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Ramanujan's Deathbed Conjecture Finally Proven
jomama717 writes "Another chapter in the fascinating life of Srinivasa Ramanujan appears to be complete: 'While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they've proved he was right. "We've solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years," Emory University mathematician Ken Ono said.
Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said.'"
Obsessed, and smart.
He had a mathematician's mind, sure. Probably not much brighter than what we consider reasonably bright and particularly attuned for maths. But what he had that sets us apart, was a raging obsession. The kind of demon that consumed Newton and possessed him to calculate pages of logarithms and Tesla to study from dusk 'til dawn and further, without respite.
I wonder what would happen if US colleges (or even earlier in our educational system) let students have free reign, and really specialize. If over in India this man had been nurtured in college, and allowed to stay in math courses (or even better conduct his own lines of study), might he have had a more enjoyable or productive life? If we recognize genius and cultivate it, what might grow in that garden?
Probably not much brighter than what we consider reasonably bright and particularly attuned for maths.
Give a reasonably bright math graduate an entire lifetime and he is unlikely to be able to reinvent all the math that Ramanujan reinvented due to not knowing it already existed, nor invent all the new math stuff that Ramanujan came up with. Ramanujan did all that in only 32 years.
The merely obsessive would get stuck in ruts or fruitless paths. Ramanujan came up with tons of stuff.
The way his mind works is pretty different:
He was sharing a room with P. C. Mahalanobis who had a problem, "Imagine that you are on a street with houses marked 1 through n. There is a house in between (x) such that the sum of the house numbers to left of it equals the sum of the house numbers to its right. If n is between 50 and 500, what are n and x?" This is a bivariate problem with multiple solutions. Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction. The unusual part was that it was the solution to the whole class of problems. Mahalanobis was astounded and asked how he did it. "It is simple. The minute I heard the problem, I knew that the answer was a continued fraction. Which continued fraction, I asked myself. Then the answer came to my mind," Ramanujan replied.
This is not the "normal" savant rapid addition/multiplication sort of stuff.