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AI-assisted claims about open problems
Resolution claims attributed to AI-assisted work, and problems that remain open. The register is updated as claims, reviews, corrections, and explanations appear.
Claims attributed to AI
AI-assisted proofs, refutations, and partial results reported by the named teams. These are attributed claims, not a list of independently confirmed solutions. A claim here does not by itself establish that a problem is closed.
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Physics
Yang–Mills existence
Can an interacting quantum Yang–Mills theory be constructed rigorously in four dimensions?
Partial resolution claimed
Existence only; the mass gap is not claimed. Materials are with an external working group.
OpenAI ·
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Mathematics
Local smoothing conjecture
How much does averaging over time limit the concentration of waves?
Proof claimed
Claims a proof in all dimensions; a writeup and Lean artifacts are publicly released.
OpenAI ·
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Mathematics
Kakeya conjecture
How small can a set containing a unit line segment in every direction be?
Consequence claimed
Claims the all-dimensional result as a consequence of its local-smoothing proof.
OpenAI ·
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Mathematics
Stein’s restriction conjecture
When can a Fourier transform be meaningfully restricted to a curved surface?
Consequence claimed
Also claimed as a consequence of the same local-smoothing result, not a separate AI discovery.
OpenAI ·
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Computer science
Exponential Time Hypothesis
Must solving fixed-width SAT require exponential time in the worst case?
Refutation claimed
A proposed refutation is under external examination. This does not settle P versus NP.
OpenAI ·
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Quantum computing & information
Aaronson–Ambainis conjecture
Does every bounded low-degree polynomial on the Boolean cube have an influential variable?
Proof claimed
PSI reports an AI-assisted proof with Lean artifacts, bearing on the structure needed for quantum query speedups.
Physical Superintelligence ·
Unresolved problems
Selected unresolved problems, with links to their statements and research context. This is a curated list, not a claim that no proposed solutions exist. Where only part of a problem has an AI resolution claim, its unresolved part is listed separately.
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Computer science
P versus NP
Can every problem whose solutions can be checked efficiently also be solved efficiently?
Still open
A refutation of ETH would not answer this question.
Clay Mathematics Institute
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Mathematics
Riemann hypothesis
Do all nontrivial zeros of the Riemann zeta function lie on the critical line?
Still open
A central question about the distribution of prime numbers.
Clay Mathematics Institute
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Mathematics
Hodge conjecture
Which geometric features of a smooth projective complex variety come from algebraic cycles?
Still open
The general conjecture remains unresolved despite known special cases.
Clay Mathematics Institute
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Mathematics
Birch–Swinnerton-Dyer conjecture
Does the behavior of an elliptic curve’s L-function determine the rank of its rational points?
Still open
The general conjecture remains open.
Clay Mathematics Institute
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Physics
Yang–Mills mass gap
Can one prove a positive energy gap above the vacuum in four-dimensional quantum Yang–Mills theory?
Still open
The existence claim above does not claim the mass gap required by the full Millennium Problem.
Clay Mathematics Institute
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Quantum computing & information
Quantum PCP conjecture
Is approximating the ground-state energy of a local quantum system with a constant error allowance per interaction still QMA-hard?
Still open
The Hamiltonian formulation remains an open target; progress on related formulations does not establish it.
Buhrman, Helsen & Weggemans (2025)
Sources reviewed . Formal verification, expert review, and the scope of a claimed result are distinct; follow the linked sources for updates.