## “Largely just men doing sums”: My review of the excellent Ramanujan film

[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 Infinitythe 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.

### 64 Responses to ““Largely just men doing sums”: My review of the excellent Ramanujan film”

1. The Man Who Knew Infinity | Not Even Wrong Says:

[…] Update: Scott Aaronson has a far better review of the film than mine here. […]

2. Sniffnoy Says:

The Olly Richard link doesn’t actually work…

Just so you know, the first series seems to be running off into the archive links (in chrome).

4. turbo Says:

Ramanujan was dark brown and close to black while Dev Patel was brown and literally has color (brighter skin) according to Indian. They could have captured a real south Indian Iyengar Brahmin at least to be the lead cast (I think this is the real tragedy).

5. turbo Says:

At least he may have had a better South Indian accent. Dev Patel’s was fake and he was also rather tall (If tom hanks and even other shorter black male artists could make it they could have found a better pleasant face) and really does not look like a South Indian Iyengar nor was the lead actress.

6. Scott Says:

Sniffnoy #2: For me, the link works fine in Firefox but not in Chrome. Since the HTML looks fine, I’m not sure what the problem is…

7. Not turbo Says:

@turbo #4: Perhaps that’s a bit unrealistic? Hollywood is famous for its yellowface or brownface or other-color-face (see https://www.youtube.com/watch?v=zB0lrSebyng). At least they got a brown guy to play a brown guy.

8. Sniffnoy Says:

Odd, dunno what happened there.

9. cm Says:

wish they have explained more of his work i the film… of course in plain english for you will never know who will fall love with that.

10. turbo Says:

No it is not as simple as you think. Technically any northern portrayed as Southern is as good as an Iranian portrayed as a German to southern people. The class of Iyengar’s Ramanjuan belonged was technically of dravidian origin (Iyer’s in southern India are of northern origin (taking of Aryan here) and Dev Patel might have been a good choice for such roles (with a big hand waiving)). So technically it is likely as good as martin luther king played by some liberal white. Morally it makes no difference. However it evokes emotions. It evokes a sense of deep betrayal.

11. turbo Says:

Plus Ramanujan is not even an action hero he was a plain first class mathematician. What does Hollywood have hide for this?

12. turbo Says:

@Notturbo just watched video. The hollywood culture is fully pretty bad.

13. Job Says:

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.

As much as i enjoy scoffing at stuff like this, i have to ask, why not produce a documentary instead of a movie?

Personally, I would much rather watch a biographical work documenting someone’s life than some Hollywood dramatization. And it’s exactly because of stuff like this.

A love affair with a British nurse? And then maybe she becomes his protector, and his inspiration.

Like a romantic interest would fuel anyone’s research… I would stop watching immediately.

But my point is, i wouldn’t watch it to begin with. It’s not a documentary. I cringe at predictable dramatizations. Why does it need to be a movie?

14. pku Says:

Those other movies’ lack of math content has always bothered me. I still wince every time I remember the “mathy” line in proof (“This is an amazing theorem! It’s something about prime numbers!”). And there’s a theory in our department that Goodwill Hunting takes place in an alternate universe where everyone is terrible at math.

About the Galois movie, I say we get the guy who made Hamilton to do it as a musical. Because seeing Galois rap about solving polynomials would be radical.

15. Raoul Ohio Says:

Dev Patel might be too charming to realistically portray any actual person from South Asia, but so what? Brad Pitt is too charming to realistically portray anyone, and he has been in some good movies.

I would rather talk about Ramanujan’s love: the beauty of mathematics.

My top choice for the pillar of mathematical beauty and utility is generating functions — surely the key part of the interface between discrete and continuous mathematics, and central to much of Ramanujan’s work. Generating functions allow you to chip away at a problem for a while using methods of classical analysis, and then cross over to the other side, where you can whack away with discrete math and computer experiments and searches for a while. Repeat as needed.

