An amateur just solved a 60-year-old math problem—by asking AI

In a stunning demonstration of AI's potential, an amateur mathematician—not a professional researcher—used a large language model (LLM) to solve a 60-year-old unsolved problem in mathematics. The problem, related to combinatorial number theory, had stumped experts for decades. The user, who posted on Reddit's r/math, described a multi-day process where they prompted the AI (likely GPT-4 or a similar model) with the problem, then iteratively refined the AI's suggestions. The AI proposed candidate proof structures, which the user checked for logical gaps, corrected, and fed back. This back-and-forth, akin to a collaborative brainstorming session, eventually yielded a complete, rigorous proof. The result was submitted to arXiv and has since been verified by professional mathematicians, who praised its elegance.

The key insight here is not that the AI solved the problem alone—it didn't. The AI lacked the deep intuition to recognize the correct path without guidance. Instead, the human user acted as the 'scaffolding,' asking the right questions, spotting errors, and steering the AI toward productive lines of reasoning. This mirrors the 'co-pilot' paradigm emerging in coding (e.g., GitHub Copilot) but applied to pure mathematics. The breakthrough underscores that LLMs can accelerate research even for non-experts, provided they have strong logical skills and persistence. It also raises questions about the future of problem-solving: as AI tools improve, will 'amateurs' with AI assistance rival professional researchers? For now, this case is a powerful proof-of-concept.