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Apr 15, 2021 at 16:52 comment added Timothy Chow Here's a non-example to illustrate the point: Christian Krattenthaler's paper on Advanced determinant calculus. This paper explains a large number of techniques for evaluating certain kinds of determinants. Krattenthaler did a great service to the mathematical community by sharing all his tricks. But I think you can see how someone with a less generous spirit might keep those tricks secret and try to get credit for evaluating specific determinants of interest one by one, rather than publish just one "bag of tricks" paper that might not seem so impressive.
Apr 15, 2021 at 16:46 comment added Timothy Chow @none It does happen more often than some people realize. As you can imagine, part of the reason is that people get credit for writing papers and solving problems (or proving theorems), so if you can generate more papers by withholding some of your secrets, you might well do so. I know people who do this, although they don't advertise that this is what they are doing. Of course it is possible only in certain circumstances, where you are able to publish a complete solution to a problem without giving away the tricks you used to come up with the solution.
Apr 15, 2021 at 7:33 comment added none Sure, I understand that a counterexample can be checked without knowing how it was found. I'm asking more specifically, whether withholding the method is a common thing in contemporary math culture. It sounds like it does happen sometimes. Btw another historical example: Newton's Principia gaved classical geometry proofs of a bunch of things he actually discovered using calculus.
Apr 15, 2021 at 6:47 history edited Zach Teitler CC BY-SA 4.0
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Apr 15, 2021 at 5:36 history answered Alessandro Della Corte CC BY-SA 4.0