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Quoting Jake Boggan
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Mathematician Jake Boggan broke his silence on 7 October 2026 with a deeply personal reaction to a claimed proof of Barnette's Conjecture, posted publicly as "problem 180" on the OpenAI/math platform. In a comment on Hacker News, Boggan said he did not know what to think about the announcement. The claim, if verified, would settle one of graph theory's most stubborn open questions. Boggan's post quickly drew attention for its unusual candor about what it feels like when a life's obsession is resolved by someone else.
Barnette's Conjecture, first proposed by Daniel Barnette in 1969, states that every three-regular, three-connected bipartite planar graph contains a Hamiltonian cycle — a closed path visiting each vertex exactly once. It has resisted solution for more than five decades and sits within the broader, notoriously hard family of Hamiltonicity problems. Because the general Hamiltonian cycle problem is NP-complete, researchers have long pursued restricted cases such as this one as tractable footholds. A correct proof would mark a significant milestone in combinatorics.
Boggan's connection to the problem runs unusually deep. He described himself as a "graph theory junkie" who once moved to Budapest to study among leading figures in the field. There he began working on Barnette's Conjecture, which occupied his thoughts on and off across 24 years while he worked in many other disciplines. He estimated spending thousands of hours on the problem and said he genuinely enjoyed it.
Boggan also revealed that as recently as the previous summer he believed, for a few days, that he had solved the conjecture himself. Hearing that it appears proven now left him with mixed feelings, which he likened to learning that an ex-girlfriend had died suddenly in a car crash. "I don't know, there's probably a lot of people feeling odd emotions tonight," he wrote. He suggested others who had wrestled with the problem might feel similarly unsettled.
The claimed proof's appearance on OpenAI/math places it amid growing public interest in machine-assisted mathematics, alongside recent coverage of OpenAI's 2026 developer conference and year-in-review pieces on large language models. Whether the resolution emerged from human effort, automated reasoning, or a combination remains unspecified in Boggan's comment. What is clear is that the announcement has already reached working mathematicians and prompted reflection rather than immediate celebration.
For now, the community's posture is cautious: a claim of this magnitude requires full scrutiny, line-by-line verification, and peer review before it can be accepted. Mathematicians who invested decades in partial results will need time to absorb the outcome and assess the argument's validity. Boggan's response captures that waiting period — grief, relief, and curiosity intertwined. If the proof holds, Barnette's Conjecture will pass from open problem to theorem, and its solvers will enter the record alongside the mathematicians who chased it for years.
