Put simply, the conjecture addresses a fundamental question in graph theory: Would it be possible to find a set of cycles in any network of vertices and edges that traverses each individual edge exactly twice? The problem was formulated independently by several mathematicians in the 1970s. Since then, there have been many partial solutions for special cases, but no generally accepted proof.
Machine persistence
According to OpenAI, the proof comes entirely from GPT-5.6 Sol Ultra. The paper was written by GPT-5.6 Sol. Mathematician Thomas Bloom of the University of Manchester calls it "a very nice proof," noting that the solution is "short, elementary, and could have been discovered in the 1980s." It doesn't need any new mathematical theories, but it cleverly combines known tools.
So why didn't humans find it? Bloom suspects the key step involved a small, counterintuitive twist in the reasoning. A human mathematician would likely have tried the obvious approach, seen it fail, and moved on. AI doesn't get discouraged; it just keeps trying small variations until one clicks.
"One can imagine trying the natural labelling first, checking the linear algebra, and when that failed shrugging and thinking 'oh well, I was expecting to fail, guess it can't be done this easily' - while the AI does not get discouraged and keeps trying small variations," writes Bloom.
