Amateur Mathematician Uses ChatGPT to Crack 60-Year-Old Erdős Problem
In what may be one of the most striking demonstrations of AI-assisted problem solving to date, an amateur mathematician has successfully solved a 60-year-old combinatorics problem originally posed by legendary mathematician Paul Erdős—with significant help from ChatGPT.
The news, first reported by Scientific American, has ignited intense discussion in the mathematical community and among developers about the evolving role of large language models in technical problem-solving.
The Problem and the Breakthrough
Paul Erdős, one of the most prolific mathematicians of the 20th century, was known for posing deceptively simple problems that often took decades to solve. This particular problem in combinatorics—a branch of mathematics dealing with counting, arrangement, and combination—had remained unsolved since the 1960s.
What makes this breakthrough particularly notable isn't just the solution itself, but the methodology. The solver, described as an amateur mathematician without formal academic credentials in advanced mathematics, used ChatGPT as an interactive research partner throughout the problem-solving process.
This approach, sometimes called "vibe mathematics" or AI-augmented reasoning, represents a fundamentally different paradigm from traditional mathematical research. Rather than working in isolation or exclusively with human collaborators, the solver engaged in an iterative dialogue with the AI, testing hypotheses, exploring proof strategies, and refining arguments.
What This Means for Developers
For software engineers and technical professionals, this breakthrough has immediate implications:
AI as a thinking partner, not just a code generator. While developers have grown accustomed to using ChatGPT and GitHub Copilot for code completion and debugging, this case demonstrates the potential for LLMs to assist with deeper algorithmic and mathematical reasoning. Complex problems in computer science—optimization challenges, algorithm design, cryptographic protocols—may similarly benefit from AI-assisted exploration.
Democratization of technical expertise. The fact that an amateur could tackle a problem that stumped professional mathematicians for six decades suggests that AI tools are lowering barriers to entry in highly technical domains. Developers without formal CS degrees or mathematical backgrounds may find themselves increasingly capable of tackling problems previously reserved for specialists.
Validation and verification still matter. Importantly, the solver didn't simply accept ChatGPT's output as gospel. The process involved extensive verification, peer review, and mathematical rigor. This mirrors best practices in software development: AI-generated code still requires human review, testing, and validation.
The Broader Trajectory of AI-Assisted Work
This breakthrough arrives at a moment when the tech industry is grappling with AI's impact on knowledge work. Just this week, reports emerged of 20,000 job cuts at Meta and Microsoft, with AI automation cited as a contributing factor.
But the Erdős problem solution suggests a more nuanced future than simple replacement. The amateur mathematician didn't compete against ChatGPT—they collaborated with it. The human provided intuition, domain knowledge, and verification capabilities; the AI provided rapid exploration of possibility spaces, pattern recognition, and tireless iteration.
This collaborative model may be the template for how AI reshapes technical work: not replacing human expertise, but amplifying it and making it accessible to a broader population.
Practical Takeaways
For developers looking to leverage AI more effectively in their own work:
- Treat AI as a brainstorming partner. Use it to explore solution spaces, not just to generate final answers.
- Iterate and verify. The mathematical breakthrough came through many rounds of dialogue and refinement, not a single prompt.
- Combine domain knowledge with AI capabilities. The solver brought mathematical intuition that guided the AI's exploration.
- Don't be intimidated by complexity. Problems that seem beyond your expertise may be more accessible with AI assistance than you think.
The amateur mathematician who cracked an Erdős problem didn't have a PhD or institutional affiliation. They had curiosity, persistence, and a powerful AI tool. In 2026, that combination might be all you need to solve problems that have stumped experts for generations.
The full story is available in Scientific American, and discussion is ongoing on Hacker News.