Born in 1887 in Erode, Tamil Nadu, Srinivasa Ramanujan was self-taught and worked in almost complete isolation from the mathematical community of his time. Living in India, unaware of the work being done around the globe, he independently proved and discovered many mathematical theorems.
Around 1912 he sent samples of his work to the University of Cambridge, where it was spotted by G.H. Hardy. Hardy recognised the brilliance of Ramanujan's work and invited him to Cambridge. Ramanujan went on to become a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge.
During his short lifetime - he died of illness and malnutrition at the age of 32 - Ramanujan independently compiled over 3900 results, most of which where later proven correct, while some of them were proven false and others filed under the 'already known' category.
Ramanujan often managed to leap from insight to insight without formally proving the logical steps in between."His ideas as to what constituted a mathematical proof were of the most shadowy description," G.H. Hardy, Ramanujan's mentor and one of his few collaborators, had once said.
Now proof has been found for a connection that he seemed to mysteriously intuit between two types of mathematical functions.
Ken Ono of Emory University in Atlanta, Georgia, who has previously unearthed hidden depths in Ramanujan's work, was prompted by Ramanujan's 125th birth anniversary, to look once more 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.
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 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 -1.
Characteristically, Ramanujan offered neither proof nor explanation for this conclusion.
It was only 10 years later that mathematicians formally defined this other set of functions, now known as mock modular forms. However, still no one fathomed what Ramanujan meant by saying the two types of function produced similar outputs for roots of 1.
Now 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.
The result confirms Ramanujan's incredible intuition, says Ono.