Specifically, will before September 2026, will there be a proof of a finitely presented discrete MF group?
If so, this would negatively resolve a long-standing open question about if all groups are MF.
This was described as a major open problem in group theory, and a “holy-grail” alongside two other questions.
GPT 5.6 Sol says the question is equivalent to: “Can every countable group be faithfully approximated by finite-dimensional unitary matrices when the approximation error is measured in operator norm?”
This question resolves YES if a proof is given this month and is generally considered valid. If it takes longer than August to verify but the proof was written in August, it still resolved YES.
If all groups are MF, this resolves NO. If no valid proof from August comes about, this resolves NO.
I will bet on this market and have insider (publicly accessible) knowledge which leads me to believe the answer will be YES.
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There is both a Lean verified proof accepted to Palomar in August and a preprint by a professor in the area in August. There have been no disputes of these results. Therefore this resolves yes.
https://palomar-registry.org/entry?id=PALOMAR-2026-08-24-000006&version=1
@user496577185415897490191 I don't see any claimed proofs and the deadline for it to be given has expired.
@SquishyBoy I haven't resolved it since I will give mathematicians a bit to find any errors in the public proofs.
@user496577185415897490191 to be clear there are multiple different proofs publicly available online posted in August
@Jasonb It won't be based off of my opinion. It must be generally considered valid by mathematicians. I don't have a great way of defining this (open to suggestions)