A Beautiful Mind Summary and Review

by Sylvia Nasar

Has A Beautiful Mind by Sylvia Nasar been sitting on your reading list? Pick up the key ideas in the book with this quick summary.

  Eccentric and reclusive personalities almost seem to go hand in hand with a great mind. Great scientists and philosophers such as René Descartes, Ludwig Wittgenstein, Immanuel Kant, Thorstein Veblen, Isaac Newton, and Albert Einstein had difficulties interacting with the more mundane among us. The Nobel Prize-winning mathematician, John Nash, had his career shaped by his personality more than most. The obsessiveness that contributed to his being diagnosed with paranoid schizophrenia later in life is impossible to detach from his consuming love of mathematics. The 2001 film,

In this summary of A Beautiful Mind by Sylvia Nasar,

 based on this book revealed to the general public a bit about Nash’s life. The film won four Oscars and was nominated for four more. Yet, as riveting as it was, there’s more to Nash’s life than that cinematic story. In this book summary, you’ll delve a deeper into the fascinating life of John Forbes Nash Jr.   In this book summary, you’ll learn
  • How a board game helped Nash fit in
  • The day inspired by John Nash at Princeton
  • How not to break off a relationship

A Beautiful Mind Key Idea #1: Just a boy

Despite being one of the greatest mathematical minds of the twentieth century, John Nash’s origins were quite humble. Born in Bluefield, West Virginia, on June 13, 1928, John’s father, John Sr., was an electrical engineer, and his mother, Margaret, was a schoolteacher. Little is known about his early childhood, but it appears Nash’s family was stable and lived a comfortable enough life. But Nash’s distinctive character kept him from fitting in. The boy who was so brilliant was extremely socially awkward at elementary school, always preferring books to people. Worried about his lack of social skills, his parents enrolled John in activities to help him socialize such as Sunday school and Boy Scouts. Unfortunately, this didn’t help much. Nash’s mathematical genius began to reveal itself at the tender age of thirteen or fourteen. His passion for mathematics seems to have been sparked by a book devoted to the lives of great mathematicians, E. T. Bell’s Men of Mathematics. You might expect someone who was to be a future genius to get good grades. This wasn’t necessarily the case. John got a B minus in fourth-grade math, for instance, being marked down because he didn’t show his work. This pattern continued into high school; where he would simply solve the problem in his head using novel, or unorthodox methods and write the answers out. When he entered the university, he decided to become a proper mathematician. With aspirations to become an engineer like his father, John enrolled with a full engineering scholarship at Carnegie Institute of Technology (CIT), in Pittsburgh, known today as Carnegie Mellon. Nash quickly found himself bored by lab experiments and mechanical drawing. On the other hand, he really liked his mathematics courses. Nash’s startlingly original methods for solving difficult mathematical puzzles astounded his professors. They convinced him to switch majors in his second year. Nash’s destiny was now fixed as a mathematician.

A Beautiful Mind Key Idea #2:

A Beautiful Mind Key Idea #3: True genius

Princeton, Harvard, Chicago and Michigan had all made him offers, so Nash found that he could take his pick when it came to grad school. While his first choice was Harvard, Princeton offered him a better scholarship. This swayed Nash and thus his nearly six-decade-long association with Princeton was formed. Princeton was perfect for Nash. The institution provided plenty of academic freedom for its mathematics students to develop intellectually rather than forcing them into more conventional programs. Princeton’s reputation as a mathematical mecca had grown since World War II. While famous intellectuals such as Einstein graced their lecture halls, more importantly, the school allowed an unusual amount of freedom to their students. Unlike most universities, new graduate students were told on their very first day that grades and class attendance were unimportant. Instead, they were asked to come to tea every afternoon, when students and professors discussed research and share ideas in an informal setting. Taking full advantage of this freedom: Nash never went to a single mathematics class. He preferred to ruminate on mathematical problems while he wandered the hallways, whistling Bach’s fugues. Every once in a while he’d scribble down notes. This behavior drove his colleagues crazy. Just as in elementary school, Nash wasn’t particularly well-liked at Princeton at first. Princeton’s awkward egghead graduates soon formed cliques under the charge of different professors. They would often go out drinking as a group. But Nash was never invited. He was a serial loner. Actually, it was his intention to stay apart from the others. He was worried that getting too close to any single professor would have a negative influence on his ideas. Few wanted to spend any time with someone who exhibited such antisocial behavior. However, Nash’s popularity skyrocketed and his fate changed when he invented a popular strategic board game. The game, christened “Nash” by its participants, was played in many university common rooms. Coinciding with the beginning of Nash’s interest in game theory, his favored mathematical field, the invention was no accident. This game was later popularly marketed as Hex.

