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| Legends from the South |
| Ramanujan: “The man who knew Infinity” |
| “His leaps of intuition confound mathematicians
even today, seven decades after his death. His papers are still
plumbed for their secrets. His theorems are being applied in
areas—Polymer chemistry, computers, even (it has recently been
suggested) cancer—scarcely imaginable in his lifetime. And always
the nagging question: What might have been, had he been discovered
a few years earlier, or lived a few years longer?” |
| To most Tamil-speaking Indians, this passage
from the prologue to “The Man Who Knew Infinity”, by American
author Robert Kanigel, will bring instant recognition of the
subject: the mathematical genius Srinivasa Ramanujan, who was
born into a poor brahmin family on December 22, 1887 at Erode,
a small town in the heart of Tamil Nadu, and ‘discovered’ by
English mathematician G H Hardy. |
| Ramanujan’s story was a fairytale, but a flawed
one, with a tragic and an abrupt end, brought about by tuberculosis,
which claimed the genius’ life at the age of 32. His was an
untamed, intuitive, mathematical gift that enabled him to arrive
at complex theorems even in his teen years. |
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| Srinivasa Ramanujan |
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| All through his school years, Ramanujan walked off
with every conceivable merit certificate and scholastic prize. The
headmaster of the school once introduced him to the audience at a
prize-giving ceremony, as “a student who, were it possible, deserved
higher than the maximum marks.” |
| An innocuous book by George Shoobridge Carr, “A
Synopsis of Elementary Results in Pure and Applied Mathematics,” changed
Ramanujan’s life forever. This was a compendium of over 5000 equations
which Ramanujan first came across in 1903, in his final year at school.
Whatever its effect on other students, in Ramanujan, the book “ignited
a burst of fiercely single-minded intellectual activity”, something
that in time became an all-engulfing passion for mathematics. |
| This, naturally, led to untold trouble for the young
scholar, who started to fail examination after examination, as a result
of his obsession with maths that made him spend every waking moment
on that subject to the exclusion of all other subjects. As a student
of Kumbakonam Government College, and later, Pachaiyappa’s College,
Madras, he failed in all exams other than maths, and lost the scholarships
he had won earlier. This ironically led to a five-year period during
which he was totally free to pursue his passion, because his college
had flunked him, and he had nothing else to do. Married in 1908, he
was supported for a while by Ramachandra Rao, civil servant, and secretary
of the Indian Mathematical Society, whom Ramanujan’s notebooks impressed
considerably with their originality. |
| It was while he was a clerk in the Port Trust that
Ramanujan started corresponding with British mathematicians, sending
them some of his original work, especially in the infinite series
of numbers. After a couple of rejections from bewildered mathematicians
who did not know whether their exotic correspondent was a genius or
an idiot savant, Ramanujan struck pay dirt with G H Hardy, a 35-year-old
mathematician who was “turning English mathematics on its ear.” His
letter read: |
| Dear Sir, |
| I beg to introduce myself as a clerk in the accounts
department of the Port Trust Office at Madras on a salary of only
£ 20 per annum. I am now about 23 years of age. I have had no University
education but I have undergone the ordinary school course. After leaving
school I have been employing the spare time at my disposal to work
at Mathematics. I have not trodden through the conventional regular
course which is followed in a University course, but I am striking
out a new path for myself. I have made a special investigation of
divergent series in general and the results I get are termed by the
local mathematicians as “startling.” |
| Third time lucky, Ramanujan was able to convince
Hardy enough of his genius for the English “aristocrat of the intellect”
to go to great trouble to bring him over to England, and pass him
through the academic rigours that his inspired solutions had hitherto
lacked. |
| In Cambridge University, Ramanujan “was a happy
man, revelling in the mathematical society he was entering and idolised
by the Indian students.” He had enough money and freedom from financial
worry to pursue maths to his heart’s content. “In this old town of
cobbled walks, grassy courts, and medieval chapels, whole universes
away from Madras, Ramanujan had found a kind of intellectual nirvana.” |
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| G H Hardy |
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| In that rarefied academic atmosphere, Ramanujan
bloomed as a mathematician, though the First World War, tuberculosis
and treatment at sanitaria interfered with his progress, especially
as there were few mathematicians now available for him to work
along with. He was elected a Fellow of the Royal Society of
Mathematicians and a Trinity Fellow, high honours indeed for
someone who rose from such a humble background. |
| Ramanujan returned to India in 1919, to have
better chances of recovery in the warm climate of his native
state. But on April 26, 1920, he died at Chetpet, Madras, now
reduced to skin and bones, with his wife Janaki by his side.
“It was always maths… Four days before he died, he was scribbling,”
his wife recalled later. |
| Hardy, mentor, friend, maths partner,
paid this tribute to Ramanujan: “He would have been a greater
mathematician if he had been caught and tamed a little in his
youth; he would have discovered more that was new, and that,
no doubt, of greater importance. On the other hand, he would
have been less of a Ramanujan, and more of a European professor,
and the loss might have been greater than the gain.” |
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| 1729 and all that! |
| “Once, in (a) taxi from London, Hardy
noticed its number, 1729. He must have thought about it
a little because he entered the room where Ramanujan lay
in bed and, with scarcely a hello, blurted out his disappointment
with it. It was, he declared, “rather a dull number,”
adding that he hoped that wasn’t a bad omen. |
| “No, Hardy,” said Ramanujan. “It is
a very interesting number. It is the smallest number expressible
as the sum of two cubes in two different ways.” |
| Finding numbers that were the sum of
one pair of cubes was easy. For example, 23
+ 33 = 35. But could you get to 35 by adding
some other pair of cubes? You couldn’t. And as you tried
the integers one by one, it was the same story. One pair
sometimes, two pair never—never, that is, until you reached
1729, which was equal to 123 + 13,
but also 103 + 93. |
| How did Ramanujan know? It was no sudden
insight. Years before, he had observed this little arithmetic
morsel, recorded it in his notebook and, with that easy
intimacy with numbers that was his trademark, remembered
it.” |
| Reproduced from The Man Who Knew Infinity
by Robert Kanigel. |
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