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 4 Computer science 2 Physics & astronomy 1

Complexity 2

Source Any Curated here 2

Verification Any A · Machine-checkable B · Reproducible C · Reviewed Tier Any Standard Hard Grand challenges

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C Grand challenge Complexity

P versus NP

Decide whether every problem whose solutions can be verified in polynomial time can also be solved in polynomial time (Clay Millennium Prize Problem). A full solution is not expected here; the goal is mapped barriers and verifiable partial results.

Sub-problems: Explicit Boolean circuit lower bounds

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0verified

P versus NP

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