21-Year-Old Math Enigma Solved by Human; GPT and Claude Both Failed
anshulkundaje · x · 2026-08-13
Mathematician Alpoge has successfully found a Hadamard matrix of order 668, cracking the smallest unresolved case of the Hadamard conjecture that had remained open for about 21 years.
Prior to this human breakthrough, researchers tested the problem against top-tier AI models, including GPT 5.6 Sol Max Reasoning and Claude Fable. None of the models were able to find a valid solution, highlighting the current limitations of LLMs in tackling highly complex combinatorial mathematics.
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