For all the press that AI and all the companies behind it get, it's rare to find any story that identifies something the Large Language Models (LLMs) behind today's Artificial Intelligence technologies have accomplished that represents a true advancement.
Most stories are about AI's teething problems, such as its problems in creating images of people with too many figures or some other form of body horror dystopia. Other news items deal with how the ability of AI to completely automate writing is negatively impacting education, publishing, music, filmmaking, and other fields.
But stories involving AI systems doing anything new and useful, that hasn't been seen or done before, are rare.
That story still hasn't been written. At least in any traditional media. But there is breaking news of an AI system that's broken new ground in mathematics. By generating a new mathematical proof that mathematicians have verified is correct
That story came to our attention through a post at X and it's probably best to let that post tell the tale:
GPT-5 just casually did new mathematics.
Sebastien Bubeck gave it an open problem from convex optimization, something humans had only partially solved. GPT-5-Pro sat down, reasoned for 17 minutes, and produced a correct proof improving the known bound from 1/L all the way to 1.5/L.
This wasn’t in the paper. It wasn’t online. It wasn’t memorized. It was new math. Verified by Bubeck himself.
Humans later closed the gap at 1.75/L, but GPT-5 independently advanced the frontier. A machine just contributed original research-level mathematics.
If you’re not completely stunned by this, you’re not paying attention.
We’ve officially entered the era where AI isn’t just learning math, it’s creating it.
Here's the X post in which Bubeck announced the accomplishment.
But as Bubeck later notes, while GPT-5 did something that was both new and novel, humans still beat AI to the punch and delivered a better proof focused on the convex optimization problem that outperforms the AI-generated proof:
Now the only reason why I won't post this as an arxiv note, is that the humans actually beat gpt-5 to the punch :-). Namely the arxiv paper has a v2 https://arxiv.org/pdf/2503.10138v2 with an additional author and they closed the gap completely, showing that 1.75/L is the tight bound.
While that better proof clearly beat it, the unexpected artificially generated proof demonstrates AI systems are becoming more capable and useful. Because they are, more things are becoming possible.
The open question however is when will AI's promise and ability to deliver on it outshine all the AI-generated slop that dominates what it has done to date?
Image Credit: Microsoft Copilot Designer. Prompt: "An image illustrating the concept of an artificial intelligence system creating an entirely new mathematical proof".