In the Pentagon "War Room" scene, the walls are lined with backlit code transparencies, and Nash infers they're lattitudes and longitudes. The Art department was creating one slide at a time in Adobe Illustrator, and people can't pick random digits, so I wrote a C program to generate all the slides, that Art could control for creative effect. As the scene drew near, I was asked to pick locations along the US/Canada border, such as Starkey Corners, Maine. Russell, fearing we were making these names up, challenged Akiva to prove they existed. Luckily I had a Maine atlas in my car.
Art made an error entering a longitude by hand. It moved the spot 200 yards, so instead of pointing this out I updated the script (mistake #1). Day of filming, Art tells me they caught the mistake, and had overnighted a corrected slide just in time. The "wrong" slide matching the script in Russell's trailer was two hours away. There was no question in Akiva's mind that we should get it. We sent a driver.
Now, I knew Ron Howard would be asking me which slides were which, when we filmed the crucial scene. I asked Art so I could move slides as needed, and was told the head of Art had spent all day positioning them. I innocently found the head of Art to ask him to relay his permission.
Oops. In front of dozens of crew he eviscerated me, telling me I was assuming too great a role, I was just a consultant, I should learn my place. (My role had indeed expanded. There's too much to do on a film.)
After we each had a word with Akiva, I discovered that the soon-arriving "wrong" slide was already in perfect position for filming. I had needlessly prevailed in a confrontation I could have avoided (mistake #2).
During preproduction I had offered to Russell that if he ever wanted to use me in a joke, I was game. Russell had missed the festivities so far. Rehearsing at a map table, he feigned not knowing where one of the locations was. The room froze for what seemed an eternity; he didn't mind. I snuck up silently to point on the map. He bellowed "Fuck off! I'm acting!" and turned to match my grin.
No one laughed. Anyone surprised I hadn't already quit that day was sure I'd quit now. Russell had no idea. He came to me later, wondering why no one laughed, he thought that was funny. I told him, "I thought it was funny. Who cares what anyone else thinks!"
We then spent half a day filming in front of the now-arrived "wrong" transparency matching the script in Russell's trailer. It turned out that Russell had memorized the coordinates (I hadn't). Yikes.
Akiva and I gave each other a silent hi-five look over this. Right call, getting a driver. This could have gone badly. So many decisions on a film set are a game of chance.
I even patched things up with the head of Art. The cinematographer Roger Deakins discovered that if he pulled down the slides the wall made a great backlight. The crew could only restore the original slide pattern because I'd made a chart. There was a strong pattern to the slide colors; this would otherwise have lead to continuity gaffes that many viewers would have noticed. So it appeared at first that I was the heathen about to destroy this artwork, when I was the person in the room who saved it.
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.