A Beautiful Mind Key Idea #4:

A Beautiful Mind Key Idea #5: Game Theory

Nash studied under the father of modern game theory, John von Neumann, at Princeton. Von Neumann’s research on game theory had laid out the basics, yet it was extremely restricted in application. Nash determined to take game theory further. The task of game theory is to develop mathematical models of rational human decision-making. These decisions specifically take place during games that involve conflict or cooperation like poker or chess. The theory von Neumann developed had a serious issue. Its mathematical proof was confined to two-player, zero-sum games, thus severely limiting its usefulness. A zero-sum contest means that the amount won by one player is equal to that lost by the other, thus there’s no benefit to cooperation, only conflict. Poker is an excellent example of a zero-sum game Von Neumann had not established the more complex mathematical proof for non-zero-sum games involving two or more players. Seeing this gap as a great challenge, Nash tackled a mathematical proof that covered the outcomes of non-zero-sum games in his 27-page doctoral thesis. This proof was crucial in making Game Theory more significant to real-world applications in fields such as economics, where cooperation is more important than conflict. Even though Neumann’s work had been useful, the truth is two-person zero-sum games aren’t that common in the real world. In most practical situations, even war, cooperation can be of benefit sometimes. The breakthrough Nash made in game theory was to distinguish between cooperative and non-cooperative games. This meant he was able to determine mathematically rational human behavior based on the possibility of mutual gain. Strictly speaking, a non-zero-sum game can be analyzed if each player independently decides on the best response to his opponents’ most advantageous strategy. Known as the Nash equilibrium, this proof ensured that Nash would win a Nobel Prize half a century later.    

A Beautiful Mind Key Idea #6: New Horizons

Nash’s thesis on Game Theory was astounding and he received wide recognition for his work. However; it wasn’t enough to earn a professorship at Princeton, which was his dream job. This was no surprise. Nash was also well known for his misanthropy and eccentricity so he was hardly an ideal candidate for a teaching position. Massachusetts Institute of Technology (MIT), did offer him a post. So, in June of 1951, Nash made the move to Boston as an instructor hoping he was on track for tenure. Yet again, Nash’s eccentricities made him stand out, and he wasn’t a particularly popular professor. His meandering lectures were difficult to track and he gave tricky exams that he graded very harshly. As a sign of their displeasure, some of his students scrawled, “THIS IS HATE JOHN NASH DAY!” on blackboards throughout the university. Despite his unpopularity as a teacher, Nash did eventually manage to form the beginnings of a normal social life in Boston. For the first time in his life, Nash began to meet with people in public places such as cafes, restaurants and beer halls. Donald Newman became his most valued friend.   Mr. Newman was a Harvard graduate and mathematician, but more importantly, Nash considered him his intellectual equal. Nash’s first uneasy involvement with the opposite sex also took place in Boston. During hospitalization for minor surgery, Nash met Eleanor Stier who was a nurse there. They began a secret relationship, which resulted in the birth of Nash’s first child. When he found out about the pregnancy and despite his initial affection, Nash defied the expectations of the day and didn’t ask Stier to marry him. Perhaps he regarded the match as unsuitable due to his high opinion of his own intellect, and his lower opinion of Stier’s. John David Stier spent his early years in foster care, as Stier was poor and Nash contributed nothing to help support his young child. Through the years, Stier held out hope that his affection would one day lead to a proposal of marriage since Nash did visit Stier and their child.  

