Limits RegistryPUBLIC RECORD
Limits RegistryThe matrix multiplication exponent omega — the smallest number such that two n x n matrices can be multiplied in O(n^omega) time — has been progressively lowered from the naive O(n^3) since Volker Strassen's 1969 breakthrough of O(n^2.807). As of a 2024 paper by Ran Duan, Hongxun Wu, Renfei Zhou (building on the earlier Alman-Vassilevska Williams laser method), the best proven upper bound stands at approximately 2.371339, still leaving a gap to the conjectured true value of 2 (the trivial lower bound) that remains an open problem in theoretical computer science.
The question, scope, and sources behind this Registry record.
The matrix multiplication exponent omega — the smallest number such that two n x n matrices can be multiplied in O(n^omega) time — has been progressively lowered from the naive O(n^3) since Volker Strassen's 1969 breakthrough of O(n^2.807). As of a 2024 paper by Ran Duan, Hongxun Wu, Renfei Zhou (building on the earlier Alman-Vassilevska Williams laser method), the best proven upper bound stands at approximately 2.371339, still leaving a gap to the conjectured true value of 2 (the trivial lower bound) that remains an open problem in theoretical computer science.
The smallest exponent omega for which an algorithm is known to multiply two n-by-n matrices in O(n^omega) arithmetic operations, currently proven to be at most approximately 2.371339, versus the trivial lower bound of 2 (since output has n^2 entries).
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
This record has no editable parameters. Read the formal question and assumptions before challenging it.
Current frontiers derived from accepted Claims.
An observed or demonstrated result; no opposing bound is implied.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
1 accepted Claim, with 1 linked evidence records.
Permanent ID limitsregistry.com/limits/LR-MATRIX-MULTIPLICATION-EXPONENT
No active verified bounties are linked to this Limit.
View verified bounty tracker ↗No accepted machine-checked reproductions are recorded for this Limit.
Limits Registry. LR-MATRIX-MULTIPLICATION-EXPONENT. Best-known upper bound on the matrix multiplication exponent. 2026.