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1011 problems

Open problems

Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.

All fields Mathematics 146Computer science 13Physics & astronomy 6Chemistry & materials 8Life sciences 2Earth & society 2
Algorithms 4Complexity 4Computability 1Optimisation 3Machine learning 1
Source Any Optimization constants 1
Verification AnyA · Machine-checkableB · ReproducibleC · Reviewed Tier AnyStandardHardGrand challenges

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B Computability · Optimization constants

Smallest n for which the value of BB(n) is undecidable

C_14 is the smallest n, such that the value of the busy beaver number BB(n) is undecidable in ZFC (or equivalently ZF). Explicitly, it is the smallest n such that there is a Turing machine with n states for which it cannot be proven in ZFC (assuming ZFC is consistent) whether it halts or not.

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