou com teoria dos jogos, geometria diferencial e equações diferenciais parciais, servindo como Matemático Sénior de Investigação na Universidade de Princeton. Compartilhou o Prêmio de Ciências Econômicas em Memória de Alfred Nobel de 1994 com Reinhard Selten e John Harsanyi.

Nash também foi conhecido por ter tido sua vida retratada no filme Uma Mente Brilhante, vencedor de quatro Óscars , baseado no livro-biográfico homônimo, que apresentou seu gênio para a matemática e sua luta contra a Esquizofrenia. Wikipedia

### Citações John Forbes Nash

### „You don't have to be a mathematician to have a feel for numbers.“

Statement of 2006, partly cited in Stop Making Sense: Music from the Perspective of the Real (2015) by Scott Wilson, p. 117

2000s

Contexto: You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers.

### „Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person.“

As quoted in A Beautiful Mind, (2001); also cited in Quantum Phaith (2011), by Jeffrey Strickland, p. 197

2000s

### „People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person in the world.“

As quoted in " A Brilliant Madness A Beautiful Madness http://www.pbs.org/wgbh/amex/nash/ (2002), PBS TV program; also cited in Doing Psychiatry Wrong: A Critical and Prescriptive Look at a Faltering Profession (2013) by René J. Muller, p. 62

2000s

### „I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.“

Statement of 1996, as quoted in Dr. Riemann's Zeros (2003) by Karl Sabbagh, p. 88

1990s

### „One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.“

"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

1950s

Contexto: We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.

### „At the present time I seem to be thinking rationally again in the style that is characteristic of scientists.“

Autobiographical essay (1994)

Contexto: At the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos.

### „A less obvious type of application (of non-cooperative games) is to the study of .“

"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951); as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel

1950s

Contexto: A less obvious type of application (of non-cooperative games) is to the study of. By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration.

### „Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration.“

"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951); as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel

1950s

Contexto: A less obvious type of application (of non-cooperative games) is to the study of. By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration.

### „The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form.“

"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

1950s

Contexto: The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation.

The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games.

### „The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games.“

"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

1950s

Contexto: The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation.

The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games.