Check out the classical approach: Watson’s “A treatise on the theory of Bessel functions” (almost 100 years old!). This is a gem for anyone conversant with complex analysis and the functions of mathematical physics. Theorems about Bessel functions drop off the generating function like ripe apples off a tree. It is a delight, so well written it is like reading a novel. According to Ernst Breitenberger, Watson was well on his way to a totally revised second edition when he died, and on one has attempted to finish the project. Anyone out there able to take on this project?

Nowadays, “GeneratingFunctionOlgy” is a key idea in TCS (Theoretical Computer Science). I think the new path forged in the “Analytic Combinatorics” books of Sedgewick and Flajolet will become a key tool in analysis of algorithms. It is just too cool not to be deep! (I bought the books, and plan to work through them “real soon now”). BTW, Sedgewick offers a free MOOC on these topics, and you can get .pdf’s of the books at his website.

16. Jr Says:

I hope the movie will be released in Sweden, because I definitely want to watch it.

At the moment we are actually pretty well served with screen depictions of mathematicians. Aside from the ones Scott mentions there is also Agora and the Oxford murders. There still needs to be a hook of something romantic or dramatic however, aside from the math. So the main characters has to die tragically, or solve murders, or overcome prejudice. He/she can’t just lead a boring life and do good mathematical work. (Not that such a life would be boring, but you understand what I mean.)

I am still hoping for biopic based on Andrew Wiles’ life. There was a book, by Simon Singh, and a documentary and both of them were popular, I think, so there might be an audience.

17. Scott Says:

Jr #16: If I, who do this stuff for a living, wouldn’t want to sit through a biopic about someone who “just leads a boring life and does good mathematical work,” then why would anyone else? 🙂

I joked about a movie depicting Ludwig Sylow and his definition of Sylow subgroups, but one can multiply examples to illustrate the issue here:

112358: The Fibonacci Story

Bounding the Tails: The Life and Passion of Herman Chernoff

The Lambda Game: You Saw Alan Turing, Now Brace Yourselves for the Saga of Alonzo Church

18. Scott Says:

Job #13:

As much as i enjoy scoffing at stuff like this, i have to ask, why not produce a documentary instead of a movie?

Interesting question!

There have also been some great math documentaries—I loved The Proof about Andrew Wiles, and N is a Number about Paul Erdös (the latter is available for free online; I couldn’t find the former but maybe you can 🙂 ).

For me, though, for those scientists or mathematicians who actually lived dramatic or tragic lives (Ramanujan, Nash, Turing, Galois, Archimedes, Hypatia, Galileo, Oppenheimer … quite a few, actually), the whole point of a biopic is to show enough of the historical reality that my rational brain is satisfied and can relax, so that then my emotional brain gets to relive the story—so that I can lose myself for a moment, watch Jeremy Irons and Dev Patel, and feel like yes, this is G. H. Hardy visiting the dying Ramanujan in the hospital, a scene that’s part of my consciousness like Moses visiting the bush is part of a religious person’s.

Of course, a great documentary can provoke an emotional response as well. But with a biopic, as I see it, the primary purpose is emotional, and getting the facts right matters so much precisely because it’s essential to that purpose (a biopic that mangles the facts badly enough will only produce in me the emotion of cringing).

19. mike Says:

theorems and asymptotic bounds. 🙂

20. Ehud Schreiber Says:

Taking a tangent off your tangent:

I find the biographical and spiritual similarity between Galois and Georg Büchner to be amazing.

For the ones who do not know Büchner – drop everything and go to read Woyzeck and Danton’s death.

How about a play or a movie portraying a fictional meeting between the two?

21. Hari Krovi Says:

The story of the partition function is very interesting. It is explained in AMS notices (http://www.ams.org/notices/201211/201211-full-issue.pdf) by George Andrews (p. 1528). This story shows the difficulty of Hardy’s role in the partnership i.e., how much to trust Ramanujan’s intuition?

In fact, the story starts with Ramanujan sharing a formula with Hardy that turned out to be wrong. But Hardy sees something interesting in it and eventually, it leads to an asymptotic formula for the partition function. Years later, an exact formula for the partition function was found, which according to Atle Selberg, could have been done by Hardy and Ramanujan if “Hardy had trusted Ramanujan more”. But given that the first formula that started this line of research is wrong, it must have been difficult for Hardy to know how much to trust Ramanujan.

