[Warning: This movie review contains spoilers, as well as a continued fraction expansion.]

These days, it takes an extraordinary occasion for me and Dana to arrange the complicated, rocket-launch-like babysitting logistics involved in going out for a night at the movies. One such an occasion was an opening-weekend screening of The Man Who Knew Infinity—the new movie about Srinivasa Ramanujan and his relationship with G. H. Hardy—followed by a Q&A with Matthew Brown (who wrote and directed the film), Robert Kanigel (who wrote the biography on which the film was based), and Fields Medalist Manjul Bhargava (who consulted on the film).

I read Kanigel’s The Man Who Knew Infinity in the early nineties; it was a major influence on my life. There were equations in that book to stop a nerdy 13-year-old’s pulse, like

$$1+9\left( \frac{1}{4}\right) ^{4}+17\left( \frac{1\cdot5}{4\cdot8}\right)

^{4}+25\left( \frac{1\cdot5\cdot9}{4\cdot8\cdot12}\right) ^{4}+\cdots

=\frac{2^{3/2}}{\pi^{1/2}\Gamma\left( 3/4\right) ^{2}}$$

$$\frac{1}{1+\frac{e^{-2\pi}}{1+\frac{e^{-4\pi}}{1+\frac{e^{-6\pi}}{1+\cdots}}%

}}=\left( \sqrt{\frac{5+\sqrt{5}}{2}}-\frac{\sqrt{5}+1}{2}\right)

\sqrt[5]{e^{2\pi}}$$

A thousand pages of exposition about Ramanujan’s mysterious self-taught mathematical style, the effect his work had on Hardy and Littlewood, his impact on the later development of analysis, etc., could never replace the experience of just staring at these things! Popularizers are constantly trying to “explain” mathematical beauty by comparing it to art, music, or poetry, but I can best understand art, music, and poetry if I assume other people experience them like the above identities. Across all the years and cultures and continents, can’t you feel Ramanujan himself leaping off your screen, still trying to make you see this bizarre aspect of the architecture of reality that the goddess Namagiri showed him in a dream?

Reading Kanigel’s book, I was also entranced by the culture of early-twentieth-century Cambridge mathematics: the Tripos, Wranglers, High Table. I asked, why was I here and not there? And even though I was (and remain) at most 1729-1729 of a Ramanujan, I could strongly identify with his story, because I knew that I, too, was about to embark on the journey from total scientific nobody to someone who the experts might at least take seriously enough to try to prove him wrong.

Anyway, a couple years after reading Kanigel’s biography, I went to the wonderful Canada/USA MathCamp, and there met Richard K. Guy, who’d actually known Hardy. I couldn’t have been more impressed had Guy visited Platonic heaven and met π and e there. To put it mildly, no one in my high school had known G. H. Hardy.

I often fantasized—this was the nineties—about writing the screenplay myself for a Ramanujan movie, so that millions of moviegoers could experience the story as I did. Incidentally, I also fantasized about writing screenplays for Alan Turing and John Nash movies. I do have a few mathematical biopic ideas that haven’t yet been taken, and for which any potential buyers should get in touch with me:

Radical: The Story of Évariste Galois

Give Me a Place to Stand: Archimedes’ Final Days

Mathématicienne: Sophie Germain In Her Prime

The Prime Power of Ludwig Sylow

(OK, this last one would be more of a limited-market release)

But enough digressions; how was the Ramanujan movie?

Just as Ramanujan himself wasn’t an infallible oracle (many of his claims, e.g. his formula for the prime counting function, turned out to be wrong), so The Man Who Knew Infinity isn’t a perfect movie. Even so, there’s no question that this is one of the best and truest movies ever made about mathematics and mathematicians, if not the best and truest. If you’re the kind of person who reads this blog, go see it now. Don’t wait! As they stressed at the Q&A, the number of tickets sold in the first couple weeks is what determines whether or not the movie will see a wider release.

More than A Beautiful Mind or Good Will Hunting or The Imitation Game, or the play Proof, or the TV series NUMB3RS, the Ramanujan movie seems to me to respect math as a thing-in-itself, rather than just a tool or symbol for something else that interests the director much more. The background to the opening credits—and what better choice could there be?—is just page after page from Ramanujan’s notebooks. Later in the film, there’s a correct explanation of what the partition function P(n) is, and of one of Ramanujan’s and Hardy’s central achievements, which was to give an asymptotic formula for P(n), namely $$ P(n) \approx \frac{e^{π \sqrt{2n/3}}}{4\sqrt{3}n}, $$ and to prove the formula’s correctness.

The film also makes crystal-clear that pure mathematicians do what they do not because of applications to physics or anything else, but simply because they feel compelled to: for the devout Ramanujan, math was literally about writing down “the thoughts of God,” while for the atheist Hardy, math was a religion-substitute. Notably, the movie explores the tension between Ramanujan’s untrained intuition and Hardy’s demands for rigor in a way that does them both justice, resisting the Hollywood urge to make intuition 100% victorious and rigor just a stodgy punching bag to be defeated.

