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Ramanujan's Challenge

·6 mins
statue of Ramanujan
A bust of Srinivasa Ramanujan in Kolkata.

Asking for Signs #

A fallen-away Catholic friend once told me that he wished the Bible predicted modern science. “If Jesus said, ‘Oh, by the way, matter is made up of atoms,’ then I would also believe him when he says he’s God,” he said.

I don’t think we should expect Jesus to have said things like that. First, it wouldn’t have helped anyone in the centuries before it could be verified. Second, it would be difficult for the human writers and copyists of the Bible to comprehend most scientific truths in a way that would let them hand them down in a recognizable way.

Third, I think we should draw a lesson from what Jesus chooses to focus on in his public ministry. He’s not here to teach us science; he doesn’t even seem all that concerned about the administrative details of the Church he’s about to found. Rather, he cares about our relationship with God. This is epitomized in the exchange in Luke 13:23-24:

And some one said to him, “Lord, will those who are saved be few?” And he said to them, “Strive to enter by the narrow door; for many, I tell you, will seek to enter and will not be able."

Jesus flatly refuses to answer the empirical question, instead giving a moral exhortation.

Fourth, Jesus sometimes refuses to give signs to people who ask for them, as in Mt 12:38-39 and Lk 16:31. It seems to happen when the people asking start out skeptical, and Jesus judges that they wouldn’t believe him anyway; or else when Jesus actually does give a sign, just not the kind of sign they want. My friend’s desire for a scientific sign falls into at least the latter category.

So my friend’s desire doesn’t succeed as an argument against Christianity. But what if someone did appear bearing such signs? What if someone spoke specific empirical truths that no one else knew at the time, and claimed that they were revealed to him by God? I would consider him a prophet, right?

And what if the prophet’s god is not my God, but a Hindu goddess?

Srinivasa Ramanujan #

is the greatest savant ever to be discovered by the mathematical community. He could do things in his head that most mathematicians couldn’t do on paper. He could do things in a week that most mathematicians couldn’t do in a hundred years.

He was born in extreme poverty, and learned math from local college students and library books.1 His teachers and employers noticed his genius, and eventually set him up with Cambridge professor G. H. Hardy. Hardy learned several new theorems from Ramanujan’s first letter, and arranged for him to come to England. They collaborated for five years before Ramanujan was diagnosed with tuberculosis, returned to India, and died the next year at age 32. Since then, hundreds of mathematicians have pored over the notebooks he left behind, trying to flesh out the extremely compact formulas, almost all of which turned out to be right.

The simplest example I know of Ramanujan’s brilliance is the taxicab incident. Hardy recalled it:

I remember once going to see [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” 2

The two ways are \(12^3 + 1^3 = 1729 = 10^3 + 9^3\).

A slightly more complicated example was presented to me in Calc 2:

$$ \sum_{n=0}^\infty \frac{(-1)^{n}(1123+21460n)(2n-1)!!(4n-1)!!}{4(882^{2n+1})32^{n}(n!)^{3}} = \frac{1}{\pi} $$

This formula converges quickly- six terms give 18 digits of accuracy.

How did Ramanujan come up with this stuff?

Well, according to him, some of his results were revealed to him by the goddess Namagiri, his family patron, in dreams.

It would be easy to oversell the mysticism here. Plenty of mathematical results look magical at first, and then make perfect sense after a few hours of explanation. I think the formula for \(\pi\) relates to class numbers and modular forms. (But I’m out of my depth here!) Ramanujan wrote far more assertions than proofs, but he might have gained that habit when he was poor and paper was expensive, or maybe his mind just held more intermediate steps at once. Either way, we shouldn’t disrespect his intelligence by pretending his work is inhuman. In fact, it is out of respect for his intelligence that I take his words seriously- including what he says about his religion.

The Challenge #

So why did the greatest savant known to history sometimes attribute his results to a Hindu goddess?

Hinduism isn’t my strong suit, but apparently Namagiri is consort of Mahavishnu, so Ramanujan’s experience is probably compatible with Vaishnavism, the largest denomination within Hinduism. According to my college comparative religions professor, 75% of Hindus are Vaishnavites. So there are hundreds of millions of people who probably see Ramanujan’s religion as a comfortable affirmation.

But most people I know aren’t Vaishnavites. I’ve never seen Hinduism as a live option, and most people I know haven’t either. What do we think actually happened?

I see three main possibilities: either Ramanujan’s revelations were from God, or from an evil spirit, or from Ramanujan himself. Despite the fact that I consider Namagiri a false goddess, I think an evil spirit is the least likely origin of the three. Demons usually lie, and when they tell the truth they do it to corrupt. It would be highly unusual for God to allow a demon to reveal as much truth as Ramanujan found. And mathematical truths don’t corrupt anyone!

Could the revelations have come from God? I can’t dismiss the possibility, but neither can I endorse it. Why would God give a vision through a Hindu goddess, rather than Himself or his angels or saints? I believe with the Church that non-Christian religions participate to varying extents in the truths of faith and revelation, and in apprehension of the mysteries of God. But I’m not sure how this specific case fits into that framework.

That leaves Ramanujan himself. All of us, of every religion, have to believe that people are sometimes fooling themselves about things that they claim come from God. It’s distressingly easy to project our own desires on the divine. But there’s a problem applying that theory to Ramanujan: the fruits. He produced truths! Shouldn’t the truth of his work make us trust his testimony about its origin?

This problem is no less acute for an atheist than for a monotheist. Atheists reject gods as an explanation, and probably reject demons as well, so they’re left with Ramanujan himself. And there, they confront exactly the same challenge as monotheists. Should they actually seek scientific signs like my friend claimed to, the challenge increases.

Unfortunately, I don’t expect I’ll find a conclusive explanation of Ramanujan and Namagiri on this side of death. I wish I could wrap it up nicely for you! But in this life, not every piece of evidence points in the same direction. I’m left with only wonder- wonder for the beauty of Ramanujan’s results, and wonder for the mysteries of revelation, both far beyond my understanding.

  1. Biographical details are from Wikipedia, and from the movie The Man Who Knew Infinity, which I recommend. ↩︎

  2. From Wikipedia, Taxicab number↩︎