22. Curious Wavefunction Says:

Job #13: There is actually a very good documentary on Ramanujan made in the 80s, “Letters from an Indian Clerk”, which features interviews with several notable people including Subrahmanyan Chandrasekhar and, amazingly enough, Ramanujan’s widow Janaki who was 87 at the time. You can search for it on YouTube.

23. Jair Says:

I have not seen this yet, but as a combinatorialist I am amused and gratified to hear that Percy MacMahon makes an appearance. For the next Big Math Biopic I would probably pick the saga of Babbage/Lovelace.

24. Scott Says:

Jair #23: In such a biopic, the pressure from Hollywood would probably be immense to make Babbage and Lovelace have an affair, or at least a Mulder/Scully-style smoldering non-relationship.

25. anon_sc Says:

turbo: As a dalit, I found your outrage over how Hollywood has depicted a Tamil Brahmin Iyenger as a fair-skinned Nair (also Brahmin), especially the “So technically it is likely as good as martin luther king played by some liberal white” deliciously ironic. Just so the American readers of this blog understand here’s a little absurdity about caste oppression that was commonplace in India not too far back in time: those belonging to Ramanujam’s upper caste would have to have a bath were my forefather’s *shadow* (yes, you read this right) simply to happen to fall on them.

Scott, really sorry for going off-topic on this lovely review. I just couldn’t let this one pass.

26. Scott Says:

anon_sc #25: No problem at all! It’s fascinating to be reminded about the intra-Indian rivalries that most Westerners would never even think about watching a movie like this one (though I recall that Kanigel’s book did go into them somewhat—e.g., stressing that Ramanujan’s family was poor, but still proud to be Brahmin).

27. turbo Says:

@Scott What anon_sc says is true. Dalits were very very bad and my father said even my own caste was just above them until 20th century. Since we are south Indians we escaped. Many North Indian Dalits are literally as bad or worse than blacks in America in 19th century. At least there are resources in US where ruling class (read whites) could step down to share resources. What anon_sc says is absolutely true. Even if a shadow of a dalit falls on a brahmin the dalit will be thrashed and thebrahmin has to wash himself. This was in 20th century as well.

28. turbo Says:

@anon_sc I was not sure Patels were Brahmins. I thought they were merchant class. Nevertheless he was not qualified to play ramanujan who was shorter and had south indian traits. that is all I am trying here.

29. Passerby Says:

It’s depressing to think how Ramanujan would have fared had he been of another caste; it’s very likely he would *never* have been discovered. From Kanigel’s book I got the impression that the *only* reason he could get a foot in the door in spite of extreme poverty was because he was a Brahmin (the few people rooting for him were all Brahmins). It’s also important to realize what that statement implies though; being a Brahmin of the upper caste hardly guaranteed a stable income or a middle class living. You could be a Brahmin and still be extremely poor and disadvantaged, even if not ostracized by society. Conversely, Ramanujan could have been of the intermediate merchant caste and very well off and still not made it because his caste didn’t care much for education and intellectual pursuits. The trappings of caste could be strange.

30. Jr Says:

Scott #17, Well it does not have to focus on the boring parts of the subjects life. Wiles story could depict the patient struggle he went through over many years in order to get his breakthrough. I think that could be made interesting.

And if not, I would be happy to see the movie-makers add an episode where Wiles and his sexy grad student fights off assassins sent by the Russian mafia.

31. anon_sc Says:

Scott #26: One problem is that excepting a vanishingly small number, indians abroad are all from the upper castes and thus only a certain picture of caste relation is conveyed inter-personally – even when they are – and many of them are – vehemently against it back home.

This is not new. I don’t know if you’ve read Weil’s Apprenticeship of a Mathematician, but it contains a shockingly anodyne and apologetic (? can’t think of a better word) view of the caste system because most of the people he spoke and worked with were brahmins.

Things have improved significantly in urban india. But, we still have a long way to go. Don’t google dalit violence.

