Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming

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Sean Moran spent a weekend using GPT-5.6 Sol, parallel agents, exact-arithmetic programs, and a Lean proof assistant to attack two hard mathematical problems. The first — constructing a Hadamard matrix of order 668 — failed: 44 search regions were closed and five standard routes to a nonexistence proof were audited, but no construction or proof emerged. The second produced a proof candidate with a machine-checked algebraic core in Lean, a full written argument, and a teaching guide — but it remains unreviewed by specialists and its novelty is not established.\n\nThe essay's central argument is that AI has made mathematical experimentation far cheaper without making accepted mathematical knowledge cheaper. Proof, understanding, novelty, and independent review are separate obligations that generating another candidate route does not settle. The workflow — LLM proposes, symbolic checker verifies, failures feed back as context — is a scaled-up version of a neuro-symbolic loop the author described in earlier writing.\n\nMoran draws a parallel to Jeff Dean's framing of AI as enabling a recursive loop over the entire scientific process. The practical takeaway for ML practitioners: AI can now close dozens of precisely scoped search regions in a weekend, but the criteria for mathematical acceptance are unchanged. This is one of the more concrete and honest accounts of AI-assisted mathematical research currently available in practitioner media.