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Ralph Sarkis (Jun 18 2021 at 18:06):Last year, I stumbled upon a very general construction for an object I was working with. I found this construction very cute and kept it in the back of my mind for a while. Using the intuition I got from my already worked out example, I tried to find other instances where I could apply my result. I did have a few leads but none of them worked out (implying, I guess, that my intuition is not that great).
I was wondering what you like to do when this stuff happens. Do you just keep the result for yourself? Do you only talk about it to people close to you? Or do you share it online?
I feel like, obviously, one would want to share it with as many people as possible in case someone can use the result. However, the amount of time possibly wasted on an incomplete idea by you and the community grows with the number of people you share it with, so I do not know if it is really that helpful to share it so much. Actually, having looked at many professor's websites, I have never seen a section for inconclusive research, so I think my opinion is probably shared.
For this time, I'll share my result here and see what happens (maybe it also gives you a better idea about what I mean).
Mike Shulman (Jun 18 2021 at 19:56):I think inconclusive research ought to be shared more than it is. Unfortunately, the publication/rewards structure is set up so as to discourage it. Blog posts are a good way to share inconclusive thoughts in a format that's a bit more permanent and citable than a zulip thread.
John Baez (Jun 19 2021 at 03:49):By the way, I don't think there's such a thing as a result in category theory that's "too abstract". There may be various other problems with some results, but not this.
Ralph Sarkis (Jun 19 2021 at 04:01):I guess I meant "too abstract" in the sense that it doesn't help you see how to use it. I started from a concrete setting which I turned abstract with categorical language and while I have intuition about the concrete result, I don't have any about the abstract one (at least that's how I feel from the failed attempts at applying it).
Jules Hedges (Jun 19 2021 at 09:23):I guess the question applies equally to any inconclusive research, not only those that arise through being too abstract. (And I think there definitely is such a thing as being too abstract, but it depends on context. For example, it could be too abstract to fit into the story of the paper you're trying to write)
Jules Hedges (Jun 19 2021 at 09:25):Also, definitely agree with using a blog for all kinds of things that you want to make public but can't fit into a paper for whatever reason
John Baez (Jun 19 2021 at 20:16):Oh, I agree - there's definitely such a thing as a result being too abstract for a given context.
John Baez (Jun 19 2021 at 20:16):However, there are lots of nice short almost "contextless" papers in math that prove little results that are mainly interesting because they're easy to state and not obvious.
John Baez (Jun 19 2021 at 20:17):So, if one trips over one of those, one shouldn't be too shy to publish it. Sometimes these results turn out to be important later.
David Michael Roberts (Jun 20 2021 at 02:55):I think in the 19th C there used to be journals that would print short letters from people with cool little facts about geometry etc that weren't particularly deep or big
David Michael Roberts (Jun 20 2021 at 03:02):Like this https://en.m.wikipedia.org/wiki/The_Lady%27s_and_Gentleman%27s_Diary
Combinatorial designs had their origin in this!
John Baez (Jun 20 2021 at 15:02):Also, mathematicians like Sylvester and Cauchy and Laplace and Jacobi wrote tons of papers, many quite short, many simply observing some cool fact or other. If one of these guys had discovered what Ralph has discovered, they would definitely have published it.
Jules Hedges (Jun 20 2021 at 15:17):If I understand correctly, back then "publishing" just meant posting a letter to some learned society and they'd just print it in their journal without any sort of refereeing?
John Baez (Jun 20 2021 at 15:18):I don't know the whole history of that stuff - I think different things happened at different times.
John Baez (Jun 20 2021 at 15:19):I know Hamilton had a lot of his papers read out loud by someone else at meetings of the Irish Royal Society, of which he was for some time the head.
John Baez (Jun 20 2021 at 15:20):He promised to do this for his friend John Graves' paper about the discovery of the octonions, but he never got around to it and Cayley published about the octonions before Graves ddid.