Why was this question put on hold? It seems to be fairly specific and it is about mathematics. You could argue that it is slightly meta-mathematical; would it then be appropriate on meta MO?
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6$\begingroup$ Hand-waving about "Grothendieck's approach" does not strike me as "fairly specific". Also the post seems laden with personal opinions like "way too seriously". The third sentence of your meta post sounds like sarcasm; I hope it's not meant seriously. If you're stuck on a problem arising in your research, that might be good for MO, but this question is not (in my opinion it has multiple problems beside those I mentioned). $\endgroup$– Todd Trimble ModCommented May 13, 2019 at 14:03
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$\begingroup$ @ToddTrimble OK Sir, I will try to edit the question. The third sentence is not sarcastic, I just did not fully understand the scope of meta MO when I was formulating the question, now I see it is about slightly different things. What are the other "multiple problems"? I want to get rid of all of them at once. $\endgroup$– user138661Commented May 13, 2019 at 14:30
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1$\begingroup$ Unfortunately I don't have a lot of time at the moment, but with regard to the question at main: have you looked at the relevant writings of Colin McLarty? This looks sort of relevant to what you seem to be asking: arxiv.org/abs/1102.1773 $\endgroup$– Todd Trimble ModCommented May 13, 2019 at 14:51
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5$\begingroup$ For anyone reading: the question which the OP links to has now been edited significantly since this meta question was first asked. $\endgroup$– Yemon ChoiCommented May 13, 2019 at 17:23
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1 Answer
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I do not think there is much evidence to support your assertion that your question is specific. You ask whether there is research on "in which mathematical universes does Grothendieck's approach succeed", and we are left with the rather formidable tasks of unpacking the terms "mathematical universes", "Grothendieck's approach", and "succeed".
When people asked for clarification in the comments, we see that the definition of "mathematical universes" is unclear, but it seems you are partial to considering arithmetic systems too weak to prove Godel's incompleteness theorem. Perhaps you would have better luck considering nonstandard models that can actually prove incompleteness. Your definition of "succeed" seems to be "thousands of pages of monographs", which is a bit stringent for work on hypothetical worlds. Finally, "Grothendieck's approach" has been reduced to something like being careful when defining things, and this hardly seems to be unique to Grothendieck.
One point I'd like to emphasize is that when you ask a question where an answer might require non-trivial effort, you should take care to remove as much ambiguity as you reasonably can, and you should at least give the impression that you will take serious answers seriously. If you haven't done your homework, you shouldn't expect others to invest time and energy helping.
answered May 13, 2019 at 14:51
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$\begingroup$ "mathematical universe" is a system of axioms, I thought that was clear from the question ("universe" does have some other meaning in mathematics I believe, but I think it was clear from the context). I am not partial to arithmetic systems, that was an example. The question was asking for research on this topic, so I think it would not require much effort to recognize what is needed (thus to answer it). I would agree that this may be a bad question and I am ok with the down-votes, but I can not agree with the decision to put in on hold. $\endgroup$– user138661Commented May 13, 2019 at 15:17
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$\begingroup$ there were some other questions on MO which were imprecise to a similar extent, but were not put on hold. Would you say that they also did not do their homework and should be put on hold? mathoverflow.net/q/117668/138661 mathoverflow.net/q/25983/138661 mathoverflow.net/q/879/138661 mathoverflow.net/q/2358/138661 $\endgroup$– user138661Commented May 13, 2019 at 15:19
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$\begingroup$ I see that people are annoyed with my take on "Grothendieck's approach". If I edit that out, can the question live? $\endgroup$– user138661Commented May 13, 2019 at 15:20
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5$\begingroup$ @sch, you're asking why the question was put on hold, you're being told why the question was put on hold, and you're coming back with "I can not agree with the decision to put in on hold." This reaction calls into question your sincerity in asking why it was put on hold. Also, it's a well-established principle here that reception of earlier questions doesn't set a binding precedent for newer ones. Membership changes, customs change. $\endgroup$ Commented May 14, 2019 at 1:47
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$\begingroup$ @GerryMyerson I am not sure how does that call in question my sincerity. If a student says to you during a class "You have multiplied these matrices incorrectly", you explain to them what exactly you did, and then they say something like "But should not we be multiplying componentwise?", do you think they are being insincere? Stupid, possibly, probably not insincere. $\endgroup$– user138661Commented May 14, 2019 at 7:00
