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I've noticed the following about some facts in probability and statistics (it is probably true more generally). Some results (formulas, for instance) may be moderately straightforward to derive and check, but they are not documented anywhere (at least anywhere easy to find). So, everyone working on that problem needs to perform (and double-check) all those calculations for themselves when doing their work.

For example, the existence and formulae for the moments of some probability distribution may not be very easy to search for but may take about an hour or two derive and check.

I feel that the research in the community would proceed quicker if these calculations were documented somewhere. What is the standard way of addressing this situation?

  • Just do the calculation yourself, and don't worry about the rest of the community
  • Write a blog post
  • Write it up on Wikipedia
  • Write a so-called "note" on something like arXiv

I should note that I am pretty new to the game of research.

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  • When you say certain formulae are easy to search for but take time to derive and check, are you talking about this in the context of an academic paper? I've been told things that in mathematics, deriving well-known equations is usually skipped ("left to the reader") in the interest of getting to the novelty.
    – tonysdg
    Feb 19, 2017 at 22:19
  • arXiv would be my go-to place for those. (Or github, if you feel arXiv being too formal.)
    – darij grinberg
    Feb 19, 2017 at 22:41
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    To avoid a lot of quibbling that I'm pretty sure is going to ensue about the precise nature of the "important but commonplace calculations" you're thinking about, can you give one very specific example of a specific calculation to which this characterization applies? A link would be fine, I just would rather not go to the trouble of writing a long, well thought out answer only to be dragged into an even longer discussion about whether my interpretation was correct (this has happened many times before here, to me and to others). I assume others would similarly appreciate some added clarity.
    – Dan Romik
    Feb 19, 2017 at 22:49
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    If the result is known and was published back in the dark ages of print journals, then the thing to do is to find and cite that reference. Or, if there's a more recent secondary or tertiary source, you can cite that. Knowing that earlier literature is something that you're supposed to know about- if you try to include it in your research paper or simply refer to a note that you wrote about, some referee will almost certainly call you on it.
    – Brian Borchers
    Feb 19, 2017 at 22:55
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    If "everyone needs to perform that calculation", doesn't that imply that someone already did? So find that paper and cite it, or see who they cite. You may also find these sorts of results in textbooks instead of journal articles.
    – Nate Eldredge
    Feb 19, 2017 at 23:18

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While my academic background is in theoretical CS rather than "pure" Math - it was mostly combinatorics and probability, so I feel qualified to tell you that:

AFAICT there isn't a standard. I suggest:

  • Leave calculations private? Definitely not!
  • Write a blog post - Most people don't have a blog. Also, a blog is not the most accessible medium for results in Math, as online resources go. It won't show up in places like, say, Google Scholar. Also, some blogging platforms are not very stable over many years. Bottom line: If you do blog about things like this, possibly write a blog post in conjuction with something else.
  • Write it up on Wikipedia If the result itself is basic and commonly-used enough to merit a Wikipedia page, then sure. But - it might only merit a mention in some other page, in which case it doesn't make sense to try and stick a proof/calculation in there.
  • Write a so-called "note" on something like arXiv ---> Do this <----. Collect severall related mini-results / calculations, describe them nicely, introduce them with a bit of motivation perhaps, find a reasonable title and publish it on arXiv.

One last option:

  • Sneak it into some book : This option is not available to grad students, but if you're a more experienced academic writing a book (perhaps something introductory, but not just in that case) - put this stuff in an appendix. A great example is Appendix A of Alon and Spencer's The Probabilistic Method, about large deviation bounds. The book uses those all over, but isn't about these strictly-probability-theory results, so they're not a proper chapter.
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    Or sneak it into an appendix to a paper.
    – Anyon
    Oct 31, 2018 at 0:16
  • @Anyon: I was assuming it doesn't fit into a paper-appendix-length space.
    – einpoklum
    Oct 31, 2018 at 13:38

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