Ramanujan

8QTS...U8hL
2 Nov 2022
3

One morning early in 1913, Hardy found, among
the letters on his breakfast table, a large untidy envelope
decorated with Indian stamps. When he opened it, he
found sheets of paper by no means clean, on which, in
a non- English script, were line after line of symbols.
Hardy glanced at them without enthusiasm.
He felt, more than anything, bored. He glanced
at the letter, written in halting English, signed by an
unknown Indian, asking him to give an opinion of these
mathematical discoveries. The script appeared to consist
of theorems, most of them, wild or fantastic looking,
one or two already well - known, laid out as though
they were original. There were no proofs of any kinds.
Hardy was not only bored, but also irritated. It seemed
like a curious kind of fraud. He put the manuscript
aside and went on with his day’s routine.
After lunch he loped off for a game of real tennis
in the university court. (If it had been summer, he
would have walked down to Fenner’s to watch cricket.)
In the late afternoon, he strolled back to his rooms.
That particular day, though, while the timetable wasn’t
altered, internally things were not going according to
plan. At the back of his mind, getting in the way of his
complete pleasure in his game, the Indian manuscript
nagged away. Wild theorems. Theorems such as he had
never seen before, nor imagined. A fraud of genius? A
question was forming itself with epigrammatic clarity:
is a fraud of genius more probable than an unknown
mathematician of genius ? Clearly the answer was no.
Back in his rooms in Trinity, he had another look at
the script. He sent word to Littlewood (probably by
messenger, certainly not by telephone, for which, like
all mechanical contrivances including fountain pens, he
had a deep distrust) that they must have a discussion
after hall.
Before midnight they knew, and knew for certain.
The writer of these manuscripts was a man of genius.
That was as much as they could judge, that night. It
was only later that Hardy decided that Ramanujan was,
in terms of natural mathematical genius, in the classof Gauss and Euler : but that he could not expect,
because of the defects of his education and because
he had come on the scene too late in the line of
mathematical history, to make contribution on the same
scale.
The following day Hardy went into action.
Ramanujan must be brought to England, Hardy decided.
Money was not a major problem. Trinity had usually
been good at supporting unorthodox talent (the college
had been the same for Kapitsa a few years later). Once
Hardy was determined, no human agency could have
stopped Ramanujan, but they needed certain amount of
help from a superhuman one.
Ramanujan turned out to be a poor clerk in Madras
(Chennai), living with his wife on twenty pounds a year.
He was usually strict about his religious observances,
with a mother who was even stricter. It seemed
impossible that he could break the ban and cross the
water. Fortunately his mother had the highest respect for
the goddess of Namakkal. One morning Ramanujan’s
mother made a startling announcement. She had a
dream the previous night, in which she saw her son
seated in a big hall among a group of Europeans and
the goddess of Namakkal had commanded her not to
stand in the way of her son fulfilling his life’s purpose.
This, say Ramanujan’s Indian biographers, was a very
agreeable surprise to all concerned.
In 1914, Ramanujan arrived in England. So far as
Hardy could detect (though in this respect I should not
trust his insight far) Ramanujan, despite the difficulties
of breaking the caste laws, did not believe much in
theological doctrine, except for a vague pantheistic
benelolence, any more than Hardy did himself. But he
did certainly believe in ritual. When Trinity put him
up in college within four years he became a fellow.
There was no ‘‘Alan St. Aubyn” self - indulgence for
him at all. Hardy used to find him ritually changed
into his pyjamas, cooking vegetables rather miserably
in a frying pan in his own room.
Their association was strangely touching one. Hardy
did not forget that he was in the presence of a genius,
but genius that was, even in mathematics, almost
untrained. Ramanujan had not been able to enter Madras
(Chennai) University because he could not matriculatein English. According to Hardy’s report, he was always
amiable and good - natured, but no doubt he sometimes
found Hardy’s conversation outside mathematics more
than a little baffling. He seems to have listened with
a patient smile on his good, friendly, homely face.
Even inside mathematics they had to come to terms
with the difference in their education. Ramanujan was
self - taught : he knew nothing of the modern rigour,
in a sense he didn’t know what a proof was. In an
uncharacteristically sentimental moment, Hardy once
wrote that if he had been better educated, he would
have been less ‘Ramanujan’. Coming back to his ironic
senses, Hardy later corrected himself and said that the
statement was nonsense. If Ramanujan had been better
educated, he would have been even more wonderful
than he was. In fact, Hardy was obliged to teach him
some formal mathematics as though Ramanujan had
been a scholarship candidate at Winchester. Hardy said
that this was the most singular experience of his life .
What did modern mathematics look like to someone
who had the deepest insight, but who had literally
never heard of most of it ?
It is good to remember that England gave
Ramanujan such honours as were possible. The Royal
Society elected him a Fellow at the age of thirty (which,
even for a mathematician, is very young). Trinity also
elected him a Fellow in the same year. He was the
first Indian to be given either of these distinctions. He
was amiably grateful. But he soon became ill.
Hardy used to visit him, as he lay dying in hospital
at Putney. It was on one of those visits that there
happened the incident of the taxi - cab number. Hardy
had gone out to Putney by taxi as usual, his chosen
mehod of conveyance. He went into the room where
Ramanujan was lying. Hardy, always clumsy about
introducing a conversation, said, probably without a
greeting and certainly as his first remark : “The number
of my taxi cab was 1729. It seemed to me rather a dull
number.” To which Ramanujan replied : “No, Hardy !
It is a very interesting number : It is the smallest
number expressible as the sum of two cubes in two
different ways”.
It was difficult, in war - time, to move Ramanujan
to a kinder climate. He died of tuberculosis, back inMadras (Chennai), two years after the war. As Hardy
wrote in the Apology, his roll - call of mathematicians
: ‘Galois died at twenty - one. Abel at twenty - seven,
Ramanujan at thirty - three, Riemann at forty. I do not
know an instance of a major mathematical advance
initiated by a man past fifty’.

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