Srinivasa Ramanujan, described as a ‘natural genius’, has finally had the mathematical functions he came up with on his deathbed proved correct.
Researchers have finally solved the cryptic deathbed puzzle renowned Indian mathematician Srinivasa Ramanujan claimed came to him in dreams.
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 behavior of black holes.
‘We’ve solved the problems from his last mysterious letters,’ Emory University mathematician Ken Ono said.
‘For people who work in this area of math, the problem has been open for 90 years,’
Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said.
Ramanujan’s letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.
Functions are equations that can be drawn as graphs on an axis, like a sine wave, and produce an output when computed for any chosen input or value.
Ramanujan conjectured that his mock modular forms corresponded to the ordinary modular forms earlier identified by Carl Jacobi, and that both would wind up with similar outputs for roots of 1.
Described as a raw genius, he independently rediscovered many existing results, as well as making his own unique contributions, believing his inspiration came from the Hindu goddess Namagiri. He overcame several hurdles to find a place among the celebrated intellectuals of Cambridge.
However, no one at the time understood what Ramanujan was talking about.
‘It wasn’t until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,’ Ono said.
Ono and his colleagues drew on modern mathematical tools that had not been developed before Ramanujan’s death to prove this theory was correct.
‘We proved that Ramanujan was right,’ Ono says.
‘We found the formula explaining one of the visions that he believed came from his goddess.’
The team were also stunned to find the function could be used today.
‘No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,’ Ono says.
‘Ramanujan’s legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died,’ Ono said.
The findings were presented at the Ramanujan 125th conference at the University of Florida, ahead of the 125th anniversary of the mathematician’s birth on Dec. 22nd.
December 22, 2012 marked the 125th birth anniversary of Srinivasa Ramanujan, the self taught mathematician born into a modest and conservative family in Kumbakonam, a relatively small town in Tamilnadu.
Ramanujan passed away at the young age of 32 of tuberculosis, but he left behind formulations in mathematics that have paved the path for many scholars who came after him.