Akiva Goldsman's instruction to me was to have Nash make gradual progress on the Riemann hypothesis, after he emerged from hospitalization. This isn't historically correct, but the film is a fictionalized account. That's challenging; most mathematicians only have experience with fiction writing for for grant proposals.
For the library scene late in the film, Nash is starting to make sense. I consulted with a few people actually thinking about the Riemann hypothesis. ("Working" on it is staring into the sun.) For those blackboards, they advised me to borrow from Pierre Deligne's work in characteristic p. I made sure that missing definitions prevented anyone from actually proving the boards were wrong. "Freeze-framing the DVD" was a stock phrase for us on the set, but in fact people mostly paid attention to the acting.
As a first year graduate student, I was struck by the similarities between covering spaces in my topology course and field extensions in my algebra course. Asking Barry Mazur in the hallway, he quite mystically intoned that everything is connected. That was the basis for the student approaching Nash in the library. Russell Crowe completely winged his long response at the table. I was seriously impressed.
Earlier, I got pilloried by some for the Harvard Lecture Hall scene where Nash is institutionalized. Hey, it comes with the territory. Nash associating spacetime with the quaternions? Brian Greene gave me such a great look when I tried this line on him that I knew we had to use it. It is crazy, and the scene required crazy. Nevertheless, complex quaternions can model geometries used in physics. The quaternions and octonions extend the complex numbers, one could look there to better understand the Riemann hypothesis. The quaternions are most famously used by game developers for efficient rotations, and one keeps seeing references (here on HN!) to the octonions as deeper. I was at a tech dinner party in Berkeley where various gamers including the founder of Second Life swarmed me to share a moment "Oh! The octonions!"
For the porch scene in question, where Nash is still pretty gorped, I had him playing with a visual notation for continued fractions. The Riemann zeta function doesn't even converge where one wants to understand its zeros. Continued fractions exhibit different convergence properties, somewhat like the light cast in a a park with trees. So I could imagine a gorped Nash obsessing on continued fractions.
For the library scene late in the film, Nash is starting to make sense. I consulted with a few people actually thinking about the Riemann hypothesis. ("Working" on it is staring into the sun.) For those blackboards, they advised me to borrow from Pierre Deligne's work in characteristic p. I made sure that missing definitions prevented anyone from actually proving the boards were wrong. "Freeze-framing the DVD" was a stock phrase for us on the set, but in fact people mostly paid attention to the acting.
As a first year graduate student, I was struck by the similarities between covering spaces in my topology course and field extensions in my algebra course. Asking Barry Mazur in the hallway, he quite mystically intoned that everything is connected. That was the basis for the student approaching Nash in the library. Russell Crowe completely winged his long response at the table. I was seriously impressed.
Earlier, I got pilloried by some for the Harvard Lecture Hall scene where Nash is institutionalized. Hey, it comes with the territory. Nash associating spacetime with the quaternions? Brian Greene gave me such a great look when I tried this line on him that I knew we had to use it. It is crazy, and the scene required crazy. Nevertheless, complex quaternions can model geometries used in physics. The quaternions and octonions extend the complex numbers, one could look there to better understand the Riemann hypothesis. The quaternions are most famously used by game developers for efficient rotations, and one keeps seeing references (here on HN!) to the octonions as deeper. I was at a tech dinner party in Berkeley where various gamers including the founder of Second Life swarmed me to share a moment "Oh! The octonions!"
For the porch scene in question, where Nash is still pretty gorped, I had him playing with a visual notation for continued fractions. The Riemann zeta function doesn't even converge where one wants to understand its zeros. Continued fractions exhibit different convergence properties, somewhat like the light cast in a a park with trees. So I could imagine a gorped Nash obsessing on continued fractions.