GPT-5.5 Pro finds counterexample disproving McKean's 1966 conjecture and the Gaussian completely monotone conjecture
Gu and Sellke (arXiv 2605.11656) presented an explicit probability measure, found by GPT-5.5 Pro, for which the 5th time-derivative of entropy along the heat flow is positive. This disproves the Gaussian completely monotone conjecture, McKean's 1966 Gaussian-optimality conjecture (1-D) and Toscani's 2015 entropy power conjecture.
Key facts
- arXiv 2605.11656 (12 May 2026)
- Counterexample found by GPT-5.5 Pro; proof written by the human authors
- Follow-ups: a hexagonal multidimensional counterexample (arXiv 2605.18081) and log-concave families (2608.30275)
Science result
- Field
- mathematics / probability / information theory
- Problem
- McKean's conjecture on entropy along the heat flow; Gaussian completely monotone (GCM) conjecture (open since 1966)
- Result
- Explicit measure on R with positive 5th derivative of entropy under heat flow, refuting three related conjectures.
- AI system
- GPT-5.5 Pro
- Human role
- AI found the counterexample; humans verified and wrote the proof
- Verification
- Human-written rigorous proof; preprint
- Status
- confirmed
What happened
OpenAI researcher Mark Sellke and a co-author used GPT-5.5 Pro to search for a distribution violating a 60-year-old monotonicity conjecture, and it produced one.
Why it matters
It is part of 2026's striking pattern of AI counterexamples: models proved especially good at finding objects that break long-believed conjectures. Suvrit Sra documented 15+ such counterexamples in "GPT, the Counterexample Machine".
Changelog
- 2026-09-29: created
Related events
- OpenAI model disproves Erdős's 80-year-old unit distance conjecture ★★★★★
- GPT-5.5 Pro-assisted construction lowers the smallest known Borsuk counterexample dimension from 64 to 63 ★★★
Sources (3)
- paperGu & Sellke: counterexample to the GCM conjecture (arXiv 2605.11656)
- paperFollow-up: multidimensional counterexample (arXiv 2605.18081)
- discussionSuvrit Sra: GPT, the Counterexample Machine (arXiv 2608.29595)
id: 2026-05-12-gaussian-completely-monotone-disproved · updated 2026-09-29 · open in the interactive timeline