A Beautiful Mind Key Idea #7: Ladies man

It was unclear what, if anything, Nash hoped to gain by his sporadic relationship with Eleanor Stier and his son. The crush that Alicia Larde, a young physics student, had on her professor, John Nash, was much less ambiguous. There were few female physics students enrolled at MIT, in the 1950s. Furthermore, in the academic environment, it was quite common for a young and attractive mathematical genius like Nash to be idolized. When Nash finally asked Larde out in the spring of 1955, they began dating occasionally. In Nash’s mind, Larde had some advantages over the mother of his child, Elanore Stier. To begin with, Larde was from the upper class. More importantly, she was intellectually and academically gifted. During this time, Nash hadn’t been honest with Stier about his new relationship. About a year after Nash began dating Larde, Stier made an unannounced visit to Boston and visited Nash’s home. She found Nash and Larde in bed together. Deciding this was the last straw and that Nash would never marry her, Stier steeled herself and did what she had not dared to do before. She hired a lawyer to sue for child support and told Nash’s parents that they had a grandchild. She also threatened to ruin his career by exposing Nash’s affair with Larde to the officials at MIT. Although he had been trying to lead separate lives, everything had collapsed around Nash. Finally, he was forced to make a decision. While he still refused to marry Stier, he agreed to begin paying child support. After this event, Nash went to New York on sabbatical. Now looking for work, Larde, was on her way to the Big Apple as well. It is unknown whether Nash proposed to Larde before or after her move to New York. The engagement went public in October of 1956. Larde went to Thanksgiving dinner as Nash’s fiancée. Nash and Larde were married in February 1957. They lived as man and wife in Manhattan’s Upper East Side.

A Beautiful Mind Key Idea #8:

A Beautiful Mind Key Idea #9: Immense stress

In 1958 Nash had not had any mathematical breakthroughs since his graduate thesis on the equilibrium. Nearing the age of 30, he became increasingly anxious. He was consumed with worry because he hadn’t yet been given tenure at MIT. It was at this time; Nash decided to work on a notoriously difficult unsolved problem related to the distribution of prime numbers called the Riemann hypothesis. Nash’s wife gave him some momentous news just as he was committing his entire intellectual capacity to the Riemann hypothesis. She was pregnant. This news only added to Nash’s anxiety. People who knew Nash started noticing small changes in his already eccentric behavior around this time. It wasn’t just preoccupation with the Riemann hypothesis, there was more to it. Nash’s friends were shocked to discover that, while he had been financially prudent in the past, he became obsessed with the stock market. Nash had invested his mother’s savings on the stock exchange. Nash was convinced his colleagues were spying on his work on the Riemann hypothesis. He even accused them of going through his trash. In January 1959, Nash announced in the MIT common room and to no one in particular that aliens were sending encrypted messages through the New York Times that only he could understand. In February things got even stranger.   An old school friend received a strange letter from Nash claiming that aliens were trying to ruin his career. He’d written it in four different ink colors. Even though everyone thought at first the behaviors were just a case of an eccentric personality enjoying an inscrutable private joke, it soon became clear that it was not a performance. In fact, the situation continued to worsen.

A Beautiful Mind Key Idea #10:

A Beautiful Mind Key Idea #11: Turning a corner

Nash’s sudden mental degeneration could not have come at a worse time.  Not only was he was the point of being offered tenure at MIT, but Nash had also been offered a prestigious professorship at the University of Chicago. Nash very politely declined Chicago’s offer. As Emperor of Antarctica, he explained in a letter, he couldn’t take up the position. The tipping point came for his wife, Alicia, when, in the middle of the night, Nash made his way to Washington, DC, to hand deliver letters announcing to a number of embassies his imminent world government. Realizing her husband urgently needed medical help, she had him involuntarily committed to a Psychiatric hospital, for observation. Nash was diagnosed with paranoid schizophrenia in April 1959 after three weeks of observation by the doctors at Harvard’s McLean Hospital. Sometimes described as cancer of the mind his illness entails a disordering of thoughts and emotions, hallucinations, and delusionary thinking. This illness had manifested for Nash as extreme detachment, a newfound belief in extraterrestrial beings, and suspiciousness of those around him. Nash was put into a treatment program on an involuntary basis. The program at McLean involved both therapy and antipsychotic medication. Nash had a pronounced response to the medication he received. So much so, he was given the all clear for release only 50 days after committed. However, his remarkable recovery was discovered to be a sham. Nash, feeling his treatment to be a form of imprisonment, had simply fabricated his recuperation so as to break free. Once out of the hospital, Nash decided it was essential for him to leave for Europe. His wife, Alicia, suspected Nash’s recovery was a ruse, and followed Nash so she could keep tabs on his situation, taking their newborn son with her. Alicia’s suspicions were well founded. Nash, in an unsuccessful attempt to surrender his American passport and be named a citizen of the world that he believed he was destined to lead, was visiting US consulates and embassies all across Europe.

