To grieve, or not to grieve?

gist

On the Xena blog, xenaproject says language models are solving hard mathematical problems humans could not, and sorts many colleagues’ reactions into denial, anger, bargaining, and depression without treating that map as a criticism. The post argues that a shift from hard theorems to human understanding may fail once models also explain proofs, and that the author wants a measurable tally of theorems correctly proved. They ask OpenAI to publish results it says it is holding. Machines look strong at problem solving, with little decisive evidence yet at theory building or conjecture.

ideas

• Many reactions fit the early stages of grief. The post illustrates denial, anger, bargaining, and depression with the Association for Human Mathematics, angry essays, the AGMAI recommendations, and colleagues shaken by the Navier–Stokes news, and says this map is not a criticism.
• Understanding is an unstable fallback. Prize talk is shifting from the hardest theorems to the deepest human understanding, and the author warns that this retreat fails if models soon explain proofs as well as they find them.
• The author wants a theorem tally. They say they never mastered every dependency of their own work, trust Lean because it rejects proof by authority, and are in it for theorems correctly proved.
• Publish the withheld results. They signed a letter asking OpenAI to dump the significant theorems it says it is holding, calling the secrecy akin to censorship and leaving human reverse-engineering for later.
• Infinity is the bound they trust. Machines already show evidence at problem solving and little decisive evidence at theory building or conjecture, and infinite mathematics outlasts any finite exponential spend.

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