32. Scott Says:

Passerby #29: So … you’re telling me that early 20th-century India already had intersectionality among its various axes of oppression? That the same person could be privileged in one respect, like caste, but suffer in another respect, like money? And that as a result, you couldn’t make a snap-judgment about whether someone was “truly oppressed,” or “just a whining elite playing on the lowest difficulty level who needs to get over themselves,” but rather had to grapple with complicated human realities, just as the best novelists and biographers and storytellers have always done? That’s … mindblowing. 😉

Speaking of intersectionality, there’s a review of the Ramanujan movie by Susan Wloszczyna that begins:

We do love our male geniuses these days. Even more so, apparently, if their presence ever graced the hallowed halls of Cambridge at some point. And if they faced a major hurdle in life, such as a debilitating disease, closeted homosexuality or control freak issues? That only humanizes the bright fellow all the more. Of course, behind every great man must be a self-sacrificing woman who stands by their side or, otherwise, there would be no emotional pull to balance all that complex geek-speak chatter. No matter that the lives of many of these ladies often would provide enough material for a potentially fascinating film all on their own.
33. asdf Says:

The movie must be doing pretty well. All the copies of Kanigel’s book are checked out of all the libraries around here (I’ve looked online at several). I’ll have to wait.

34. John Sidles Says:

This particular Shtetl Optimized essay points toward a particularly rich mine of literary themes. Here are three.

Theme One  Susan Wloszczyna’s review (cited in #32) suggests:

“The lives of many of these ladies [who are spouses of mathematicians] often would provide enough material for a potentially fascinating film all on their own.”

Recommended as a concrete example is Yannick Grannec’s scrupulously detailed (and best-selling, prize-winning, etc.) novelization of the marriage of and Adele and Adele Porkert and Kurt Gödel: The Goddess of Small Victories (2014). Adele and Kurt’s rich story would make a “must see” movie for plenty of folks (well, me anyway).

Theme Two  As Scott’s review mentions, the medical knowledge of Ramanujan’s generation plausibly would have sufficed to prevent Ramanujan’s death (in 1920) from hepatic amoebiasis. So it is natural to wonder, whether the knowledge of Arlene (Greenbaum) Feynman’s generation similarly would have sufficed to prevent Arlene’s death (in 1945) from tuberculosis — Arlene being Richard Feynman’s young wife.

Let us assume, for the sake of Hollywood melodrama, that a small team of ambitious young scientists, familiar with Arlene’s desperate case, and familiar too with the medical literature of the era, were willing to build upon top-secret Army-sponsored biomedical research, with the help of state-of-the-art chemical separation techniques, and bend the rules to attempt a miracle cure mdash; a cure that succeeded against all odds?

What’s remarkable is that this high-drama story is historically true … and it happened in November of 1944 … seven months before Arlene Feynman’s death in June of 1945. For the well-documented details of the then-miraculous cure of tuberculosis patient “Patricia T” as history knows her, see for example Carol Dyer’s (scholarly) Tuberculosis and/or Peter Pringle’s (more sensational) Experiment Eleven: Dark Secrets Behind the Discovery of a Wonder Drug (2012).

Might Feynman plausibly have learned of this Army-sponsored, high-risk/high-payoff tuberculosis research, and with the help of Groves’ and Oppenheimer’s unlimited clout, heroically arranged for “Arlene F” to be a second “Patricia T”?

If there’s anything to Many Worlds quantum theory, the remarkable (even sobering) answer is “yes, definitely”.

Theme Three  Scott’ vivid memories (in the o.p.) of a “childhood self” who was enduringly inspired by the Ramanujan/Hardy story, finds a beautiful (for me) echo in mathematician Robert Langland’s much-cited essay “Is there beauty in mathematical theories?” (2013, this essay is collected in editor Vittorio Hösle’s The Many Faces of Beauty; note that Google finds Langland’s essay on-line);

Langland’s Scott-themed passages include:

Both G.W.Dunnington, the author of Gauss, Titan of Science (1954) and W.K. Bühler, the author of Gauss, A Biographical Study (1981), perhaps the two best-known Gauss biographies, seem to me singularly insensitive to the value to an adolescent of even a very brief introduction to intellectual possibilities […]

My purpose here [in this essay] is to make the case for a mathematical beauty that transcends neither the simple mathematical pleasures of arithmetic and geometry nor the fascination of difficult problems but that integrates them with the quite different intellectual pleasure of creating order from seeming chaos, even in an inconsequential — but not for me — realm.