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$\begingroup$ @GerryMyerson regarding the second part: OK, that is so, but what is the exact period of time after which they fail to set a precedent? One of the questions was last edited in April 2017, that is slightly more than 2 years ago. I do not know who were the moderators back then, but probably some of the current moderators were around during that time too. I guess there should be a separate page on this site where they explain exactly the changes in exactly what is acceptable at each point of time, otherwise it is somewhat hard to guess. $\endgroup$– user138661Commented May 14, 2019 at 7:06
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$\begingroup$ @sch, if a student asks me what he did wrong on some problem, and I explain what he did wrong, and in reply he tries to tell me that what he did was right, then he wasn't sincere in asking me what he did wrong, because he didn't really believe he was wrong. On the other matter, identity of the moderators is irrelevant, as moderators rarely put questions on hold; that's left up to users who have accumulated enough points to acquire the privilege of voting to close. Different times, different voters. Things evolve over time. Asking for exact times is like asking for the exact time [continued] $\endgroup$ Commented May 14, 2019 at 7:46
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$\begingroup$ [continued] that one species evolved into another. Incidentally, you can find out who the moderators have been at meta.mathoverflow.net/questions/753/history-of-mathoverflow $\endgroup$ Commented May 14, 2019 at 7:46
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$\begingroup$ By the way, of the four questions you cite, the most recent was asked in 2012, and was closed 2 hours after it was posted (and then reopened some hours later). $\endgroup$ Commented May 14, 2019 at 7:52
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$\begingroup$ @GerryMyerson OK, I understand the part about the voters. Regarding the example with a student, it just can't be non-trivial to see where you are wrong. I mean, I personally was agnostic about whether my question was acceptable or not when I asked the question. S. Carnahan did provide some reasons, I thought that those reasons did not prove his claim completely (and pointed out possible counterexamples), that does not mean I believed his claim was wrong, just that I was not convinced. Then you come along and explain the stuff about voters, reasonable enough. $\endgroup$– user138661Commented May 14, 2019 at 7:58
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$\begingroup$ But I lacked that information at the time I was posting my comments and was genuinely not convinced (and genuinely agnostic about my question). You claim I am being a liar. I am not; ignorant about MO and not able to reason quickly, possibly, not a liar or an insincere person. $\endgroup$– user138661Commented May 14, 2019 at 7:59
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2$\begingroup$ Since I was the only person who posted an answer to this question, which I'll fully admit was not an answer, but a step 0-attempt at clarification, I want to mention why I did this. At some point, I remember someone saying a suitable mathoverflow question is a question concerning mathematics which you'd be comfortable asking at a math tea in a mathematics department. This seems to be obviously false, but I don't want to start a war. More so, I'm curious if there is a forum where this mantra is taken seriously, and is actually frequented by mathematicians. $\endgroup$ Commented May 16, 2019 at 15:57
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1$\begingroup$ This issue is reflected by something that I view as inevitable, but still unsettling, which is that the mathematical prestige of the poster can effect the perceived quality of the question, which I'm sure is a topic that's been beaten to death in here, though I don't frequent the meta, so I'm just ignorant. Anyway, my point is not that we should tighten the rules, and delete every question that has even a hint of speculation, but that letting a question that has some speculation survive might not totally destroy the community. Nonetheless, moderating is hard, and I'm not doing it... $\endgroup$ Commented May 16, 2019 at 16:02
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2$\begingroup$ @AndySanders Something like that mantra used to be true in the early days of MO, but I think you're right it no longer holds water. The more frequently cited mantra these days is "questions should be research level". Now that can mean many things to many people, and the mantra can serve different purposes, some useful, some arguably harmful. But for speculative questions, I think it could mean that the poster should put in some hard thought into the question first. I think my main inner gripe about the original question is that it was lazy, requiring an answer to do a lot of work for the OP. $\endgroup$– Todd Trimble ModCommented May 18, 2019 at 0:01
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1$\begingroup$ @ToddTrimble Thank you very much for this clarification, and I agree that under the mantra "should be research level" the question we're discussing is likely too speculative and/or imprecise. I feel like generally most questions are closed because they either don't make any sense, or are obvious quackery, or are real questions, but obviously not research level. This question was a little bit different, in that I think it's an interesting question which could receive interesting answers (not mine), but I understand one must draw a line somewhere. $\endgroup$ Commented May 18, 2019 at 17:32