Ramanujan & Pi

G H Hardy, a prominent and highly accomplished English mathematician, one of whose best-known works to non-mathematicians is a signature essay on the aesthetics of mathematics (“A Mathematicians Apology”) was the mentor of Srinivasa Ramanujan, an Indian student of Hardy’s at Cambridge who was a brilliant and innately talented mathematician.

Working at the beginning of the 20th century, Ramanujan discovered new formulas for pi, remarkable for their elegance and inherent mathematical depth. Typical of Ramanujan’s work was a formula series derived from the theory of modular functions, and converging quickly to muliple decimal point extensions of pi. But containing only sparse explanation, and no proof, Ramanujan’s received little distribution or publication.

It was Ramanujan’s mentor Hardy, and individual attuned to an inherent beauty and order in mathematics, who recognized the value of Ramanujan’s discoveries.

And so, it is perhaps thanks to Hardy that they survived as a body of work, to be rediscovered when a new tool – the computer – was available to unlock its innate power. Ramanujan’s work came to public attention around 1985, when William Gosper made use of it in calculating 17 million decimals of pi.

Greogry and David Chudnovsky, made use of ideas found in Ramanujan, and went on to set computing records for pi, and Ramanujan’s formulas became a foundation for calculating pi on handheld and personal computers – although supercomputers now use newer methods that go beyond it.

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