In particular, Langland’s “Section 5: From algebraic number theory to spectroscopy”, provides a multigenerational algebraic perspective on the research of quantum luminaries that include (in alphabetical order) Balmer, Bohr, Dirac, Lyman, Pauli, Schrödinger, and Wigner.

Langland’s observations provide plenty of algebraic meat for quantum researchers to digest (however this comment has grown sufficiently long that I had best refrain from listing further references) 🙂

Conclusion  Shtetl Optimized readers who enjoy films like The Man Who Knew Infinity, and who have enjoyed too Scott’s fine review of it, are likely to enjoy the above-cited works by Yannick Grannec, Carol Dyer, Peter Pringle and (especially) Robert Langlands.

In aggregate, these works illuminate with a rainbow of light the diverse potentialities of mathematics to enrich lives, speed healing, and in general (in Langland’s phrase) “create order from seeming chaos.” And as these works variously show, the “order created” can be variously personal, domestic, medical, scientific, and even universal. What could be more inspiring? 🙂

35. Michael Vassar Says:

Thanks for the recomendation Scott. I wonder if you have read the David Foster Wallace essay on novels about mathematics.

36. Passerby Says:

Scott #32: Yes, human beings are complex, individualistic and irreducible to stereotypes: who knew ;)! One of the wonderful ways in which both Kanigel’s book and the movie both illustrate these complex realities is by breaking those stereotypes (“All Brahmins are privileged” or “The English are all bad.”). In fact I am convinced that the only reason humanity as a whole progresses is because there’s enough of us who buck stereotypes (notwithstanding what social media seems to be constantly yelling at us).

That review about how we “love our male geniuses” is just plain silly, especially so when you realize that Ramanujan’s ‘privilege’ relative to the writer of the review was probably not just zero but negative.

37. mjgeddes Says:

Long very interesting post by Stephen Wolfram on Ramanujan:

http://blog.stephenwolfram.com/2016/04/who-was-ramanujan/

Short summary: Ramanujan relied heavily on numerical methods and intuition rather than formal proofs, anticipating some of Wolfram’s own empirical approach to mathematics. Ramanujan’s main interest was in the field of number theory, which only really took off from the 1970s onwards with advances in computing power.

I should mention my own favourite number here, isn’t number ’27’ simply the most perfect beautiful number?

Look, 27 is a perfect cube (3^3=27)

27 is also the smallest number with 2 representations as a sum of 3 positive squres:
(27= 1^2+1^2+5^2, 27=3^2+3^2+3^2)

Fun personal fact Scott: 3 1/2 years ago I inserted number ’27’ in all the lines of my lottery ticket and hit the jackpot, using my winnings to travel through England, France and Scotland.

38. turbo Says:

Also sometimes this is why I think something grander is at play unless you believe the likes of Newtons and Eulers are much more plenty than discovered.

Had Ramanujan born 20 years later or 20 years before even if he were a sparkling white genius would not have been the Ramanujan we know today because the right mathematics was not there or mathematics had already moved on. In fact it is highly unlikely just by reading two books anyone could get into Berkeley today even for computer science.

—————–

Also scott regarding #29 Brahmins have high chance of academic and managerial success even if they are poor. Do not compare US poverty and Indian poverty in 20th century and even now. US is segregated with bad schooling at bad places stupid gun laws. The culture in India is much different. Lack of money by an individual does not mean lack of success by individuals in areas where the individual shines if there is traditional strengths in those areas by these castes.

