INSIGHTS | P E R S P E C T I V E S
RETROSPECTIVE
John Forbes Nash Jr. (1928–2015)
O
n 23 May, John Nash and his wife Alicia were killed in a car accident in New Jersey. This tragedy came just after he received, at age 86, yet another distinguished award. John’s contributions were in pure mathematics and game theory, which continues to influence the behavioral sciences. His achievements were remarkable, especially given his constant battle with mental illness. In the fall of 1949, many graduate students at Princeton University were assigned rooms in the Graduate College. In one suite, John Nash inhabited a single room, while I shared the double with Lloyd Shapley. John and Lloyd were the mathematicians and I was the economist, and together we pursued our interest in game theory. John was one of the youngest students at the Graduate College. He was from West Virginia, where his father was an engineer and his mother a Latin teacher. He graduated from the Carnegie Institute of Technology with bachelor’s and master’s degrees in mathematics, and arrived at the math department in Princeton in 1948. Highly engaged with game theory, all three of us recognized that a key problem in cooperative games involved establishing a “threat point” from which any bargaining procedure could proceed. Mathematician John Von Neumann and economist Oskar Morgenstern had faced this problem. They had developed a sophisticated theory of cooperative games based on an evaluation of what every subset (S), out of all players (N), could obtain by itself if it did not cooperate with the remaining excluded players (N-S). But they did not give a reasonable way to do this evaluation. Shapley and I worked on this problem, but it was Nash who produced a mathematically elegant solution, as is seen in his paper, published in Econometrica in 1953. With the publication of his thesis, John proved the full generalization of the Cournot equilibrium. When I asked John if he had heard of Cournot, he said that he had, in an economics course. Augustin Cournot conceived of the equilibrium in 1836, but it was not until John generCovles Foundation, Yale University, New Haven, CT, 06520. E-mail: [email protected]
1324
alized it that others started to pick it up, augmenting its influence in economics and other fields. The basic idea behind John’s solution was self-fulfilling expectations. In other words, if individual 1 guesses what individual 2 will do, and vice versa, there will be a pair of actions such that both will be right and neither will be motivated to change. For this, he shared the Nobel Prize in Economics in 1994. John, Lloyd, and I were competitive in our research, which John enhanced with practical jokes such as removing the light bulb from a fixture in our joint bathroom and filling it with water, poised to drench his roommates. Many of us at Princeton also enjoyed inventing playable games that illustrated points and difficulties in game theory development. John had invented a board game called Nash (coincidentally also invented in Denmark as “Hex”), but he also helped craft a game we called So Long Sucker, which required that individuals form coalitions but, in order to win, someone in a coalition had to double-cross his partner. Nash, Shapley, John McCarthy (computer scientist), and I were playing So Long Sucker at tea time in Fine Hall. At a
critical point in the game, Nash saw that a coalition with McCarthy was helpful, and to win, he would have to double-cross McCarthy. Nash did just that. McCarthy was furious and used his last remaining resources to prevent Nash from winning. Nash was completely hurt and surprised. He turned to McCarthy and said, in essence, I do not understand why you are mad at me; you could do the backward induction to have seen that it was completely rational for me to double-cross you, and it was not personal. After receiving his doctorate from Princeton, John joined the mathematics faculty at the Massachusetts Institute of Technology from 1951 to 1959, where he was absorbed with abstract geometry. He married Alicia during that time, but his mental decline escalated and he would face years of hospitalization. John’s battle with schizophrenia became popular knowledge through the 2001 film “A Beautiful Mind.” When in the hospital, he’d send me postcards that were either numerology or Little Richie Rich cartoons. When I finally saw John after his hospital stays in Boston, he was standing in front of the Princeton library looking like a wraith. Gradually over the years, and especially with the boost of a 1/3 share in the Nobel prize, he seemed somewhat stronger and far less disturbed, but the piercing light appeared to have gone out. My wife and I were delighted to see him and Alicia on occasion. We regarded Alicia as a truly wonderful woman who was John’s support and mainstay for much of his life. The last time I saw John was at Stony Brook University a few years ago at a game theory conference. I congratulated John after the announcement of the 2015 Norway award in mathematics (Abel Prize), which he shared with mathematician Louis Nirenberg. I heard from another friend that when John was asked about whether he rated it higher or lower than the Nobel Prize, he replied “is 1/2 better than 1/3?” 10.1126/science.aac7085
sciencemag.org SCIENCE
19 JUNE 2015 • VOL 348 ISSUE 6241
Published by AAAS
PHOTO: ROBERT P. MATTHEWS/PRINCETON UNIVERSITY TRUSTEES
By Martin Shubik
Downloaded from www.sciencemag.org on June 18, 2015
A distinguished mathematician and Nobel laureate dies tragically
John Forbes Nash Jr. (1928−2015) Martin Shubik Science 348, 1324 (2015); DOI: 10.1126/science.aac7085
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The following resources related to this article are available online at www.sciencemag.org (this information is current as of June 18, 2015 ): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/348/6241/1324.full.html This article appears in the following subject collections: Economics http://www.sciencemag.org/cgi/collection/economics
Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright 2015 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS.
Downloaded from www.sciencemag.org on June 18, 2015
Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here.
