Synthesis Debt

A field can accumulate results faster than it assimilates them. The gap is synthesis debt. It is the difference between what has been proved and what has been converted into reusable understanding.

AI can worsen this debt. It accelerates the production side: more lemmas, more counterexamples, more formal derivations, more candidate proofs. The digestion side is slower. It requires compression, pedagogy, analogy, judgment about which proof is canonical, and a sense of which results are special cases of a larger object.

An undigested theorem can still close a question, block a false conjecture, or provide a certificate. But it contributes less to cumulative knowledge than a result that can be taught, generalized, and reused. If machine-generated proofs become long, opaque, and numerous, a field can become formally richer and intellectually less navigable.

The unit-distance episode is instructive because the human-written follow-up verified the answer and produced a digested version. That act is part of the mathematics. Without it, the proof would settle a problem while leaving little usable structure behind.

The main risk is a change in the ratio between production and assimilation. If the theorem count rises faster than the digestion capacity of the community, the archive grows while understanding becomes more expensive.

Blog Use

Use this after the capability discussion. It explains how AI can increase output while making a field harder to understand.

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, “AI accelerates production but not digestion” and “Proof has three stages”.
• See reference_inventory.md for full source status.