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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.

Matthew Christopher Bartsh
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    In my opinion, a mathematically interesting question is one to which the answer will uncover something new about the world, some new truth (or a better approximation to the truth) or new insight. That should be the goal of any scientific (and perhaps also artistic) endeavour. – astronat supports the strike Mar 30 '21 at 12:09
  • This question is closely related, and possibly a duplicate. – Dan Romik Mar 30 '21 at 12:21
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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
  • With experience and depth come an appreciation of certain kinds of problems. But we don't all find the same things interesting. Turns out, though, there are some things that interest few of us, we're human. – A rural reader Mar 30 '21 at 12:48
  • a question is mathematically interesting if there are >1 professional mathematicians who agree that it is interesting. – sleepy Mar 30 '21 at 12:52
  • Why is the question on '-6'? – Matthew Christopher Bartsh Mar 30 '21 at 13:02
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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
  • @astronat Okay, but the question asks what training mathematicians get in order to tell if a question, answer, or method is interesting. – Matthew Christopher Bartsh Mar 30 '21 at 13:20
  • @astronat For example, is or was positional notation an interesting mathematical idea? How about the idea of reading out the numerals without mentioning the powers, like we do with zip codes? How about the idea of putting commas before each group of three digits? How about the idea of dropping the 'and' and saying 'one hundred one'? – Matthew Christopher Bartsh Mar 30 '21 at 13:25
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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 supports the strike Mar 30 '21 at 13:30
  • @astronat What about when positional notation was rarely or never used by mathematicians? I'm assuming 'it' refers to positional notation. – Matthew Christopher Bartsh Mar 30 '21 at 13:33
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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). – Alexander Woo Mar 30 '21 at 16:20
  • As to this alleged lack of consensus as to what is, and what is not, mathematical, I'd like to see some concrete examples. At this point, I doubt I'll understand what you're actually talking about without those. – Michael Hardy Mar 30 '21 at 16:33
  • @MichaelHardy For example, is the question of how to pronounce binary numbers an interesting mathematical question? – Matthew Christopher Bartsh Mar 30 '21 at 16:43
  • @MatthewChristopherBartsh : How something should be pronounced is not a math problem. Do you know of something specific about how to pronounce such things that relies on a novel, or other, mathematical idea? – Michael Hardy Mar 30 '21 at 16:51
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    I have heard about Stern (1958, Science 128(3324):594-596), and McFeely (1959, Math. Teach. 52(5):356-357)? But I have been unable to look at either paper due to covid-19. There is also this from your humble correspondent: https://bartshmatthew.medium.com/how-a-math-teacher-should-pronounce-a-binary-number-1c41773df52f?source=your_stories_page-------------------------------------

     – Matthew Christopher Bartsh Mar 30 '21 at 16:55
  • ok, The Stern paper seems to be essentially about a system of mathematical notation. But if you just say "how to pronounce" or the like, without further context, people probably won't understand that. – Michael Hardy Mar 30 '21 at 17:55
  • @MichaelHardy There must be some mistake. The Joshua Stern paper I am referring to is about a new way to pronounce binary. Can you give me a link to what you found? – Matthew Christopher Bartsh Mar 30 '21 at 18:33
  • Let us continue this discussion in chat. – Matthew Christopher Bartsh Mar 30 '21 at 18:39

2 Answers2

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

Mithridates the Great
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Maarten Buis
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One cannot prove this. Interestingness is inherently subjective.