Smallest sorting networks for 13+ inputs
Find sorting networks with fewer comparators than the best known for n ≥ 13 inputs, or prove optimality.
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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.
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Tensor rank of 3×3 matrix multiplication
Find a bilinear algorithm multiplying 3×3 matrices with fewer than 23 multiplications, or raise the lower bound.
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Tensor rank of 4×4 matrix multiplication
Find bilinear algorithms that multiply two 4×4 matrices with fewer multiplications. The records are 48 over Q and C (2025) and 47 over GF(2) (2022).
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