"Vibe Math" Just Solved a 60-Year-Old Problem that Stumped Mathematicians

Why It Matters

The breakthrough shows AI can generate genuinely novel mathematical insights, potentially accelerating solutions to long‑standing problems and redefining research collaboration.

Key Takeaways

• 23‑year‑old solves 60‑year primitive set conjecture using ChatGPT.
• AI discovered novel connection missed by professional mathematicians.
• Primitive sets generalize primes; conjecture limits their “score” to ≤1.
• New proof method could unlock many unresolved number‑theory problems.
• “Vibe math” showcases AI’s potential to augment mathematical research.

Summary

A 23‑year‑old without formal training solved a six‑decade‑old conjecture on primitive sets by prompting ChatGPT, marking the first high‑profile mathematical result attributed to a large‑language model.

Primitive sets are collections where no element divides another, extending the concept of primes. The conjecture, posed six decades ago, asserts that a certain “score”—the sum of 1/(n log n) over the set—cannot exceed one as the numbers grow. Decades of attempts by leading number theorists failed, all following similar analytic routes.

ChatGPT suggested a previously unseen structural link, allowing the score bound to be proved. Mathematicians called the argument “obvious in hindsight” but admitted they never considered that perspective. The episode has been dubbed “vibe math,” echoing the viral “vibe coding” trend.

If the AI‑derived technique extends to related problems, it could reshape how researchers approach unsolved conjectures, positioning language models as collaborative tools rather than mere calculators.

Original Description

Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT Pro subscription, which gives him access to the latest large language models from OpenAI. Learn more about the newly solved problem and how the solution might help mathematicians tackle other Erdős problems at scientificamerican.com.

Host: Joe Howlett

Editor: Kylie Murphy

#math #ai #erdos #chatgpt #vibemath