For my taste, the movie could’ve gone even further in the direction of “letting the math speak”: for example, it could’ve explained just one of Ramanujan’s infinite series. Audiences might even have liked some more T&A (theorems and asymptotic bounds). During the Q&A that I attended, I was impressed to see moviegoers repeatedly pressing a somewhat-coy Manjul Bhargava to explain Ramanujan’s actual mathematics (e.g., what exactly were the discoveries in his first letter to Hardy? what was in Ramanujan’s Lost Notebook that turned out to be so important?). Then again, this was Cambridge, MA, so the possibility should at least be entertained that what I witnessed was unrepresentative of American ticket-buyers.

From what I’ve read, the movie is also true to South Indian dress, music, religion, and culture. Yes, the Indian characters speak to each other in English rather than Tamil, but Brown explained that as a necessary compromise (not only for the audience’s sake, but also because Dev Patel and the other Indian actors didn’t speak Tamil).

Some reviews have mentioned issues with casting and characterization. For example, Hardy is portrayed by Jeremy Irons, who’s superb but also decades older than Hardy was at the time he knew Ramanujan. Meanwhile Ramanujan’s wife, Janaki, is played by a fully-grown Devika Bhise; the real Janaki was nine (!) when she married Ramanujan, and fourteen when Ramanujan left for England. J. E. Littlewood is played as almost a comic-relief buffoon, so much so that it feels incongruous when, near the end of the film, Irons-as-Hardy utters the following real-life line:

I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people, “Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms.”

Finally, a young, mustachioed Bertrand Russell is a recurring character. Russell and Hardy really were friends and fellow WWI pacifists, but Hardy seeking out Bertie’s advice about each Ramanujan-related development seems like almost certainly just an irresistible plot device.

But none of that matters. What bothered me more were the dramatizations of the prejudice Ramanujan endured in England. Ramanujan is shown getting knocked to the ground, punched, and kicked by British soldiers barking anti-Indian slurs at him; he then shows up for his next meeting with Hardy covered in bruises, which Hardy (being aloof) neglects to ask about. Ramanujan is also depicted getting shoved, screamed at, and told never to return by a math professor who he humiliates during a lecture. I understand why Brown made these cinematic choices: there’s no question that Ramanujan experienced prejudice and snobbery in Cambridge, and that he often felt lonely and unwelcome there. And it’s surely easier to show Ramanujan literally getting beaten up by racist bigots, than to depict his alienation from Cambridge society as the subtler matter that it most likely was. To me, though, that’s precisely why the latter choice would’ve been even more impressive, had the film managed to pull it off.

Similarly, during World War I, the film shows not only Trinity College converted into a military hospital, and many promising students marched off to their deaths (all true), but also a shell exploding on campus near Ramanujan, after which Ramanujan gazes in horror at the bleeding dead bodies. Like, isn’t the truth here dramatic enough?

One other thing: the movie leaves you with the impression that Ramanujan died of tuberculosis. More recent analysis concluded that it was probably hepatic amoebiasis that he brought with him from India—something that could’ve been cured with the medicine of the time, had anyone correctly diagnosed it. (Incidentally, the film completely omits Ramanujan’s final year, back in India, when he suffered a relapse of his illness and slowly withered away, yet with Janaki by his side, continued to do world-class research and exchanged letters with Hardy until the very last days. Everyone I read commented that this was “the right dramatic choice,” but … I dunno, I would’ve shown it!)

But enough! I fear that to harp on these defects is to hold the film to impossibly-high, Platonic standards, rather than standards that engage with the reality of Hollywood. An anecdote that Brown related at the end of the Q&A session brought this point home for me. Apparently, Brown struggled for an entire decade to attract funding for a film about a turn-of-the-century South Indian mathematician visiting Trinity College, Cambridge, whose work had no commercial or military value whatsoever. At one point, Brown was actually told that he could get the movie funded, if he’d agree to make Ramanujan fall in love with a white nurse, so that a British starlet who would sell tickets could be cast as his love interest. One can only imagine what a battle it must have been to get a correct explanation of the partition function onto the screen.

In the end, though, nothing made me appreciate The Man Who Knew Infinity more than reading negative reviews of it, like this one by Olly Richards:

Watching someone balancing algorithms or messing about with multivariate polynomials just isn’t conducive to urgently shovelling popcorn into your face. Difficult to dislike, given its unwavering affection for its subject, The Man Who Knew Infinity is nevertheless hamstrung by the dryness of its subject … Sturdy performances and lovely scenery abound, but it’s still largely just men doing sums; important sums as it turns out, but that isn’t conveyed to the audience until the coda [which mentions black holes] tells us of the major scientific advances they aided.

On behalf of mathematics, on behalf of my childhood self, I’m grateful that Brown fought this fight, and that he won as much as he did. Whether you walk, run, board a steamship, or take taxi #1729, go see this film.

Addendum: See also this review by Peter Woit, and this in Notices of the AMS by Ramanujan expert George Andrews.