Anthropic researcher Levent Alpöge, along with two human collaborators, used the Claude model to construct a 668-order Hadamard matrix, solving a problem that had stumped mathematicians for 30 years. The work includes 12 matrices, clearing all unresolved Hadamard orders below 2000, and has been marked as "solved by AI" in the FrontierMath benchmark.
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Anthropic researcher Levent Alpöge, along with two human collaborators and Claude, constructed a 668th-order Hadamard matrix, resolving all 12 outstanding orders below 2000 in one go. The problem is included in the FrontierMath benchmark, and EpochAI has temporarily marked it as 'solved by AI.'
Anthropic researcher and mathematician Levent Alpöge reported that they found a solution for the 668th-order Hadamard matrix, thanking a team of three humans and Claude. Participants include Alpöge, Philippe Voinov, Saul Reynolds-Haertle, and Claude. Alpöge joked that he only claims the bad suggestions.
A Hadamard matrix is a square matrix with entries only +1 and -1, where any two rows, when multiplied element-wise and summed, must equal exactly 0. The 668th-order matrix had previously stumped all large language models with 'deep reasoning' capabilities, as well as human mathematicians for 30 years.
The problem is included in the FrontierMath benchmark, which was co-authored by over 60 people, including three Fields Medalists such as Terence Tao and top IMO coaches. EpochAI has temporarily marked this open problem as 'solved by AI,' explicitly noting that the conclusion may be adjusted based on subsequent information.
This report is primarily based on a retelling by Quantum Bits. Core facts (such as the successful construction and EpochAI's marking) come from Alpöge's tweet and EpochAI's page, but there is no full technical report or independent third-party verification yet. EpochAI's marking is 'temporary' and explicitly subject to adjustment. VibeMathed's reproduction is an independent third-party verification, but detailed methods were not provided.
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