A New Era of Mathematical Discovery
In a groundbreaking development, an amateur mathematician, utilizing OpenAI's GPT-5.4 Pro, has cracked a 60-year-old combinatorics problem, a feat that has eluded specialists for decades. This achievement signifies a pivotal moment for artificial intelligence, demonstrating its ability to contribute to frontier discovery in mathematics in a truly collaborative fashion. The significance lies not just in the problem's resolution, but in the *method* of its resolution, showcasing AI as an active research partner capable of exploring novel angles and surfacing connections previously unconsidered by human experts.
The problem, a research-level conjecture about prime numbers posed by mathematicians Paul Erdős, Andras Sárközy, and Endre Szemerédi in 1966, had resisted conventional approaches. Historically, mathematicians working on this problem adopted a probabilistic approach, a method so ingrained it was rarely questioned. However, GPT-5.4 Pro diverged from this established path, employing a different mathematical language and utilizing the von Mangoldt function, a tool often considered unusual or arbitrary by human mathematicians.