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

or
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.

The Engines of Our Ingenuity is
Copyright © 1988-1997 by John H.
Lienhard.

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