Amateur Mathematician Uses ChatGPT to Crack a 60-Year-Old Erdős Problem
A non-professional mathematician used ChatGPT in an iterative back-and-forth to solve a combinatorics problem posed by Paul Erdős that had stumped professionals for six decades, raising new questions about AI-assisted mathematical discovery.
Original sourceOne of mathematics' most celebrated unsolved problems — posed by the legendary Paul Erdős roughly six decades ago — has been cracked. The solver isn't a tenured professor or a Fields Medal candidate. It's an amateur mathematician who spent weeks in dialogue with ChatGPT, gradually refining approaches, testing edge cases, and following the AI's suggestions until a valid proof emerged.
The technique, which some are calling "vibe math" — a riff on "vibe coding" — involves using AI not as a calculator but as a mathematical thinking partner. The user would pose conjectures, ask the model to find counterexamples, request alternative framings, and iterate. The AI couldn't produce the proof directly, but it dramatically accelerated the exploration space.
The Erdős problem in question falls in the realm of combinatorics, where Erdős scattered thousands of open problems across his lifetime with prize money attached. This one carried a $500 prize — modest by math competition standards, but the symbolic weight of solving an Erdős problem is enormous in the mathematical community.
The development has reignited debate about what counts as mathematical authorship, how AI should be credited in research, and whether competition mathematics — particularly olympiad problems — needs to revisit its rules in the AI era. Several prominent mathematicians have already weighed in, with reactions ranging from excitement about democratized mathematics to concern about the rigor of AI-assisted proofs.
Panel Takes
The Builder
Developer Perspective
“This is exactly the kind of human-AI collaboration that produces outcomes neither could achieve alone. The amateur brought domain intuition and creative framing; ChatGPT provided exhaustive case exploration. The workflow is teachable and replicable — that's the exciting part.”
The Skeptic
Reality Check
“We should be careful about the narrative here. AI-assisted proofs need rigorous peer review — LLMs are known to hallucinate mathematical reasoning convincingly. The story is compelling, but 'solved by ChatGPT user' risks overstating the AI's role and understating the verification work still ahead.”
The Futurist
Big Picture
“This is the moment where AI stops being a tool for professionals and becomes a force multiplier for the intellectually curious everywhere. The barriers to contributing to human knowledge are collapsing. An Erdős problem solved from a living room is a proof of concept for something much larger.”