Srinivasa Ramanujan, a genius mathematician who sadly died way too young, is the subject of Saturday's Google doodle.
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
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.
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.
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.
settled on a discussion in the last known letter that Ramanujan wrote
to Hardy, concerning a type of function now called a modular form.
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.
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.
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.With inputs from PTI