x.com/AISafetyMemes/status/2107622121618964829
3 corrections found
Suddenly, AI has solved 90 of the 500 most important open problems in mathematics
This overstates what the underlying list shows. The cited Top 500 list still classifies all 500 entries as open, open with only subcases solved, disputed, under review, or on conditional hold—not as 90 solved problems.
Full reasoning
The underlying ProofAtlas Top 500 page does not present 90 of these problems as solved.
Its current edition explicitly says it is a list of open problems and shows the status breakdown for all 500 entries as:
- Open (238)
- Open · disputed claim (11)
- Open · subcases solved (243)
- Resolution claim under review (6)
- Reviewed hold · conditional rank (2)
Those categories add up to all 500 entries. In other words, the page the post is drawing from is still treating these as open problems or unresolved claims, not as 90 completed solutions.
The same site also says this is a "model-based assessment" of importance and "not an expert consensus", so calling them simply "the 500 most important open problems" is itself stronger than the source warrants.
Several examples named in the post—such as Hilbert's Tenth Problem over Q, the Unique Games Conjecture, Hadwiger's Conjecture, and Kaplansky's Zero-Divisor Conjecture—are separately described by the same source as still open or as proof claims under review, not settled theorems. So the headline claim that AI has already solved 90 of these problems is not supported by the source it appears to rely on.
3 sources
- Top 500 Open Math Problems: LLM-assessed Importance - ProofAtlas
The page is explicitly titled 'Top 500 open problems in mathematics' and shows the status counts: Open (238), Open · disputed claim (11), Open · subcases solved (243), Resolution claim under review (6), Reviewed hold · conditional rank (2). It also says: 'This is a model-based assessment of mathematical importance, not an expert consensus or a forecast of which problems will be solved next.'
- Hilbert's Tenth Problem over Q | ProofAtlas
The page says 'The answer over Q remains unknown' and 'Hilbert's Tenth Problem over Q asks whether one algorithm can decide rational solvability for every integer polynomial; it remains open.'
- Unique Games Conjecture | ProofAtlas
The page states: 'The full one-to-one conjecture remains open' and 'The full Unique Games Conjecture remains open.'
Hilbert's Tenth Problem over the Rationals - FULL CLAIM
Hilbert's Tenth Problem over Q is not solved. Current status pages describe it as an open problem and say the purported route still leaves decisive steps unproved.
Full reasoning
This problem is still open.
ProofAtlas's current page for Hilbert's Tenth Problem over Q says plainly that "The answer over Q remains unknown" and that the problem "remains open." It further explains that the retained work only proposes an undecidability route and "explicitly leaves its decisive normalization lemma open."
The same page's status section labels it "Open problem" and states that ordinary H10(Q) remains open even though there are related undecidability results for strengthened variants with extra height-comparison conditions. So presenting this as a completed "FULL CLAIM" in a list of problems AI has solved is misleading: the ordinary problem over the rationals has not been established as solved.
2 sources
- Hilbert's Tenth Problem over Q | ProofAtlas
The page says 'The answer over Q remains unknown' and 'Hilbert's Tenth Problem over Q asks whether one algorithm can decide rational solvability for every integer polynomial; it remains open.' It also says the proposed route 'explicitly leaves its decisive normalization lemma open.'
- Top 500 Open Math Problems: LLM-assessed Importance - ProofAtlas
In the Top 500 list, the entry for Hilbert's Tenth Problem over Q is marked 'Status: Open' and says: 'Hilbert's tenth problem over Q remains open.'
BPL = L (Derandomizing Bounded-Error Logspace) - FULL CLAIM
BPL = L is still listed as open. The current Top 500 status page explicitly marks this derandomization question as unresolved.
Full reasoning
The derandomization question BPL = L is still open on the source list itself.
On the current ProofAtlas Top 500 page, the entry for "BPL = L (Derandomizing Bounded-Error Logspace)" is marked "Status: Open." The page gives the exact statement—whether every bounded-error logarithmic-space probabilistic computation can be simulated in deterministic logarithmic space—but does not present it as solved.
So calling this a "FULL CLAIM" in a post asserting AI has solved these problems overstates the actual recorded status.
1 source
- Top 500 Open Math Problems: LLM-assessed Importance - ProofAtlas
The entry for 'BPL = L (Derandomizing Bounded-Error Logspace)' is listed with 'Status: Open' and gives the exact unresolved class-equality question.