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Mathematics, as we all know, is a diverse forest full of interesting, strange, natural, obscure, appealing, highly abstract, and intuition-defeating topics: depending on which researcher you ask the labels vary from area to area.

It is my impression that the topics I find especially appealing (combinatorics finite and infinite, set theory, general topology) are "over-represented" on MathOverflow as I see a lot of activity in these areas, but comparatively little activity in what I perceive to be "hot topics" like algebraic geometry and analysis.

Question. Is my perception skewed? Or is MathOverflow (for some reason to be determined) more attractive to foundationalists as opposed to mathematician working in fashionable areas?

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    $\begingroup$ There is an algorithm to show you questions that you're more interested in and might be more likely to search/want to read/be able to answer. There's a way to get the report of how the algorithm sees you, but I don't remember it right now (it is not a moderator-only thing, that's my point). $\endgroup$ Commented Feb 4, 2025 at 16:36
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    $\begingroup$ Somewhat related posts: What areas/aspects of mathematics are underrepresented on MO? and arXiv vs MathOverflow - popularity of disciplines. $\endgroup$ Commented Feb 4, 2025 at 17:14
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    $\begingroup$ Algebraic geometry is certainly very well-represented, just look at tags. However I share the impression that analysis is comparatively (to the size of communities) less represented. $\endgroup$ Commented Feb 4, 2025 at 22:10
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    $\begingroup$ And also it sounds weird to me to view algebraic geometry as less "foundational" than combinatorics. $\endgroup$ Commented Feb 4, 2025 at 22:11
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    $\begingroup$ Analysis of all flavors (e.g. PDEs), and applied math (which is often mostly analysis), are extremely underrepresented on MO compared to what you would see in a typical math department at a university in the United States. $\endgroup$ Commented Feb 6, 2025 at 15:26
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    $\begingroup$ I don't mean to be hostile to this question, which is probably interesting in its own right, but I wonder if you could say something about its motivation. Suppose that the answer were yes—what would we do about it? Or should we do anything about it? It seems to me that what is in fashion on MO will change over time as it does anywhere else, and that it's probably not necessary to try to shape it too much (not that you suggested we should!). $\endgroup$ Commented Feb 6, 2025 at 20:08
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    $\begingroup$ A very good question, @LSpice. I don't think we should do anything about it. Maybe it means nothing that the interests in MO lean more towards foundations than to other subjects (if that is indeed the case, which I don't know). But for me, it would be interesting to note that there has been 1 Fields Medal in Foundations (Cohen / Forcing), and a lot more Fields medals in areas that don't appear so much on MO $\endgroup$ Commented Feb 6, 2025 at 20:53
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    $\begingroup$ To add some data to analysis being underrepresented, math.AP (Analysis of PDE) had about twice as many papers on arxiv last year than math.AG (Algebraic geometry). Yet for the corresponding tag, the latter has 5 times as many questions. As someone from PDE, I think that might simply be a misfit between the topic and the scope of MO. A lot of the difficulty in the PDE is more the length and not the depth of the problem. So short questions are often easy enough for MSE, while long questions get posed a open problems and answered in papers. $\endgroup$ Commented Feb 6, 2025 at 22:17
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    $\begingroup$ Could it be that applied mathematicians have less of an open culture? I'm seeing a lot less OA publishing (both of preprints and of final versions) in applied fields, and I know for a fact that people working in the industry face more serious disincentives (including sometimes NDAs) against publicly discussing the problems they are working on. $\endgroup$ Commented Feb 7, 2025 at 5:25
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    $\begingroup$ @darijgrinberg Also consider that a good chunk of applied mathematics lives on Computational Science rather than on MO. $\endgroup$ Commented Feb 7, 2025 at 9:06
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    $\begingroup$ @AsafKaragila The report should be on mathoverflow.net/users/tag-future/current . For me it only says "No predictions could be made", but it might be because I have opted out of personalization in the past. $\endgroup$ Commented Feb 7, 2025 at 9:10
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    $\begingroup$ One naturally expects MO to be biased toward fields with an abundance of simply stated problems with (potentially) succinct answers. That perhaps explains a bias toward combinatorics. But MO does seem to have a bias toward "foundations" (defined in the narrow sense of logic and set theory), and I can't explain that. Questions about forcing or large cardinals or stationary sets are not accessible to most non-set-theorists, whereas I imagine there are many questions in analysis that non-analysts could at least understand and appreciate even if they can't answer them. $\endgroup$ Commented Feb 7, 2025 at 22:20
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    $\begingroup$ For what it's worth, I think foundations is just generally overrepresented online. Perhaps due to the proximity to computer science, but I think this explanation is insufficient. $\endgroup$ Commented Feb 9, 2025 at 0:10
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    $\begingroup$ I think "foundational" is the wrong word, as others have pointed out. Maybe "elementary"? As you say, a lot of questions in graph theory can be asked in a way that makes them immediately understandable to everyone with a basic math background. And most of us like to think about interesting questions even if they are outside of our immediate area of expertise. So I think more elementary areas of math naturally end up as a kind of "common denominator" that performs well on MO. $\endgroup$ Commented Feb 13, 2025 at 9:05
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    $\begingroup$ I think a nontrivial reason for the popularity of foundations is also that it is acceptable for mathematicians to know little about it. Given that many graduate programs require little or no coursework in the area, there is less of a risk in posting a question that someone will close it as being about material everyone is supposed to know. $\endgroup$ Commented Mar 1, 2025 at 9:00

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