A Beautiful Mind Key Idea #12:

A Beautiful Mind Key Idea #13: Vicious Cycle

Eventually, after nearly a year of wandering between various American embassies in Europe, Nash was deported back to the United States. Even though he was back in treatment, Nash’s condition didn’t improve much. He existed in a vicious cycle through much of the 1960s. He caught in a seemingly endless cycle of institutionalization, medication, seeming to recover, relapsing and heading once more to Europe. Finally, Alicia could take no more. After a few rounds of this repeating pattern, she filed for divorce in early 1963. The divorce was finalized May. Despite the divorce, Nash and Alicia continued to see one other over the years. Nash fluctuated wildly, which made the relationship very difficult. He vacillated between hope to be reconciled with Alicia and resentment of her, as he was convinced she’d had him detained against his will. Nash no longer had any income without Alicia. During this time he was forced to rely on friends and family for survival. Nash moved to West Virginia in 1967 to live with his mother and sister. But Nash’s sister also found his mental state was too much for her. She had him committed for what would be the final time. When Nash was released in February 1970, there was only one place left where Nash felt at home. He spent much of the 1970s and 1980s roaming the corridors at his alma mater, Princeton. There he left odd messages on blackboards in the mathematics department. New students were often perplexed before they realized the silent man who seemed to haunt the corridors wrote the messages. This behavior earned him a nickname: the “Phantom of Fine Hall.” Of course, rumors began to circulate and Nash was held up as a cautionary figure. He was considered an example of what may happen to a mathematician who, like Icarus, attempts to fly too close to the sun. Who attempts to solve the insoluble.

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A Beautiful Mind Key Idea #15: Rewards

Just when all seemed lost, Nash miraculously began to recover from his illness. It’s nearly impossible to pinpoint exactly when Nash’s paranoid schizophrenia began to abate as it happened in stages. Nash was improving, but it took several years for others to notice. The first sign of Nash’s recovery was that, by the late 1980s, mathematicians at Princeton began to notice that Nash’s “research” was now actual mathematics as opposed to the bizarre, incomprehensible numerology he had become known for. By 1992, a friend from his Princeton graduate years noticed that real, lucid conversation was not beyond Nash. Later, when Nash himself described the de-escalation of his illness he revealed that, although paranoid thoughts still tormented him, it was now possible for him to recognize and reject them. Accompanying his improvement was more good news. For the first time, Nash finally achieved recognition for his earlier seminal work on game theory, a boon that coincided with his period of remission from schizophrenia. As well as being repeatedly cited in esteemed economics journals; Nash was also being named as a possible Nobel Prize recipient. Harold Kuhn, Nash’s closest friend at the university, suggested they have a walk in the forest in 1994. This was a moment he’d carefully rehearsed. During this walk, Harold broke the news to Nash that should expect a call later that evening from the Swedish Academy of Sciences. Nash was chosen for the Nobel Prize in Economics. After a nearly 30 years absence from academia, the award signaled a new phase in Nash’s career. A rehabilitated Nash was accepted as a professor at Princeton. Furthermore; Nash spent his remaining years reconnecting with the friends and family members from whom his illness had caused estrangement. In 2001, nearly 40 years after their divorce, Nash and Alicia remarried. This was the icing on the cake of his recovery. The couple lived out the rest of their lives together in their home at Princeton.

A Beautiful Mind Key Idea #16:

A Beautiful Mind Key Idea #17: In Review

  The key message in this book: The story of John Forbes Nash Jr. is one of genius, schizophrenia, and recovery. Nash was diagnosed with paranoid schizophrenia after producing a startlingly original graduate mathematics thesis on game theory that earned him wide recognition. He lived with the condition for three decades. After a long and difficult recovery, he was awarded the Nobel Prize in Economics for his earlier work.  

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