A problem is considered solved if it is deemed solved by a majority consensus of the most expert mathematicians, according to my best impressions, to avoid resolving on technicalities. For example, for the Odd Perfect Numbers question, by my current understanding of the statement, proving that an odd perfect number exists (including via a non-constructive proof) will count as a disproof of the conjecture and thus solved.
"by June 2027" means "by EoM June 2027". Same for years.
Poincaré and NS count toward ≥4 and ≥6.
For the option OpenAI Open Problems saturated by Jan 2028, saturated means 100% excluding the problems deemed impossible. The standard meaning of 'saturated' in AI benchmarking.
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Could you add normality of any number not constructed for normality (including but not limited to pi, e, sqrt(2), etc.)? I would suggest the weakest definition of normality (eventually containing all finite strings in some particular integer base), since even that is considered unapproachable.
@BionicD0LPH1N It's a fairly well-known category of open questions, see e.g. https://mathoverflow.net/questions/51853/what-is-the-state-of-our-ignorance-about-the-normality-of-pi or https://mathoverflow.net/questions/437041/have-any-numbers-been-proven-to-be-normal-that-werent-constructed-to-be. You can ask it in stronger or weaker forms, but the state of the problem seems to be that even the strongest forms are almost certainly true and even the weakest forms seem to have no suggestions of progress, so IMO it doesn't currently matter that much what version you pick.
@Melquiades The reason I stayed on really famous clearcut problems with a name is that I really don't want any of these questions to fail to resolve positively for lack of trying / interest, or due to me simply not having heard about the fact that they were solved. For that reason, I'd rather not add this, unless you can find a specific famous version with a clear name and a clear resolution. For what it's worth, I don't expect I'll add this category of question.
Would you consider including the abc conjecture? Before the recent NS drama, it was the one that probably encouraged the most popcorn eating. I suppose the big labs are investing at least some effort into it – either in trying to patch the gap in Mochizuki's proof, or tackling the problem through an entirely different angle. I think either case should count.
@BionicD0LPH1N my pleasure! And just to be clear - "odd perfect numbers" here means either an example or a proof they're impossible, right?
@BionicD0LPH1N Is it correct? What if we get a non-constructive proof that an odd perfect number greater than 1 must exist? (Don't ask me how, this is a resolution question not a math question.)
@b575 Oh shoot, good point! That's my bad. Apologies if anyone bet on my previous response.
To avoid similar problems in the future, I'm stating that a problem is 'solved' if it's considered solved by an by-my-best-impression-estimated majority of the mathematicians with most expertise. Or something like that. I want to avoid any of these questions mis-resolving on a technicality. In this case, it's pretty clear that proving that an odd perfect number greater than 1 must exist, is directly in contradiction with the typical Odd Perfect Numbers conjecture statement that says that says no such does.
@Bayesian 100% excluding the problems deemed impossible. The standard meaning of 'saturation' in evals.
I'm at ~50% [held lightly] on each of these statements resolving positively (individually, though obviously their resolution is highly non-independent).