So far I can tell, the real-world implications of this are "sod all" on the direct front. Which is fine with me - God knows I'm in no position to judge.
In terms of demonstrating what AI can do, it's bit of a mixed bag. For raw capabilities this appears impressive :
For decades, Sarnak has argued that mathematicians should approach the Riemann hypothesis by considering the zeta function as just one member of a broader family of functions, and then proving statements about that family. “But it was not clear exactly how to do so, or which family to consider,” said Michael Rubinstein(opens a new tab) of the University of Waterloo.As it turns out, Sarnak had the right intuition. But the family that OpenAI’s model identified had previously been overlooked. Finding the right family required obscure mathematical objects called metaplectic forms, which Dunn has spent the past five years studying. “Nobody expected this,” he said. Metaplectic forms had been somewhat uncommon in number theory until now, he added, “so I hope this beautiful and esoteric theory gets the attention it deserves.”
In retrospect, Radziwiłł said, mathematicians who study the branch of number theory that all this work belongs to were mistaken in thinking that their tools weren’t strong enough to resolve the quasi-Riemann hypothesis. They’d been convinced that proving it would require techniques from another branch of number theory entirely. The AI model’s “belief” that their tools might be enough was a crucial perspective. “That was a pretty bold belief to have!” Radziwiłł said.
Whereas in terms of explanatory power, it's rubbish :
As with many recent AI-generated results, both papers “are horribly written (in a way that would lead to immediate rejection at any mathematical journal),” Radziwiłł said in an email. “They fall short of the standard of exposition and clarity in our area by a wide margin.”
In my experience, GPT 6 is great at writing code to do the things I want to do. It's excellent at immediately finding gaps and problematic interconnections i wouldn't find for months, or necessarily even care about. It's far more likely to fix edge cases than I would bother with. It even does a good job of documenting its plans and explaining what it did afterwards.
Where it does considerably less well is in designing GUIs, which remains (as in GPT 5) passable for testing but completely inadequate for real use. And in terms of writing user guides, it's a miserable failure. It confuses development documentation with user instructions, and I cannot make it understand that intended users aren't computer scientists. One example of extreme and pointless pedantry : it wanted to correct "approximately two" to 2.154. This is after giving it custom instructions explaining the intended audience and project scope.
AI Proved the Quasi-Riemann Hypothesis. What Happens Now? | Quanta Magazine
Unlike other recent AI proofs, this one has been unpacked by human experts. The implications, one mathematician said, are “staggering.”Konstantin Kakaes (Quanta Magazine)
