Srinivasa Ramanujan, the young genius who died at the age of 32, often managed to jump from insight to insight without formally proving the logical steps in between.
Now the proof was found for a connection that he seemed to mysteriously comprehend between two types of mathematical functions.
It was Ken Ono of Emory University in Atlanta, Georgia who had previously unearthed hidden depths in Srinivasa Ramanujan’s work, and now he was prompted by. Ramanujan’s 125th birth anniversary to look once more at his writings.
Ken Ono settled on a discussion in the last known letter that. Ramanujan wrote to Mathematician 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 had 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 came to understand what Ramanujan meant by saying the two types of function produced similar outputs for roots of 1.
Therefore, 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 had indicated.