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I'm looking for a list/table/survey of what is known (and what is not known) about homotopy groups of spheres, for example: which are known, which are known stably, which are known primally, non-$0$ etc.

I'm aware of what is on Wikipedia, but I doubt it's exhaustive...

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    $\begingroup$ In terms of the stable homotopy groups of spheres at prime $2$, I think the recent work of Isaksen-Wang-Xu (arxiv.org/abs/2001.04511) is the current state of the art. $\endgroup$
    – Piotr Pstrągowski
    Commented May 3, 2020 at 10:43
  • $\begingroup$ Typically these types of questions are closed on Math Overflow, as the discussion is more appropriate for a Wikipedia entry/chat than this forum. I certainly sympathize with threads like these as I imagine they would have more utility than a Wikipedia page. Anyhow, this isn't the place for that kind of discussion. $\endgroup$
    – Ryan Budney
    Commented May 3, 2020 at 20:30
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    $\begingroup$ The efforts put forward to a thread like this are more appropriate for the Wikipedia page. en.wikipedia.org/wiki/Homotopy_groups_of_spheres $\endgroup$
    – Ryan Budney
    Commented May 3, 2020 at 20:31
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    $\begingroup$ @Ryan I view it as a completely reasonable question, since there is a lot "known to experts" in homotopy theory that is not easy to find. And this is the whole point of MO. Pointing someone to a Wikipedia page not intended for such detailed information is not the most helpful thing. $\endgroup$
    – David Roberts ♦
    Commented Jan 13, 2021 at 1:13
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    $\begingroup$ Well, when the person explicitly says they are aware of the content at Wikipedia, and judging by their other questions, aren't exactly a random noob, then pointing them twice to Wikipedia in comments seems a bit odd to me. And I don't view the question as asking for a discussion, either. I have also, in the past, wondered about this question and would like a better reference than WP, namely a decent survey paper, if there is one. $\endgroup$
    – David Roberts ♦
    Commented Jan 13, 2021 at 7:03

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