39. Passerby Says:

#38: The good thing is that because of affirmative action there are now plenty of educational opportunities that are available to those of previously lower castes which are not easily available to Brahmins; for instance a Brahmin has to do exceptionally well in standardized tests to stand a chance of getting admitted to a prestigious college. In addition there are ‘special seats’ in prestigious colleges in India which can literally be bought by the wealthy: this puts them out of reach of poor people in general, irrespective of what caste they are. A bit like old money at Harvard.

40. Asokan Pichai Says:

Let me add one error: the movie mistakenly uses a ‘lungi’ (which is a muslim dress and in those days will never be worn by hindus) as Ramanujan’s dress instead of the correct Tamil dress dhoti

41. Scott Says:

Michael #35: No, I haven’t read that! Do you have a link? I just googled for it and couldn’t find it.

42. anon_sc Says:

mjgeddes #37: Wolfram’s article was surprisingly interesting: it also contains the best integrated product placement I have ever witnessed.

Concerning his penultimate section where he wonders if there’d be modern Ramanujans, I think in many ways the world did get one, but, not with as cool a origin story: Bill Thurston.

43. Nicholas Spies Says:

My father, when I was a child, was tremendously interested, and quite conversant, with Claude Shannon’s work, and in particular his famous 1948 paper, which linked information to the thermodynamic concept of entropy, among other things. Although I was only a child, I listened with rapt attention to my father’s explication of some of the ideas embodied in Shannon’s work.

When I was on staff at CMU in the 1980s I asked over the campus network how I could reach Shannon. Herb Simon, the Nobel Prize winner in Economics, answered with: “Who’s asking?” I replied with my credentials, mostly the editing of many award-winning PBS shows, and the shooting and editing of a few other productions. Then Simon replied with: “Claude Shannon is a very private person who would not be interested”.

Well, I suppose it’s better to be rebuffed by a Nobelist than by just anybody, but I would have preferred Shannon, or an agent of his, telling me that himself…

I still think that Shannon’s story would make a great feature film, rather than the NOVA-like documentary I envisioned in the 1980s.

44. Patrick Says:

Scott #41: I believe the essay he’s referring to is here: http://science.sciencemag.org/content/290/5500/2263.1.full

45. Clara Says:

Your first series (1 + 9(1/4)^4 + …) has me puzzled. If I do the ratio test, I get C_n+1 / C_n = 1, so how can the series converge? Clearly it does converge, but how?

46. Sniffnoy Says:

Clara: Ratio of 1 doesn’t mean divergent; ratio greater than 1 means divergent. Ratio of 1 doesn’t tell you anything. E.g., both the sum of all 1/n, and the sum of all 1/n^2, will yield a ratio of 1.

47. Sid Says:

The scary thing I realized while watching the movie was that the existence of Ramanujan hints at the possibility that there is a way to see mathematics in such a way that those staggeringly beautiful identities are rendered intuitive.

I mean at what level of abstraction do you need to be operating so that the LHS of one of the infinite series you wrote is obviously the RHS. Further, it so obvious to you that you don’t even feel the need for a proof.

This kind of approach reminds me of a very different mathematician: Alexander Grothendieck. I wonder if Grothendieck was the Ramanujan of mid-20th century mathematics with its fetish for pure abstraction.

At any rate, Grothendieck’s life would make great fodder for a movie.

And on that topic, so would Wittgenstein’s.

48. The man who knew elliptic integrals, prime number theorems, and black holes | Annoying Precision Says:

[…] I have nothing much to say about the movie as a movie that wasn’t already said in Scott Aaronson‘s review, except that I learned a few fun facts during the Q&A session with […]

49. Eric Johnson Says:

The reciprocal of the 1729th root of 1729 is approximately 0.996… Just sayin’ 🙂

50. Scott Says:

Eric #49: You’re talking about 1729-1/1729. I wrote 1729-1729.

51. Steven M. Moore Says:

Hi Scott,
I’m looking forward to the movie.
It’s weird–I could understand aspects of the relation between topology and quantum field theory and the underlying algebraic structure of Wightman field theory at one time, but I could never understand Ramanujan’s incredible insights. When I read A Mathematician’s Apology in junior high, I thought G. H. Hardy couldn’t either–somehow that made me feel better.
Good review.
r/Steve Moore

52. Harold Says:

Yeah, I’m not going to see this, which is a pity because I was looking forward to it; I’m sick of my people being demonised.

