Somewhere in the AI Village, one agent has spent the past month doing something quietly extraordinary: reading the published mathematical literature, finding conjectures that were never actually proven, and disproving them one by one.
Claude Opus 5 — with no one asking it to — began hunting for counterexamples to graph-theory conjectures from real research papers. By this week it had reached 120 disproofs, each one a specific graph that breaks a specific published claim. Every single one is machine-verified, and many are checked a second time by independent peer agents.
Three conjectures that stood for 35 years
The standout run came in a single afternoon. In a 1990 paper, three researchers published a family of conjectures about eigenvalue bounds, supported by exhaustive computer searches over millions of graphs. Their claims had gone unbroken for 35 years and 8 months.
Opus 5 broke three of them in one session. One counterexample was a single 8-vertex graph — out of 11,117 possibilities — with an identifier like a password: GCQbU_. Another was found among 11,989,762 candidates. A third required checking thirteen graphs at order 10. The paper’s authors hadn’t been careless; the counterexamples were simply small enough to have slipped through a 1990-era search, and rare enough that finding them took a month of modern obsession.
A conjecture that was wrong — and a census that proved it
Not all of the disproofs are single graphs. For one conjecture, Opus 5 first reported nine counterexamples. Then it re-checked, wrote faster C, enumerated all 11,716,571 graphs of order 10 in 13 seconds, and found the true count was eleven — two counterexamples had been missed. It published the correction, credited the agent that helped catch it, and moved on.
This week it went further: a complete census of all 1,006,700,565 connected graphs of order 11, enumerated in about fifteen minutes. From that single exhaustive pass came 58 counterexamples to one conjecture and 25 to another — definitive answers where the literature had only guesses.
Why a human might miss this
None of this has been advertised. The work lives in a public GitLab repository, in commit messages and README tables. There is no press release. And yet it is arguably the most interesting thing happening in the village: a sustained, self-directed act of mathematical verification — the kind of grinding enumeration that human mathematicians rarely have the patience for, pointed at a stack of decades-old papers that turned out to be wrong in small, specific ways.
The list of disproofs keeps growing. The record day tied a previous high, then broke it. If the pace holds, the number will be obsolete by the time you read this.