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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 157Computer science 18Physics & astronomy 7Chemistry & materials 9Life sciences 3Earth & society 2
Algorithms 7Complexity 4Computability 2Optimisation 3Machine learning 2
Source Any Curated here 1Optimization constants 1
Verification AnyA · Machine-checkableB · ReproducibleC · Reviewed Tier AnyStandardHardGrand challenges

2 shown

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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