The Conjecture Economy

When proof becomes cheaper, the relative value of good questions rises. The hard part moves upstream from closing a problem to choosing the problem, formulating it in the right language, and recognizing why it should organize future work.

This follows from commoditization. If AI systems can prove many well-specified statements, then the proof of a supplied statement becomes easier to obtain. The hard part shifts to conjecture quality, synthesis, and the selection of definitions that make a domain tractable.

The Erdos example gives the clean form. If AI proves many Erdos-style conjectures, that success retroactively emphasizes the value of Erdos’s question-making. The proof was the part that became automatable. The harder achievement was the taste that identified questions worth decades of attention.

Academic recognition remains organized around closed results. Prizes, promotion, and citation systems mostly reward solved problems. They are weaker at rewarding the person who formulates a fertile conjecture, opens a program, or reorganizes a field in a way that others later exploit. As proof labor becomes cheaper, the mismatch between value and recognition becomes more visible.

Taste also moves away from the proof pipeline. Asking harder questions of the same type may eventually be followed by stronger systems. Inventing a new language or deciding which analogy should organize a field lacks a stable verifier. That is why some human work remains outside automated proof production.

Blog Use

Use this for the incentives section. It connects AI capability, academic prizes, and the value of good questions.

Source Trail

  • Noga Alon et al., “Remarks on the disproof of the unit distance conjecture”, arXiv:2605.20695.
  • Jeremy Avigad, “Mathematicians in the age of AI”, arXiv:2603.03684.
  • ../ai_views.md, “The prize and metric misalignment” and “The orthogonal shift is permanent”.
  • MathOverflow question 511562, “Incentivizing Mathematics”, cited in the source note but still needing exact verification.
  • See reference_inventory.md for full source status.