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No. 495:

Today, we try to explain genius. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Late in WW-I, a young Indian, Srinivas Ramanujan, lay ill in a London hospital. G.H. Hardy, the leading mathematician in England, visited him there. "I came over in cab number 1729," Hardy told Ramanujan. "That seems a rather dull number to me."

"Oh, no!" Ramanujan shot back. "1729 is the smallest number you can write as the sum of two cubes, in two different ways." You or I would use a computer to figure that out. Ramanujan did it from his sickbed without blinking.

Ramanujan was born to a poor family in South India in 1887. He was clearly smart, but he couldn't afford an education. His teenage math training consisted of reading two books. One was a standard trigonometry text. The other was a handbook of 6000 theorems -- stated without proof!

That book set his mathematical style. He began writing out his own theorems -- without proof -- hundreds -- thousands of them. His talent finally did get him into college, but he didn't fit. The furious activity in his own head absorbed him. He couldn't relate to instruction.

So he wrote theorems and worked as a clerk. In 1913 he wrote to Hardy at Cambridge. Hardy would've ignored the letter, but he took a moment to glance at 120 theorems Ramanujan had included. It was the oddest pastiche. Here were familiar results, reinvented. There were others that, Hardy said, had to be true. No one would have the imagination to just cook them up.

So Hardy brought Ramanujan to England. He trained him, and he learned from him. Ramanujan wrote theorems. He also kept the strictest Hindu practice. Trying to eat by his dietary laws in England was next to impossible. His health began failing.

He finally went back to India, gravely ill, in 1919. There he wrote theorems for one more year. Then, like another of the huge geniuses of all time -- like Mozart -- he died at 36.

Mathematicians have mined his theorems ever since. They've figured out how to prove them. They've put them to use. Only recently, a lost bundle of his notebooks turned up in a Cambridge library. That set mathematics off on a whole new voyage of discovery.

And where did all this unproven truth come from? Ramanujan was quick to tell us. He simply prayed to Sarasvathi, the Goddess of Learning, and she informed him. The unsettling thing is, none of us can find any better way to explain the magnitude of his eerie brilliance.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

Borwein, J.M. and Borwein, P.B., Ramanujan and Pi. Scientific American, Vol. 258, February 1988, pp. 112-117.

Hoffman, P., Archimedes' Revenge: The Joys and Perils of Mathematics, New York: Fawcett Crest, 1988, Chapter 2.

I've paraphrased the words attributed to Hardy and Ramanujan. How he did the calculation so rapidly remains a question, although it was probably a combination of his prodigious memory and quick thinking. Just for the record:

   1729 = 1 cubed + 12 cubed
   1729 = 9 cubed + 10 cubed

Since I did this script a new book on Ramanujan was published. It is: R. Kanigel, The Man Who Knew Infinity. (Abacus, 1992).

For more on Ramanujan, see the many useful links, including the Wikipedia article on his life.