“As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "Non-Cooperative Games," also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph. D. thesis with the other results.”

—  John Nash

Autobiographical essay (1994)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea whic…" by John Nash?
John Nash photo
John Nash 23
American mathematician and Nobel Prize laureate 1928–2015

Related quotes

Reinhard Selten photo

“My master's thesis and later my Ph. D. thesis had the aim of axiomatizing a value for e-person games in extensive form. This work made me familiar with the extensive form, in a time when very little work on extensive games was done. This enabled me to see the perfectness problem earlier than others and to write the contributions for which I am now honored by the prize in memory of Alfred Nobel.”

Reinhard Selten (1930–2016) German economist

"Reinhard Selten - Biographical," 1994

Reinhard Selten photo

“My first contact with game theory was a popular article in Fortune Magazine which I read in my last high school year. I was immediately attracted to the subject matter and when I studied mathematics I found the fundamental book by von Neumann and Morgenstern in the library and studied it.”

Reinhard Selten (1930–2016) German economist

"Reinhard Selten - Biographical," 1994

“It was not until my second year as a doctoral student that I began to understand that mathematics was an ever-expanding universe. My thesis advisor at Princeton was Emil Artin, one of the great algebraists of the century. Unfortunately, or perhaps fortunately, he offered me no advice in the selection of a thesis topic. I think it was a fluke that I got started at all. But once I did, a whole new world opened up, to which I would devote a vast amount of time and energy for over thirty years.”

O. Timothy O'Meara (1928–2018) American mathematician

[The Idea of a Catholic University: A Personal Perspective, Marquette Law Review, Winter 1995: Symposium on Religiously Affiliated Law Schools, 78, 2, 389–396, http://scholarship.law.marquette.edu/cgi/viewcontent.cgi?article=1579&context=mulr]

Nicholas Murray Butler photo

“1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.”

Nicholas Murray Butler (1862–1947) American philosopher, diplomat, and educator

Editor's Introduction, The Teaching of Elementary Mathematics https://books.google.com/books?id=NKoAAAAAMAAJ (1906) by David Eugene Smith

David Eugene Smith photo

“1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.”

David Eugene Smith (1860–1944) American mathematician

David Eugene Smith, "Editor's Introduction," in: The Teaching of Elementary Mathematics https://books.google.com/books?id=NKoAAAAAMAAJ (1906)

“Early in 1954 I was appointed Lecturer in Economics at the University of Queensland in Brisbane. Then, in 1956, I was awarded a Rockefeller Fellowship, enabling me and Anne to spend two years at Stanford University, where I got a Ph. D. in economics, whereas Anne got an M. A. in psychology. I had the good fortune of having Ken Arrow as advisor and as dissertation supervisor. I benefitted very much from discussing many finer points of economic theory with him. But I also benefitted substantially by following his advice to spend a sizable part of my Stanford time studying mathematics and statistics. These studies proved very useful in my later work in game theory.”

John Harsanyi (1920–2000) hungarian economist

"John C. Harsanyi - Biographical," 1994

James K. Morrow photo

“The universe,” says Wyvern, “is a Ph. D. thesis that God was unable to successfully defend.”

James K. Morrow book Only Begotten Daughter

Source: Only Begotten Daughter (1990), Chapter 13 (p. 221)

John Nash photo

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

John Nash (1928–2015) American mathematician and Nobel Prize laureate

"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
Context: 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.

Carl Friedrich Gauss photo

“If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

The World of Mathematics (1956) Edited by J. R. Newman

George Pólya photo

“I shall often discuss mathematical discoveries… I shall try to make up a likely story how the discovery could have happened. I shall try to emphasize the motives underlying the discovery, the plausible inferences that led to it… everything that deserves imitation.”

George Pólya (1887–1985) Hungarian mathematician

Induction and Analogy in Mathematics (1954)

Related topics