I have always been intrigued by the extraordinary insights of the self-taught mathematician Srinivasa Ramanujan. He worked in almost complete isolation from the mathematical community, and independently rediscovered many existing results while also making his own unique contributions. He didn’t even share notation with the rest of the community, somehow finding his way without being led. I’m convinced that this remarkable life must be showing us something about the very nature of the thoughts he followed – something we have neglected about the nature of mathematics itself.
He was brought to my attention again when Scientific American wrote about India’s response to his 125th birthday on December 22. Last year Prime Minister Manmohan Singh declared 2012 to be a National Mathematics Year in India in honor of Ramanujan.
But then, even more newsworthy, I found a number of reports about how mathematicians were able to show that a hunch Ramanujan had about the properties of a class of functions (that were never before heard of) was correct. The story was reported in the Daily Mail on December 28.
While on his death-bed in 1920, Ramanujan wrote a letter to his mentor, English mathematician G. H. Hardy, outlining several new mathematical functions never before heard of, along with a hunch about how they worked.
Decades years later, researchers say they’ve proved he was right – and that the formula could explain the behaviour of black holes.
‘We’ve solved the problems from his last mysterious letters,’ Emory University mathematician Ken Ono said.
In each of the accounts of this development, some reference was made to the fact that Ramanujan’s insight was contained in a dream. From Daily News and Analysis:
Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri. However, no one at the time understood what he was talking about.
The same statement appeared in the Daily Mail with an image of the goddess.
A more thorough discussion of Ramanujan’s insight can be found in the article What is a Mock Modular Form? published by the American Mathematical Society.
From the Huffington Post:
Ramanujan believed that 17 new functions he discovered were “mock modular forms” that looked like theta functions when written out as an infinte sum (their coefficients get large in the same way), but weren’t super-symmetric. Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.
Ramanujan died before he could prove his hunch. But more than 90 years later, Ono and his team proved that these functions indeed mimicked modular forms, but don’t share their defining characteristics, such as super-symmetry.
In developing mock modular forms, Ramanujan was decades ahead of his time, Ono said; mathematicians only figured out which branch of math these equations belonged to in 2002.
“Ramanujan’s legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died,” Ono said.
I enjoyed this video posted on youtube that helps bring both the math story and the personal story to life. It was suggested here that, given Ramanujan’s religious life, it isn’t really a surprise that he would attribute his vision to a Hindu goddess. But a statement like that is just suggesting that we needn’t think about it. There is something to think about, and it’s not whether mathematics is really divine or not. While there may be no easy way to address this question, the peculiarities of Ramanujan’s work should encourage some of us to wonder about how spiritual vision, dream vision, waking vision, and what I’m tempted to call cognitive vision (the perception of pure structural meaning) are related.