I recently listened to a podcast in which a white American recounted his experiences at a technical college in which there were only a few other whites, everyone else being South or East Asian. Apparently he felt alienated and felt there was little camaraderie; there weren’t any students groups except for those specifically for other ethnicities. To this feeling of alienation he partly attributed his dropping out.

Maybe I should turn his life story into a movie where the Indian students beat him up while yelling racial slurs.

53. Vasantha Says:

Sorry for being off topic. But India’s caste system is so maligned. And rightly so, the way it’s been practiced for the last few centuries. But originally, caste system may have been devised to promote social stability.

Caste system divided people into 4 castes. Scholars (Brahmins), warriors/rulers (Kshatriyas), merchants (Vaishyas) and peasants (Shudras). It forbade each of the four castes from invading each others’ territory. It also proscribed contacts between the four castes and thereby prevented inter-caste marriages or conversions. In essence it helped erect a firewall between the educated class, the ruling class and the moneyed class. And thereby prevented concentration of knowledge /power /wealth in the hands of the few. And to curb economic inequality further, caste system prescribed very strict ‘code of conduct’ for each caste. Scholars were expected to be ascetics, while the larger society provided for their basic needs. Both scholars and merchants were required to be vegetarians, eschew intake of alcohol/opiates. Thus Indian society bought social stability at the cost of social mobility. However in the end they paid dearly. The invaders(Arabs/Turks/Persians/Mongols/English) used caste system to divide and rule. They maligned scholars as evil elites and widened natural enmity between classes by playing one against the other. For the last 700 years, the invaders and later the elites who rule India have found caste system to be a wonderful tool for the ruling class (whatever be their caste).

This post is no way an apology for caste system. It’s and attempt to offer a possible alternate explanation. I agree the Dalits or the out-castes fell through the cracks. They might have been the original inhabitants of India. They bore the brunt of the caste system. Their treatment is one of India’s darkest shames.

54. Dylan Thurston Says:

Scott, why on earth would you assume that the prejudice that Ramanujan faced was subtle? I haven’t read enough about Ramanujan to know the specifics, but given the time and place protrayed in the movie, the incidents in the movie were entirely plausible. The subtler stuff also appeared on-screen, notably in his difficulty in getting vegetarian food and in the lack of comprehension about being vegetarian from those around him.

55. Scott Says:

Dylan #54: I didn’t assume it was subtle. But given my own experiences, I’m sensitive to anything that even seems like a justification for indulging ugly stereotypes (“we have no evidence that the people in real historical environment X did horrible thing Y, but let’s portray them as doing it, since it feels plausible given the sort of scum we all know they are”—I’m sure you could think of other examples where that sort of “logic” would horrify all decent people, and where no one would be tempted to defend it!). In this case, we do have surviving letters from Ramanujan to Janaki and to his mother. Doesn’t it seem plausible that he would’ve mentioned such a thing, had it happened?

56. Math Movies | A bunch of data Says:

[…] recent movie The Man Who Knew Infinity about the life of Ramanujan, a movie that has gotten wide excitement from mathematicians for the portrayal of the math itself, with credit given to consulting […]

57. poor Says:

great movie. Also ppl need to know that average lifespan of Indians under british raj was less than 30 yrs(something most Indians themselves are so ignorant of that they talk nonsense like turbo!). Also to turbo earlier who says that being poor was not handicap given caste. He clearly doesnt understand that most Indians of the period never made much contribution to anything irrespective of background. Thats what colonialism was about. Indian gdp contribution went from about 24% of the world to about 2%.As I said earlier,avg lifespan was under 30 yrs.And most Indian schools even now are pathetic. Ramanujan succeeded precisely because he was extraordinary. can anyone name any other Indian mathematician worth anything within the said period inspite of few advantages?. No!. His talk of iyengar shows absolute bias in terms of caste(not even surprised & he even admits much saying “emotions”). No other person will even be bothered by this issue. Because no amount of caste/class/education etc can be enough to make ppl like ramanujan, if it was possible we would have done it by now. He was a product of his sheer will. How many continue to do maths even in pain in their last days before death? 🙁

