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A course of mathematical analysis by Khinchin A.

By Khinchin A.

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Sample text

I want to try to explain. Archimedes took a compass and straightedge that he made a mark on, which is not allowed; you can't do that. He put a mark on it with a pencil or something. He drew his half circle and marked it off in some certain way; I can't explain it to you, but anyway he did it that way. That's not fair. But he was a pretty intelligent man; don't get me wrong. : Well, anyway, I'm proud of him and he's proud of himself. I said he's never get any recognition for it, and he said he probably wouldn't, but I said, if you think you've done it, this is fine.

Why would a mathematician allow a trisector to continue a search for an impossible "proof"? Probably because at each face-to-face meeting, the easiest thing was to point out a new flaw, hoping that D. would not be able to get around it and would thus never come back. But the persistence of some trisectors goes beyond any limit that a mathematician can understand. Also, it becomes second nature for teachers to encourage students to try to master material when they know that in all probability they will not.

A lot of things in mathematics have changed too, over the years. No. Once a theorem is proved, it does not change. There are fashions in mathematics, and subjects come and go ... ME: But why do I keep reading in mathematics books, there's a great big thing I'm reading just now, that there have always been changes made in mathematics right along. Euclid has been proven wrong in lots of cases. : mE: Yes, in the past standards of proof were not what they are today, and it wasn't insisted on that the logic be perfect in every detail.

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