GPT-5.4 Pro used von Mangoldt chains to solve several of the most difficult number theory conjectures.
A high-level AI model identified a specific method that human mathematicians overlooked since the problem was first posed in the 20th century. Paul Erdős offered cash prizes for these proofs because he believed they touched on the deepest properties of divisibility and prime numbers. These primitive sets are collections of integers where no number divides another, and their density was a central mystery in number theory for eighty years. The AI suggestion successfully bridged the gap between these sets and the distribution of primes, resolving multiple long-standing conjectures at once. This breakthrough suggests that future mathematical discoveries will increasingly rely on machine-led intuition to solve problems humans find too complex. It marks the first time a major unsolved conjecture has been cracked using a strategy explicitly proposed by an artificial intelligence.