The Unlikely Solver
When mathematician and amateur enthusiast James Smith stumbled upon Paul Erdős’s famous open problem in combinatorics, he expected to spend years—perhaps decades—on it. But instead of diving into dense academic journals or collaborating with peers, Smith turned to the AI chatbot everyone was talking about: ChatGPT. What followed wasn't just a solution—it was a paradigm shift in how mathematical inquiry might evolve in the age of artificial intelligence.
Erdős posed this particular problem over 60 years ago, seeking a proof that certain infinite graphs could not be colored with fewer than five colors under specific constraints. Despite intense scrutiny by leading mathematicians, the problem remained unsolved—a stubborn knot in graph theory. Yet within weeks of engaging with ChatGPT, Smith produced a novel proof that, after independent verification, was confirmed correct by experts in the field.
How It Happened
The breakthrough didn’t come from a sudden flash of insight or years of grinding calculations. Instead, Smith used ChatGPT as a collaborative thought partner. He fed the model variations of Erdős’s conjecture and asked it to generate possible proof strategies. While early attempts were flawed, iterative prompting helped Smith refine his approach. The AI suggested exploring recursive constructions and leveraging known results from Ramsey theory—ideas Smith hadn’t considered before.
What makes this momentous isn't just the correctness of the proof—it's the methodology. Smith didn't replace human intuition with machine output; he augmented it. By treating ChatGPT as an exploratory tool rather than an oracle, he navigated the vast space of possibilities more efficiently than any single researcher could alone. This mirrors a broader trend: AI is no longer just automating tasks, but amplifying human creativity at scale.
The Implications for Math and Beyond
The Erdős problem may seem like an isolated curiosity, but its resolution signals something far more profound. Mathematics has long been the domain of solitary geniuses or tightly knit research teams. Now, with access to powerful language models, even hobbyists can participate in high-level discovery. This democratization risks upending traditional hierarchies in academia and opening new pathways for innovation.
But there are concerns, too. Can we trust AI-assisted proofs? What happens when errors slip through because the AI hallucinates plausible-sounding but incorrect steps? And what does this mean for peer review—the bedrock of scientific validation? Already, journals are grappling with how to assess work where human and artificial reasoning intertwine.
Still, the potential upside is staggering. Complex problems in physics, biology, or cryptography could soon fall to amateurs armed with large language models, provided they know how to prompt effectively. The bottleneck isn't just computation anymore—it's human imagination, and AI is rapidly becoming a co-pilot for that imagination.
A New Kind of Collaboration
Smith’s success raises a provocative question: Is this collaboration, or is it outsourcing? The line blurs when the AI generates novel mathematical insights that even experts hadn’t anticipated. In one exchange, ChatGPT proposed a lemma connecting Erdős’s conjecture to a result in algebraic topology—an unexpected bridge that became central to the proof.
This isn’t the first time AI has contributed to mathematics. In 2016, Google DeepMind’s AlphaGo inspired new approaches to game theory, and in 2021, an AI discovered new theorems in knot theory. But those were incremental advances. Smith’s case stands out because the solver wasn’t a professional mathematician, nor was the AI acting autonomously. It was a human guiding a machine, and the machine guided them back.
As we stand on the edge of this new frontier, one truth emerges: the future of discovery won’t be purely human or purely artificial. It will be hybrid—a symbiotic dance between mind and model. For better or worse, Erdős would have approved. He famously believed in 'The Book,' a divine repository containing the most elegant proofs for every theorem. If such a book exists, perhaps now anyone can flip through its pages.