# Ramanujan

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’.