OpenAI's GPT-5.6 Sol Ultra Proves Fifty-Year-Old Open Math Conjecture

On July 11, 2026, OpenAI published a paper crediting its newest model, GPT-5.6 Sol Ultra, with independently generating a proof of the Cycle Double Cover Conjecture, a graph theory hypothesis that had remained open for fifty years. The model reportedly completed the proof in under an hour by running 64 subagents in parallel, each exploring a different line of reasoning.

This marks the first time OpenAI has publicly attributed authorship of a mathematical proof solely to a model, rather than to a team of researchers assisted by AI. The company also released the full text of the prompt used to launch the process, allowing other teams to replicate the experiment on their own problems.

How the proof process worked

According to the published prompt, the model was instructed to run up to 64 concurrent subagents and manage them dynamically rather than assigning them fixed roles upfront. In early rounds, agents were deliberately kept unaware of the most promising approach developed by other threads, to avoid the entire process converging prematurely on a single attractive but incomplete idea. Some agents served an adversarial function, actively hunting for gaps and common errors in every proof candidate submitted by the other threads. Only after many rounds of this internal verification did the system assemble a final, coherent version of the reasoning into a single document.

What the conjecture states

The Cycle Double Cover Conjecture concerns bridgeless graphs, meaning graphs in which no single edge, if removed, would split the network into two disconnected parts. The conjecture states that for every such graph, there exists a set of cycles that covers each edge exactly twice. The question sits at the intersection of graph theory and combinatorics, with implications for research into network structure and optimization algorithms.

Mathematicians react

Thomas Bloom, a mathematician at the University of Manchester, was among the first independent researchers to analyze the published proof and share his impressions publicly.

A very nice proof - Thomas Bloom, mathematician, University of Manchester

Bloom did point out a significant gap: the proof fails to cite the 1983 paper by Bermond, Jackson, and Jaeger, whose ideas it partly builds on, as well as more recent research by Mačajová and Škoviera on related cycle-cover hypotheses. For a mathematician, that is a sign that the model can reproduce correct reasoning but does not always place it accurately within the context of existing literature.

History of failures and community caution

The Cycle Double Cover Conjecture has already drawn several alleged proofs, including papers posted on the arXiv server that, upon closer inspection, turned out to contain logical gaps or were withdrawn by their authors. That history is why the mathematical community, despite praising the elegance of the new reasoning, is for now treating it as a claim to be verified rather than a settled result. OpenAI itself stressed in its announcement that it wants a response from the scientific community outside the company, and encouraged mathematicians to keep analyzing the proof and try to find errors in it.

Yesterday we made GPT-5.6 Sol Ultra publicly available. Today we're sharing that the model generated a proof of the fifty-year-old Cycle Double Cover Conjecture using 64 subagents in under an hour. We're releasing the prompt and the proof, and we're curious what you'll do with it - Ethan Knight, OpenAI

GPT-5.6 Sol Ultra is a variant within the GPT-5.6 family, which had previously been presented mainly as a coding tool. The publication of a mathematical proof shows that OpenAI is now also betting on the use of its models in fundamental research, where what matters is not just the correctness of a single answer but the ability to sustain hours-long, multi-step reasoning.

What this means for science and Poland

If the proof survives full review by the mathematical community, it will be one of the first documented cases of a language model independently solving an open mathematical problem without being led by hand through every step by a human. For Polish universities and research institutes, which are increasingly testing AI tools as support for scientific work, this is a signal that it is worth building verification procedures for results generated by such systems now, rather than waiting until similar tools become standard in laboratories.

Formal peer review and attempts by independent mathematical teams to reproduce the proof will likely take months. Until then, the work stands as a strong but unconfirmed claim, much like earlier attempts to resolve the same conjecture.

Sources: The Decoder (the-decoder.com), OfficeChai (officechai.com)