Ramanujan

Srinivasa Ramanujan was born in India, near Madras, in 1887. By the age

of 10, it became clear that Ramanujan was not like the other children. As a

child, he had already derived Euler’s identity between trigonometric func-

tions and exponentials. After receiving little formal education, he worked

as a junior clerk in the Port Trust of Madras. He then mailed some of the

results to his ‘dreams’ to three well-known mathematicians, hoping for

contact with other mathematical minds. One was received by the brilliant

Cambridge mathematician, Godfrey Hardy. The letter contained 120 theo-

rems totally unknown to Western mathematicians. On reading the letter,

Hardy was stunned. He came to the conclusion that it could only be written

by a mathematician of the highest class. In terms of mathematical skills,

Hardy later rated Ramanujan even higher than David Hilbert, universally

recognised as one of the greatest Western mathematician of the nineteenth

century.

Unfortunately, neither Hardy nor Ramanujan were interested in the

thinking process by which Ramanujan discovered these incredible theo-

rems, especially when these theorems came pouring out of his ‘dreams’ with

such frequency. Hardy noted, ‘It seemed ridiculous to worry him about how

he had found this or that known theorem, when he was showing me half a

dozen new ones almost every day.’ Ramanujan used to say that the goddess

of Namakkal inspired him with the formulae in dreams. He kept a note pad

next to his bed to write down the formulae that he claimed were revealed to

him in dreams. On the spot, Ramanujan could recite complex theorems in

arithmetic that would require a computer to prove. Working in total isola-

tion from the main currents of his field, he was able to rederive 100 years’

worth of Western mathematics on his own. Jonathan Borwein says, ‘He had

such a feel for things that they just flowed out of his brain.’5

We know that the left brain is active for most of the day and when we

go to sleep, activity shifts to the right brain. In dreams, right brain activity

is evident.

One interesting aspect of Ramanujan’s powers is that he often took

hours or even months to labouriously verify and prove what he often re-

ceived in an instant, and that sometimes his insight turned out to be wrong!

Ideas arrived at by intuition, just as ideas derived from deliberate conscious

thinking, can contain errors.