A Beautiful Mind

Nonfiction | Biography | Adult | Published in 1998

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Part 1, Chapters 18-20Chapter Summaries & Analyses

Chapter 18 Summary: “Experiments, RAND, Summer 1952”

In the summer of 1952, Nash takes a cross-country trip from Bluefield to Santa Monica. Graduate mathematics student John Milnor joins him in his own car. They are accompanied by Nash’s sister Martha, travelling in Milnor’s car, and Ruth Hincks, a journalism student who travels with Nash.

Ruth, “slim, attractive, intelligent” (147), is surprised that Nash pays her little interest, “never even notic[ing] I was there” (147). Part way through the trip, they have a falling out, and Martha is “forced, reluctantly, to ride with her older brother for the remainder of the journey” (148). Ruth leaves the group when they reach Santa Monica, but the other three rent an apartment near RAND where the two mathematicians will be working temporarily over the summer.

Nash and Milnor “spend most of their waking hours inside the RAND headquarters” (149), largely working on solo projects. They do, however, collaborate on an experiment “designed to test how well different theories of coalitions and bargaining [hold] up when real people [are] making the decisions” (149). They design a series of games in which players are “told they [can] win cash by forming coalitions” but will only receive the money if they “commit in advance to a given division of the winnings” (149-150).

As with the Prisoner’s Dilemma experiment, contrary to Nash’s theory, the experiment finds that “players’ decisions [are] often motivated by concerns about fairness” (150). Nash and, especially, Milner become disillusioned, questioning “the predictive power of game theory” (150). Although Nash and Milner consider the experiment a failure, economists will return to it decades later as a useful model for economic research.

After Nash makes a pass at Milnor and is rejected, the relationship breaks down and Milnor moves out of the apartment. Despite this, Nash’s feelings towards Milnor may be “something close to love” (151).

Chapter 19 Summary: “Reds, Spring 1953”

In the early 1950s, Cold War paranoia leads to the rise of McCarthyism “which blame[s] the setbacks in [the Cold War] on sinister conspiracies and domestic subversion” (152). Everyone from film stars to academics is accused of being communist sympathizers collaborating with the enemy.

Several MIT mathematicians, including Norman Levinson, are among the accused and are forced to testify. Levinson, who had indeed been a member of the Communist Party at one stage, manages to give “a series of forceful and elegant answers” (153) that both defend the “youthful idealism that led him into the party” (153-154) and deny that communism is truly “a threat to the nation” (154).

While many universities turn their back on academics accused of being communist sympathizers, MIT supports its staff. Thanks in part to Levinson’s strong testimony, the accused academics manage to keep their jobs. Despite this, the incident is a reminder to the academics around them, including Nash, that “the world they very much [take] for granted [is] dangerously fragile and vulnerable to forces beyond its control” (153).

Chapter 20 Summary: “Geometry”

In 1953, Nash becomes an assistant professor at MIT, much to the annoyance of his colleague Warren Ambrose. A genuine “radical and nonconformist” (156), he is irritated by Nash’s pretenses as a “free thinker” as well as his arrogance and childishness.

For his part, Nash regularly plays pranks on Ambrose and is frequently dismissive of his work. On one occasion, Ambrose responds by saying, “If you’re so good, why don’t you solve the embedding problem for manifolds?” (156). The problem is “notoriously difficult” (156) and has remained unsolved since being posed in the nineteenth century. Spurred on by Ambrose’s challenge, Nash sets out to solve the problem, working with incredible dedication, “mostly at night in his MIT office – from ten in the evening until 3:00 a.m.” (160).

Eventually Nash succeeds, demonstrating that “you could fold the manifold like a silk handkerchief, without distorting it” (158), something nobody had predicted. Nash’s findings and methods are so original and idiosyncratic that “even the experts [have] tremendous difficulty understanding what he [has] done” (162). Eventually, however, like his other work, it is celebrated for its “incredible originality” (158). To his credit, Ambrose’s “applause [is] as loud or louder anyone else’s” (163).

Chapters 18-20 Analysis

Sexuality and relationships return as significant themes in chapter 18, both in terms of Nash’s lack of interest in Ruth and his failed attempt to seduce Milnor. Many of the times Nash is drawn to another person, it is another man, usually a highly intelligent mathematician, who catches his eye.

Isolated by his intellect and idiosyncratic thought processes, it is perhaps understandable that Nash is able to relate most to other mathematically-minded people with whom he shares a common language, the vast majority of whom are men. However, in the extremely homophobic climate of 1950s America, pursuing this attraction on a romantic or sexual level is difficult.

It is not only a fear of homosexuality that dominates the national mood. With the rise of McCarthyism, the fear that communist sympathizers are collaborating with the enemy is everywhere and several MIT professors are accused. Although they get off and keep their jobs, the incident reminds academics like Nash that the bubble of academia is not invulnerable to wider forces, something that will later come back to haunt Nash when he is caught in a sting operation targeting homosexuals.

Around the same period, Nash loses interest in game theory when experiments again show that people are generally “motivated by concerns about fairness” (150) rather than self-interest as his theories and perspective on life predict. He explores other areas of mathematics and makes a particularly remarkable breakthrough in geometry, solving a problem that has vexed mathematicians for a century. Once again, it is the “incredible originality” (158) of his thought processes and working methods that allow him to make this breakthrough.