Nash turns 30 in June 1958 and becomes fearful that “the best years of his creative life were over”: for even the best mathematicians, mathematics can feel “like an intramural competition, a race,” and Nash feels that time was running out for him to accomplish something truly ground-breaking. As a result, he decides to start working on two new problems: one of these is the Riemann Hypothesis, known as “the holy grail of mathematics,” about the distribution of prime numbers. Since 1859, a number of mathematical giants had attempted, unsuccessfully, to prove the hypothesis: now, Nash is determined to do what others had found impossible.
Concerned that his career might be bottoming-out, Nash doubles down on his intellectual pursuits and pushes forward with the mathematical “race.” Determined to get ahead of other mathematicians, Nash is drawn to problems that others might find too challenging: he is utterly convinced of his own abilities as a thinker and scholar.
Nash decides to try to prove the hypothesis “by logic, by internal consistency of the system”: he hopes to find another number system in which the hypothesis is true. Just as Nash’s work in the past has been met with skepticism, his conjectures about the Riemann Hypothesis attract doubt. It is Nash’s desire to “scale” this “most difficult, dangerous peak” that will prove to be his undoing. That summer, Nash also begins to exhibit compulsive behavior surrounding money and finances: he becomes interested in stocks and starts believing that there is a “secret theorem” to the market that will allow him to make significant returns on his investments.
Nash pushes forward with the difficult work of solving the Riemann Hypothesis, yet his mask of normalcy is beginning to slip: Nash is beginning to become highly paranoid and convinced of certain far-fetched ideas.