Claude-assisted constructions complete Hadamard matrices for every order below 2000, including 668
Claude-assisted searches constructed Hadamard matrices for the 12 remaining unknown orders below 2000 (668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948, 1964). Order 668 had been the smallest open case of the Hadamard conjecture for about 21 years.
Key facts
- Orders constructed: 668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948, 1964
- Order 668 was the smallest unknown order since 428 was constructed in 2005
- People: Levent Alpöge, P. Voinov, S. Reynolds-Haertle; order 668 was an Epoch AI 'open problem' entry
Science result
- Field
- mathematics / combinatorial design theory
- Problem
- Hadamard conjecture: a Hadamard matrix exists for every order divisible by 4
- Result
- Explicit Hadamard matrices for all 12 previously unknown orders below 2000.
- AI system
- Claude
- Human role
- AI-assisted search directed by human researchers
- Verification
- Computer-checkable constructions
- Status
- confirmed
What happened
Guided searches built the missing matrices, verifiable by simple matrix multiplication.
Why it matters
It closed a famous "smallest unknown case" that had stood for two decades, with an easily verified result.
Changelog
- 2026-09-29: created
Related events
- Claude proves more than two-thirds of Riemann zeta zeros are simple and on the critical line (up from 41.6%) ★★★★★
- Claude-assisted search breaks the elliptic curve rank record: rank 30, then 31 ★★★
Sources (2)
- officialEpoch AI open problems: Hadamard matrix of order 668
- discussionJohn D. Cook: Constructing Hadamard matrices
id: 2026-08-12-claude-hadamard-matrices-below-2000 · updated 2026-09-29 · open in the interactive timeline