Now proof has been found for a connection that he seemed to mysteriously intuit between two types of mathematical functions.
“His ideas as to what constituted a mathematical proof were of the most shadowy description,” GH Hardy, Ramanujan’s mentor and one of his few collaborators, had once said.
Ken Ono of Emory University in Atlanta, who has previously unearthed hidden depths in Ramanujan’s work, was prompted by Ramanujan’s 125th birth anniversary, to look at his writings.
“I wanted to go back and prove something special,” Ono said.
Ono settled on a discussion in the last known letter that Ramanujan wrote to Hardy, concerning a type of function now called a modular form.
The functions looked unlike any other modular forms, but Ramanujan wrote that their outputs would be very similar to those of modular forms when computed for the roots of 1 like the square root of -1.
It was only 10 years back that mathematicians formally defined this other set of functions, now known as mock modular forms.
Ono and colleagues have exactly calculated one of Ramanujan’s mock modular forms for values very close to -1, and said the difference in the value of the two functions, ignoring the functions signs, is tiny when computed for -1, just like Ramanujan said.