Claude clears all Hadamard matrices below order 2000, striking another open problem off the math list

Chinese tech outlet QbitAI reports that Anthropic's Claude has cleared all Hadamard matrices below order 2000, striking a long-standing open problem in combinatorics off the math to-solve list.

Hadamard matrices are square matrices whose entries are only +1 and -1 and whose rows are mutually orthogonal; they appear widely in coding theory, signal processing and quantum information, and their existence question has been a classic hard problem in combinatorics for decades.

The report stresses that the breakthrough hinged on the mathematician's approach rather than the choice of model, with Claude serving as the reasoning tool in the effort.

The result is another sign that large models can contribute to serious mathematical research, demonstrating practical value in long-chain combinatorial reasoning and moving AI from a problem-solving tool toward a participant in mathematical discovery.

The report has not yet disclosed the full proof details or verification process; the open questions are whether the result can withstand rigorous peer review and whether the methods generalize to constructing Hadamard matrices at higher orders.

For the AI industry, mathematical breakthroughs of this kind are becoming a hard metric for reasoning capability, and the idea of AI clearing open math problems is moving from slogan toward reality.