François Fleuret: proofs are exponentially proliferating webs of reusable elements, not isolated artifacts
francoisfleuret · x · 2026-09-17
Former Apple/FAIR research scientist François Fleuret posted a short thread on what makes a math proof intelligible, with implications for LLM reasoning:
- A proof must be more than a valid sequence of symbols—it has to be recursively composed of elements simple enough to be grasped holistically, so subjective correctness aligns with formal validity.
- Because of this constraint, proofs consist of elements generally reusable in other contexts; proofs participate in an exponential proliferation of reusable proof elements.
The thread implicitly criticizes purely formal LLM-generated proofs: symbolic validity without intelligibility misses the mechanism by which mathematical knowledge spreads and gets reused.
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