Limits RegistryPUBLIC RECORD
Limits RegistryIn 1960, within a week of Andrey Kolmogorov's Moscow State University seminar at which Kolmogorov conjectured that multiplying two n-digit numbers needs on the order of n^2 operations, 23-year-old Anatoly Karatsuba found a method using three half-size multiplications instead of four, giving O(n^log2(3)) ≈ O(n^1.585). It was published in 1962 and opened the field of fast arithmetic.
The question, scope, and sources behind this Registry record.
In 1960, within a week of Andrey Kolmogorov's Moscow State University seminar at which Kolmogorov conjectured that multiplying two n-digit numbers needs on the order of n^2 operations, 23-year-old Anatoly Karatsuba found a method using three half-size multiplications instead of four, giving O(n^log2(3)) ≈ O(n^1.585). It was published in 1962 and opened the field of fast arithmetic.
The year Anatoly Karatsuba discovered a divide-and-conquer multiplication algorithm running in O(n^1.585) time, refuting Kolmogorov's conjecture that Θ(n^2) was optimal.
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-KARATSUBA-SUBQUADRATIC-MULTIPLICATION
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-KARATSUBA-SUBQUADRATIC-MULTIPLICATION. First sub-quadratic integer multiplication algorithm (Karatsuba). 2026.