If you’ve been keeping up with news in the math world, the story will sound strikingly familiar, right down to its cast of characters.
Using a proprietary internal large language model (LLM), OpenAI just released a result mathematicians have been chasing for decades: a formal proof validating the “quantum chromodynamics” that underpin physicists’ best, most successful description of the universe.
The new proof also scoops the work of two human mathematicians, one of whom just happens to be employed by OpenAI’s rival Anthropic. The duo—Anthropic’s Levent Alpöge and Ethan Sussman, a mathematician at Northwestern University—had publicly disclosed their progress on their own independent proof in the weeks leading up to OpenAI’s historic announcement.
“I’m not going to say that I’m not disappointed,” Sussman says. He and Alpöge first revealed their burgeoning collaboration to the world on October 6. Notably, the pair updated their public GitHub repository with a new set of intermediate results the night before OpenAI’s announcement. “I think we were on the way and maybe even as close as a few weeks away,” Sussman says.
“This is a major advance,” says Michael R. Douglas, a theoretical physicist and artificial intelligence proponent at Harvard University. “Mathematicians have been trying to make quantum field theory rigorous for over 50 years and have made steady progress, but real-world theories like quantum chromodynamics always seemed out of reach—until now. This is just the start..., but we can hope for rapid progress.”
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