Sunday, December 23, 2012

Ramanujan's Divine Patterns

"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. Expansion of modular forms is one of the fundamental tools for computing the entropy of a modular black hole.

Ono and two colleagues from Stanford drew on modern mathematical tools that had not been developed before Ramanujan's death to prove that a mock modular form could be computed just as Ramanujan predicted. "We proved that Ramanujan was right," Ono says. "We found the formula explaining one of the visions that he believed came from his goddess."

Ono and his students revisited the paragraph in Ramanujan's last letter that gave a vague description for how he arrived at the functions. That one paragraph has inspired hundreds of papers by mathematicians, who have pondered its hidden meaning for eight decades. "For the first time, we can prove that the exotic functions that Ramanujan conjured in his death-bed letter behave exactly as he said they would, in every case."
Science 2.0: Divine Patterns? Ramanujan's Magical Mind Gets A Math Formula