- Gelfand: You mentioned computers. What has changed in mathematics since their appearance?
- Manin: What has changed in pure mathematics? The unique possibility of doing large-scale physical experiments in mental reality arose. We can try the most improbable things. More exactly, not the most improbable things, but things that Euler could do even without a computer. Gauss could also do them. But now, what Euler and Gauss could do, any mathematician can do, sitting at his desk. So if he doesn’t have the imagination to distinguish some features of this Platonic reality, he can experiment. If some bright idea occurs to him that something is equal to something else, he can sit and sit and compute a value, a second value, a third, a millionth. Not only that. People have now emerged who have mathematical minds, but are computer oriented. More precisely, these sorts of people were around earlier, but, without computers, somehow something was missing. In a sense, Euler was like that, to the extent that he was just a mathematician— he was much more than just a mathematician— but Euler the mathematician would have taken to computers passionately. And also Ramanujan, a person who didn’t even really know mathematics. Or, for instance, my colleague here at the institute, Don Zagier. He has a natural and great mathematical mind, which is at the same time ideally suited to work with computers. Computers help him study this Platonic reality, and, I might add, quite effectively. I myself am not this sort of person at all, but I understand what this is about and would be glad to have collaborators who might help me in this. So this is what computers have done for pure mathematics.
My reality tunnel
Watch this space for a collection of amusing things found on the Web.
See also superadditive.com. Any questions?
November 14, 2009
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