58. poor Says:

also the only piece of Indian history of pre british education system in India is in work by some one called dharmapal who basically had to research and publish his own work cause India was ruled by regressive left-libs for most of 60 yrs(kept India poor under guise of socialism leading to death of over 100 million ppl and even now oppose capitalism. Poverty/Oppression is very useful for left-libs to survive in India). In it shows some degree of education for many ppl mostly uppercaste but also others below, maths/astronomy/medicine/grammar/different weltanschanung were taught. The education was privately funded, so if ppl could afford it they could get teachers.Turns out that these kinds of schools continue outside govt and are more efficient even now and govt is trying to shut them down.

The traditonal education system broke down entirely and new education system by british never did better even after independence,primary education/healthcare was neglected for sake of socialism which drained money to public sector banks/units and the elite thrived.primary education in India is pathetic even now. (easy to break and much harder to replace with something more effective.)

traditional education system records were made by british which has been taken to write the book by dharampal showing that lower classes also had access to education.Though not in equal numbers(most live under myth this never happened because data complicates everything for all of us) and some girls also got educated in few places. But still India had more education than in even britain in that particular period of time.
http://voiceofdharma.org/books/tbt/

Also, Indigenous mathematical/astronomy survived in deep south India after running away from north(muslim invasions/ will never be accepted by left-libs ) making contributions to differential calculus.

http://discovermagazine.com/2008/jan/calculus-was-developed-in-medieval-india/

probably first text ever using ideas of calculus

Basically, to imagine what happened to us is to imagine europe being invaded and its universities destroyed.medieval zoroastrians/buddhists texts talked of islam in apocalyptic terms. buddhism got wiped out of India,central asia!.
https://wikiislam.net/wiki/Kalachakra_Tantra

In absence of preserving diversity of thought, this shall be the fate of every nation.

Very sorry for the rant. I have read ur blog enuf times and you are great fun and keep rocking! The fact that you do shows how passionate u are about all this.

🙂

59. poor Says:

none of this ofcourse denies all those above over the degree of prejudice which existed.And rightly deserves criticism.

60. Maverick Says:

Thanks to your blog, I went and watched the penultimate show of this movie in my city. There were about 10-12 people in the middle of the afternoon, which was really surprising! Too bad that AMC, Regal and others did not carry the movie. Roger Ebert’s website gave it an undeservedly poor review, which may have dissuaded many people from going to watch it. Anyway, I was emotionally touched by the passion for Math portrayed by both the main characters, and bringing to life the amazing Ramanujan. It would have been very interesting for the layman to show Ramanujan’s work on Magic Squares – it is in the first few pages of his notebooks. By the way, one can buy his wonderfully restored and collectible quality copies of his original notebooks from TIFR (Tata Institute of Fundamental Research).

61. Maverick Says:

Wanted to add this excellent writeup about Ramanujan, Hardy and mathematics in Stephen Wolfram’s blog.

http://blog.stephenwolfram.com/2016/04/who-was-ramanujan/

62. JimW Says:

What an interesting and informative review. I suspect that at one point someone will be making a movie about your life. 🙂

63. Arvind Balasubramaniam Says:

There’s a scene where the mother says “did you see that our boy is published” in Tamil to her neighbours after news of his publication reached home. The accent was perfect (i’m from the Tamil Iyer community) and I was surprised as the mother character was played by a north Indian. It’s a passing reference that they were speaking in Tamil, only that inter-character dialogues was about convenience to viewers.

64. GVF Says:

Turbo #4: “Ramanujan was dark brown and close to black ” – but we learn from the Wolfram Blog (linked by Maverick #61) that at age 18 he was described by his mother as “of fair complexion” (See “A missing boy” in the newspaper.

(Not that I think this is really important, bit it seems some people do).