- Theory came to Srinivasa Ramanujan in a dream on his deathbed in 1920 - but has never been proved
- Discovery could now be used to explain the behaviour of parts of a black hole
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Srinivasa Ramanujan, described as a 'natural genius', has finally had the mathematical functions he came up with on his deathbed proved correct
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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 behaviour 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.
Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.
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| Ramanujan claimed the patterns in numbers were revealed to him by a Hindu goddess |
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.
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| A highlight of working on a film about Ramanujan's life was getting to browse through some of the Indian master's original notebooks, said Ken Ono, right
'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 last month at the Ramanujan 125 conference at the University of Florida, ahead of the 125th anniversary of the mathematician's birth on Dec. 22nd.
A NATURAL GENIUS
December 22, 2012 marks 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 Tamilnad.
'Raw genius' Ramanujan at Cambridge (centre)
Ramanujan was self-taught and worked in almost complete isolation from the mathematical community of his time.
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 spent so much time thinking about math that he flunked out of college in India twice.
He overcame several hurdles to find a place among the celebrated intellectuals of Cambridge.
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.
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