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Moonshine’s shadows
In 1913, the English mathematician G. H. Hardy received a letter from an accounting clerk in Madras, India, describing some mathematical formulas he had discovered. Many of them were old hat, and some were flat-out wrong, but on the final page were three formulas that blew Hardy’s mind. “They must be true,” wrote Hardy, who promptly invited the clerk, Srinivasa Ramanujan, to England, “because, if they were not true, no one would have the imagination to invent them.” Ramanujan became famous for seemingly pulling mathematical relationships out of thin air, and he credited many of his discoveries to the goddess Namagiri, who appeared to him in visions, he said. His mathematical career was tragically brief, and in 1920, as he lay dying in India at age 32, he wrote Hardy another letter saying that he had discovered what he called “mock theta” functions, which entered into mathematics “beautifully.” Ramanujan listed 17 examples of these functions, but didn’t explain what they had in common. The question remained open for more than eight decades, until Sander Zwegers, then a graduate student of Zagier’s and now a professor at the University of Cologne in Germany, figured out in 2002 that they are all examples of what came to be known as mock modular forms.
I’ve read that while working a problem there were a couple instances when Ramanujan invented/derived his own method for getting from A to the solution at B, and in doing so had basically re-invented an already established methodology/discipline within mathematics.
Someone needs to tell Ed Witten about this!!
originally posted by: netbound
Srinivasa Ramanujan was a gargantuan genius among geniuses. His incredible mental abilities were so towering as to be almost beyond belief. He was truly operating on another plane. What a drag he passed away so early in life; he probably had so much more to contribute. I guess the good die young...
Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field.