“Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package.”
― The Man Who Knew Infinity: A Life of the Genius Ramanujan
― The Man Who Knew Infinity: A Life of the Genius Ramanujan
“The place had enormous possibilities. He realized that at once. The stream, of course, was perfect for sailing toy boats, for skipping stones, and, in the event of failing inspiration, for falling into. Several of the trees appeared to have been specifically designed for climbing, and one huge, white old birch overhanging the stream promised the exhilarating combination of climbing a tree and falling into the water, all at one time.”
― Guardians of the West
― Guardians of the West
“Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”
― A Mathematician's Apology
― A Mathematician's Apology
“I use the example as computed by the mathematician Michael Berry. If you know a set of basic parameters concerning the ball at rest, can compute the resistance of the table (quite elementary), and can gauge the strength of the impact, then it is rather easy to predict what would happen at the first hit. The second impact becomes more complicated, but possible; you need to be more careful about your knowledge of the initial states, and more precision is called for. The problem is that to correctly predict the ninth impact, you need to take into account the gravitational pull of someone standing next to the table (modestly, Berry's computations use a weight of less than 150 pounds). And to compute the fifty-sixth impact, every single elementary particle of the universe needs to be present in your assumptions!”
― The Black Swan: The Impact of the Highly Improbable
― The Black Swan: The Impact of the Highly Improbable
“When {Born and Heisenberg and the Göttingen theoretical physicists} first discovered matrix mechanics they were having, of course, the same kind of trouble that everybody else had in trying to solve problems and to manipulate and to really do things with matrices. So they had gone to Hilbert for help and Hilbert said the only time he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert didn't know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger’s wave mechanics six month earlier if they had paid a little more attention to him.”
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