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Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the conver… - Paul Halmos
" "Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
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About Paul Halmos
Paul Richard Halmos (Hungarian: Halmos Pál) (March 3, 1916 – October 2, 2006) was a Hungarian-born Jewish American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, functional analysis (in particular, Hilbert spaces), and mathematical logic.
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Paul R. Halmos
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Paul Richard Halmos
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Additional quotes by Paul Halmos
Mathematics is not a deductive science — that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared.
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