Should there be more than one sort of math community?
There are, to my mind, two very different but important kinds of mathematical question. There is the kind that the Codidact and SE communities both like: Straight-forward "give the proof/calculation" questions. This can be "How do I solve this?" or "Why is this wrong?" or a few other variations.
But there are "soft" math questions that are not about the math itself but about the philosophy of math ("Is math invented or discovered?"), or the psychology of math ("When I see a problem like this, what methods or theorems should I think of to solve it?"), or for book recommendations, and so on. Of course the Codidact and SE communities both strongly discourage these questions. It's understandable in that they are often harder to answer.
BUT that doesn't mean that they are bad questions, or that one shouldn't ask them, or that there aren't good answers, or that a community shouldn't exist to help with them.
I can see reasons why maybe Codidact might not want to take on the challenge of hosting a community for these kinds of questions. It will probably have a low answer-acceptance rate; it will probably be prone to debate and therefore difficult to moderate; Codidact is small and other features are probably higher-priority to implement, I suppose.
So I understand if we ultimately don't want to have such a community. But I just wanted to bring up the possibility and see what people's thoughts are.
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I'm not a mathematician so maybe I'm missing something, but I would think that "When I see a problem like this, what methods or theorems should I think of to solve it?" would be an appropriate type of question. It starts with a problem and asks not for a formula or proof but, instead, methods. Similar questions on Software Development, Tabletop RPGs, and Cooking have done ok, from what I've seen.
(The philosophy question you posed sounds broader to me but, again, I am not an expert.)
Each Codidact community gets to decide what kinds of content it wants to support. It's ok if communities on our network take different approaches. We also have a tool not available on SE, categories, which allows for high-level separation of types of content, if the community wants to have that separation. Physics, for example, has a Problems category, for attempted solutions to problems. If Mathematics wants to have philosophy questions (which will be more open-ended and opinion-based) but wants to separate them, we can set that up for you.
I'm offering options, not trying to push in a particular direction. Codidact communities have more flexibility available than SE ones; y'all can take advantage of that if you want. We'll be happy to help with details and suggestions, but it's your decision, not ours, how the community is set up.
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I think that our community is too small as such, so I wouldn't like to split it further. So I prefer Monica's approach that there's just one community but we add categories. (thus, perhaps should have made this a comment under Monica, but that seemed to go under OP's comment there so I cancelled)
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It's not always easy to draw the line. I read this question just now because it was bumped, and immediately thought of this question. It was, at least in part, a question about philosophy of mathematics, but I don't think the asker realised that. Their goal was to understand the context of a paper.
I think most philosophers of mathematics are mathematicians, or at least were mathematicians who moved field (and the boundary between philosophy and mathematical logic is very thin); similarly, historians of mathematics; so probably the main reason for trying to build a separate community would be not to annoy mathematicans who aren't interested in the philosophical or historical aspects. But mathematics is already such a wide field that most people are interested in specific subareas rather than the field as a whole.
Taking those two points together, I'm not convinced that categories are necessary or even particularly valuable. I think that tags for history-of-mathematics and philosophy-of-mathematics are sufficient.
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