GPT-5.6 Sol Ultra Claims a 50-Year Mathematical Prize — Experts Are Not Yet Convinced

A PDF uploaded to OpenAI's content delivery network purports to show that GPT-5.6 Sol Ultra has produced a proof of the Cycle Double Cover Conjecture, an open problem in graph theory dating to approximately 1978. The conjecture holds that for every bridgeless graph there exists a collection of cycles covering every edge exactly twice — simple to state, and resistant to proof for nearly half a century despite serious effort from accomplished combinatorialists. The document generated close to four hundred Hacker News comments, with credentialed mathematicians actively working through the argument.

Early reactions in the thread ranged from cautious optimism to pointed skepticism, and both responses reflect something real. AI-generated mathematical text can be syntactically well-formed — correct terminology, familiar proof structures, plausible-sounding logical steps — while containing subtle errors that only domain experts catch after sustained scrutiny. Formal verification tools such as Lean or Coq can mechanically check proofs, but only when the AI produces output in those constrained formal languages rather than readable prose. Until the document receives peer review from specialists in that corner of combinatorics, appropriate skepticism is warranted.

If the proof does hold up, it would carry implications beyond the specific result. Mathematical proof has long been treated as the domain where human reasoning is least replaceable — the creative leap, the sense for which approach might work, what the hosts described as the aesthetic instinct guiding mathematical discovery. A verified AI proof of a significant open problem would push that boundary in ways the field is not fully prepared to process.

Also trending on Hacker News was the 'AI 2040: Plan A' scenario-planning document, which drew two hundred ninety comments. The framing — 'Plan A' implying the existence of alternatives — reflects a community appetite for serious long-horizon thinking about multiple qualitatively different futures, not merely variations on a single trajectory. Separately, Xiaomi published detailed technical work on inference optimization for its MiMo v2.5 model, advancing what the company calls 'Hybrid SWA' efficiency — a Sliding Window Attention approach designed to reduce the quadratic computational cost of attention at longer sequence lengths. That work is notable partly because it comes from a hardware company with strong incentives to make models run efficiently on its own chips.