Amateur armed with ChatGPT 'vibe-maths' a 60-year-old problem (www.scientificamerican.com)

Liam Price, a 23-year-old with no formal mathematics training, recently solved a longstanding mathematical problem that has baffled experts for 60 years, using ChatGPT Pro. This marks a significant milestone in the AI/ML community as it represents a unique instance where AI not only provided a solution but also introduced a novel approach to the problem of "primitive sets" of whole numbers—sets where no number can divide another. This method diverges from traditional attempts, suggesting the possibility of broader applications in mathematics, something rarely seen in AI's prior mathematical achievements. The problem, rooted in Paul Erdős's conjectures, involves calculating a "score" for these primitive sets, a concept previously touched upon by researchers but left unresolved for decades. Price's interaction with ChatGPT has led to a solution that, while initially requiring expert refinement, highlights a fresh direction in thinking about large numbers. Mathematicians like Terence Tao and Jared Lichtman view this as a breakthrough that could reshape understanding in number theory and stimulate innovative cognitive pathways in solving complex mathematical problems. The outcome reaffirms a growing belief that AI tools can extend and enrich human inquiry, despite existing limitations in their outputs.