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Mathematicians don't seem to have a consensus on which questions are mathematical, and which ones are interesting but sometimes one pronounces with an air of authority on a question or solution or unfamiliar new method. So what exactly is the training that mathematicians have had that allows them to be so sure about their answers?

What would be a valid way for a mathematician to prove or at least demonstrate or argue that a question or technically valid solution is not interesting or not mathematical.

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    If you need to ask the question about a particular piece of work, then it probably isn't.
    – Buffy
    Mar 30 '21 at 12:36
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    @MatthewChristopherBartsh why do you keep asking why your questions have the score they do? The answer is the same every time. It is the number of upvotes minus the number of downvotes.
    – Chris H
    Mar 30 '21 at 13:18
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    @MatthewChristopherBartsh Because at least six people found that this question either did not show any research effort, or was unclear, or was not useful, or any combination of the three. This website, like mathematics, like science, is a social construct. Not all six of those voters are going to give you the reasoning behind their votes. My guess would be that the majority of the downvoters would find having this question answered on this site to be, ironically, not interesting. But it's just a guess. Mar 30 '21 at 13:18
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    @MatthewChristopherBartsh I'm not a mathematician but to be blunt with you, no. How does that help me gain new insight into the world? It's not maths, it's more like semantics and most (all?) mathematicians have much bigger fish to fry. It's like asking if I find the alphabet interesting. I'd much rather read a novel.
    – astronat
    Mar 30 '21 at 13:30
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    As a first approximation, a piece of mathematics is interesting if it suggests some method for solving the Langlands conjectures. (j/k, but with a grain of truth). Mar 30 '21 at 16:20
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One cannot prove this. Interestingness is inherently subjective.

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It is your job to convince others that your work is interesting, not their job to prove it is not.

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