RETROSPECTIVE
John Forbes Nash Jr. (1928–2015)
O
n 23 May, John Nash and his wife Alicia were killed in a car accident in New Jersey. This tragedy came just after he received, at age 86, yet another distinguished award. John’s contributions were in pure mathematics and game theory, which continues to influence the behavioral sciences. His achievements were remarkable, especially given his constant battle with mental illness. In the fall of 1949, many graduate students at Princeton University were assigned rooms in the Graduate College. In one suite, John Nash inhabited a single room, while I shared the double with Lloyd Shapley. John and Lloyd were the mathematicians and I was the economist, and together we pursued our interest in game theory. John was one of the youngest students at the Graduate College. He was from West Virginia, where his father was an engineer and his mother a Latin teacher. He graduated from the Carnegie Institute of Technology with bachelor’s and master’s degrees in mathematics, and arrived at the math department in Princeton in 1948. Highly engaged with game theory, all three of us recognized that a key problem in cooperative games involved establishing a “threat point” from which any bargaining procedure could proceed. Mathematician John Von Neumann and economist Oskar Morgenstern had faced this problem. They had developed a sophisticated theory of cooperative games based on an evaluation of what every subset (S), out of all players (N), could obtain by itself if it did not cooperate with the remaining excluded players (N-S). But they did not give a reasonable way to do this evaluation. Shapley and I worked on this problem, but it was Nash who produced a mathematically elegant solution, as is seen in his paper, published in Econometrica in 1953. With the publication of his thesis, John proved the full generalization of the Cournot equilibrium. When I asked John if he had heard of Cournot, he said that he had, in an economics course. Augustin Cournot conceived of the equilibrium in 1836, but it was not until John generCovles Foundation, Yale University, New Haven, CT, 06520. E-mail: [email protected]
1324
alized it that others started to pick it up, augmenting its influence in economics and other fields. The basic idea behind John’s solution was self-fulfilling expectations. In other words, if individual 1 guesses what individual 2 will do, and vice versa, there will be a pair of actions such that both will be right and neither will be motivated to change. For this, he shared the Nobel Prize in Economics in 1994. John, Lloyd, and I were competitive in our research, which John enhanced with practical jokes such as removing the light bulb from a fixture in our joint bathroom and filling it with water, poised to drench his roommates. Many of us at Princeton also enjoyed inventing playable games that illustrated points and difficulties in game theory development. John had invented a board game called Nash (coincidentally also invented in Denmark as “Hex”), but he also helped craft a game we called So Long Sucker, which required that individuals form coalitions but, in order to win, someone in a coalition had to double-cross his partner. Nash, Shapley, John McCarthy (computer scientist), and I were playing So Long Sucker at tea time in Fine Hall. At a
critical point in the game, Nash saw that a coalition with McCarthy was helpful, and to win, he would have to double-cross McCarthy. Nash did just that. McCarthy was furious and used his last remaining resources to prevent Nash from winning. Nash was completely hurt and surprised. He turned to McCarthy and said, in essence, I do not understand why you are mad at me; you could do the backward induction to have seen that it was completely rational for me to double-cross you, and it was not personal. After receiving his doctorate from Princeton, John joined the mathematics faculty at the Massachusetts Institute of Technology from 1951 to 1959, where he was absorbed with abstract geometry. He married Alicia during that time, but his mental decline escalated and he would face years of hospitalization. John’s battle with schizophrenia became popular knowledge through the 2001 film “A Beautiful Mind.” When in the hospital, he’d send me postcards that were either numerology or Little Richie Rich cartoons. When I finally saw John after his hospital stays in Boston, he was standing in front of the Princeton library looking like a wraith. Gradually over the years, and especially with the boost of a 1/3 share in the Nobel prize, he seemed somewhat stronger and far less disturbed, but the piercing light appeared to have gone out. My wife and I were delighted to see him and Alicia on occasion. We regarded Alicia as a truly wonderful woman who was John’s support and mainstay for much of his life. The last time I saw John was at Stony Brook University a few years ago at a game theory conference. I congratulated John after the announcement of the 2015 Norway award in mathematics (Abel Prize), which he shared with mathematician Louis Nirenberg. I heard from another friend that when John was asked about whether he rated it higher or lower than the Nobel Prize, he replied “is 1/2 better than 1/3?” 10.1126/science.aac7085
sciencemag.org SCIENCE
19 JUNE 2015 • VOL 348 ISSUE 6241
Published by AAAS
PHOTO: ROBERT P. MATTHEWS/PRINCETON UNIVERSITY TRUSTEES
By Martin Shubik
Downloaded from www.sciencemag.org on June 18, 2015
A distinguished mathematician and Nobel laureate dies tragically
John Forbes Nash Jr. (1928−2015) Martin Shubik Science 348, 1324 (2015); DOI: 10.1126/science.aac7085
This copy is for your personal, non-commercial use only.
If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here.
The following resources related to this article are available online at www.sciencemag.org (this information is current as of June 18, 2015 ): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/348/6241/1324.full.html This article appears in the following subject collections: Economics http://www.sciencemag.org/cgi/collection/economics
Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright 2015 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS.
Downloaded from www.sciencemag.org on June 18, 2015
Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here.
