Now, researchers say they have proved Ramanujan was right, and that the formula could explain the behaviour of black holes.

"We've solved the problems from his last mysterious letters," Ken Ono, a mathematician from Emory University in Georgia, US, was quoted as saying.

"For people who work in this area of math, the problem has been open for 90 years," he said.

Ono said Ramanujan, a self-taught mathematician born in a village in southern India, spent so much time thinking about math that he flunked out of college in India twice.

Ramanujan's letter to Hardy described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.

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.

"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 told the daily.

Ono and his colleagues drew on modern mathematical tools that had not been developed before Ramanujan's death to prove that his theory was correct.

"We proved that Ramanujan was right. We found the formula explaining one of the visions that he believed came from his goddess," Ono said.

"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," he said.

The findings were presented in November at a Ramanujan conference held at the University of Florida, ahead of the 125th anniversary of the mathematician's birth Dec 22.