cyranoVR's Journal: Heroes of Mathematics: Srinivasa Ramanujan

I thought Good Will Hunting was entertaining, but I found its premise rather implausible - a lower-class kid with no higher education is some sort of mathmatical genius? Please. Only in the movies.

It turns out it's not so implausible after all. I was doing some Googling to supplement my reading of Brian Greene's popular theoritical physics work The Elegant Universe, when I stumbled upon the amazing story of Srinivasa Ramanujan. One of his theorems on a modular function forms the bedrock of modern Superstring theory. His life story is presented below, excerpted from this Usenet posting (which in turn excerpted the passage from Michio Kaku's Hyperspace):

Reinventing 100 Years of Mathematics

Ramanujan was born in 1887 in Erode, India, near Madras. Although his family was Brahmin, the highest of the Hindu castes, they were destitute, living off the meager wages of Ramanujan's father's job as a clerk in a clothing merchant's office.

By the age of 10, it was clear that Ramanujan was not like the other children. like Riemann before him, he became well known in his village for his awesome calculational powers. As a child, he had already rederived Euler's identity between trigonometric functions and exponentials.

In every young scientist's life, there is a turning point, a singular event that helps to change the course of his or her life. For Einstein, it was the fascination of observing a compass needle. For Riemann, it was reading Legendre's book on number theory. For Ramanujan, it was when he stumbled on an obscure, forgotten book on mathematics by George Carr. This book has since been immortalized by the fact that it marked Ramanujan's only known exposure to modern Western mathematics. According to his sister, it was this book which awakened his genius. He set himself to establish the formulae given therein. As he was without the aid of other books, each solution was a piece of research so far as he was concerned.... Ramanujan used to say that the goddess of Namakkal inspired him with the formulae in dreams.

Because of his brilliance, he was able to win a scholarship to high school. But because he was bored with the tedium of class work and intensely preoccupied with the equations that were constantly dancing in his head, he failed to enter his senior class, and his scholarship was canceled. Frustrated, he ran away from home. He did finally return, but only to fall ill and fail his examinations again.

With the help of friends, Ramanujan managed to become a low-level clerk in the Port Trust of Madras. It was a menial job, paying a paltry 20 pounds a year, but it freed Ramanujan, like Einstein before him at the Swiss patent office, to follow his dreams in his spare time. Ramanujan then mailed some of the results of his "dreams" to three well-known British mathematicians, hoping for contact with other mathematical minds. Two of the mathematicians, receiving this letter written by an unknown Indian clerk with no formal education, promptly threw it away. The third one was the brilliant Cambridge mathematician Godfrey H. Hardy. Because of his stature in England, Hardy was accustomed to receiving crank mail and thought dimly of the letter. Amid the dense scribbling he noticed many theorems of mathematics that were already well known. Thinking it the obvious work of a plagiarist, he also threw it away. But something wasn't quite right. Something nagged at Hardy; he couldn't help wondering about this strange letter.

At dinner that night January 16,1913, Hardy and his colleague John Littlewood discussed this odd letter and decided to take a second look at its contents. It began, innocently enough, with: "I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office of Madras on a salary of only 20 pounds per annum." But the letter from the poor Madras clerk contained theorems that were totally unknown to Western mathematicians. In all, it contained 120 theorems. Hardy was stunned. He recalled that proving some of these theorems "defeated me completely." He recalled, "I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class."

Littlewood and Hardy reached the identical astounding conclusion: This was obviously the work of a genius engaged in rederiving 100 years of European mathematics. "He had been carrying an impossible handicap, a poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe," recalled Hardy.

Hardy sent for Ramanujan and, after much difficulty, arranged for' his stay in Cambridge in 1914. For the first time, Ramanujan could communicate regularly with his peers, the community of European mathematicians. Then began a burst of activity: 3 short, intense years of collaboration with Hardy at Trinity College in Cambridge.

Hardy later tried to estimate the mathematical skill that Ramanujan possessed. He rated David Hilbert, universally recognized as one of the greatest Western mathematicians of the nineteenth century, an 80. To Ramanujan, he assigned a 100. (Hardy rated himself a 25)

Unfortunately, neither Hardy nor Ramanujan seemed interested in the psychology or thinking process by which Ramanujan discovered these incredible theorems, especially when this flood of material 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."

Hardy vividly recalled:

I remember going to see him once when he was lying ill in Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to he rather a dull one, and that I hoped that it was not an unfavorable omen. "No",- he replied,---itis a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."

(It is the sum of 1 X 1 X 1 and 12 X 12 X 12, and also the sum of 9 x 9 X 9 and 10 X 10 X 10.) On the spot, he could recite complex theorems in arithmetic that would require a modern computer to prove.

Always in poor health, the austerity of the war-torn British economy prevented Ramanujan from maintaining his strict vegetarian diet, and he was constantly in and out of sanitariums. After collaborating with Hardy for 3 years, Ramanujan fell ill and never recovered. World War I interrupted travel between England and India, and in 1919 he finally managed to return home, where he died a year later.

Modular Functions

Ramanujan's legacy is his work, which consists of 4,000 formulas on 400 pages filling three volumes of notes, all densely packed with theorems of incredible power but without any commentary or, which is more frustrating, any proof. In 1976, however, a new discovery was made. One hundred and thirty pages of scrap paper, containing the output of the last year of his life, was discovered by accident in a box at Trinity College. This is now called Ramanujan's "Lost Notebook.---Commenting on the Lost Notebook, m athematician Richard Askey says, "The work of that one year, while he was dying, was the equivalent of a lifetime of work for a very great mathematician. What he accomplished was unbelievable. If it were a novel, nobody would believe it." To underscore the difficulty of their arduous task of deciphering the "notebooks," mathematicians Jonathan Borwein and Peter Borwein have commented,"To our knowledge no mathematical redaction of this scope or difficulty has ever been attempted."

Looking at the progression of Ramanujan's equations, it's as though we have been trained for years to listen to the Westem music of Beethoven, and then suddenly we are exposed to another type of music, an eerity beautiful Eastern music blending harmonies and rhythms never heard before in Western music. Jonathan Borwein says, "He seems to have functioned in a way unlike anybody else we know of. He had such a feel for things that they just flowed out of his brain. Perhaps he didn't see them in any way that's translatable. It's like watching somebody at a feast you haven't been invited to."

good stuff.

[mekkab]

Nice read.

I seem to recall another tragic figure in math (or was it economics? Or econometrics?), a brilliant speed-freak who went the way of most rock stars- trying to score that next hit and, oh yeah, producing genius. If I get off my keyster I'll google for him.

Good Will Hunting

[lucasw]

There's a scene in Good Will Hunting where Robin Williams is telling Matt Damon about Ramanujan. I thought it was interesting for Williams' character not to mention his untimely death, but I suppose that would have undermined his argument...

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