Ramanujan's Mock Modular Forms: Indian Mathematician's Dream Conjecture Finally Proven
Date 2013/1/1 17:59:24 | Topic: Hindu Press International
USA, December 27, 2012 (Live Science): While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they've proved he was right.
"We've solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years," Emory University mathematician Ken Ono said.
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. But he sent mathematicians letters describing his work, and one of the most preeminent ones, English mathematician G. H. Hardy, recognized the Indian boy's genius and invited him to Cambridge University in England to study. While there, Ramanujan published more than 30 papers and was inducted into the Royal Society.
It was on his deathbed in 1920 that he described mysterious functions that mimicked theta functions, or modular forms, in a letter to Hardy. Ramanujan believed that 17 new functions he discovered were "mock modular forms" that looked like theta functions when written out as an infinite sum, but weren't super-symmetric. Ramanujan, a devout Hindu, thought these patterns were revealed to him by the Goddess Namagiri. [HPI: Ramanujan attributed all his discoveries to the Goddess--see Hinduism Today's article on him at http://www.hinduismtoday.com/modules/ ... tion/item.php?itemid=3159.] Ramanujan died before he could prove his hunch.
The expansion of mock modular forms helps physicists compute the entropy, or level of disorder, of black holes. 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. 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. 22.