Claude pushes the bound
Claude pushed the bound on the Riemann Hypothesis to 67.2%, reportedly in about 30 hours. Krishna and Lester clarify that no matter how close this method gets to the critical line, it cannot actually prove the Riemann Hypothesis, because only reaching 100% counts. The value of Claude's approach, they suggest, is that AI can connect existing mathematical ideas in ways human experts had not noticed, giving mathematicians new forks in the road to explore.
- Claude's result was announced on what appears to be a tweet, not a formal paper release.
- The hosts use a fog-and-forks metaphor: AI clears enough fog to reveal paths that trained mathematicians can then actually walk down.
Transcript
This chapter, from the episode video's captions · 321 words
53:39>> The remon hypothesis is at 100. >> Mhm. >> Okay. We're getting closer. >> Yes. Yes. However, this is the case because of what you just talked about with the infinities because what I'm thinking now is like, well, we could get to 99. >> Mhm. >> 9999. >> Yeah. >> And it doesn't mean anything. >> Doesn't mean anything for the Remon hypothesis. It doesn't, >> right? Because what really matters is >> is the 100. And um Claude and other mathematicians have acknowledged that the way that Claude did this, it's not going to get you to 100. Okay? There is a limit to how we push this. Okay. >> Okay. We're not going to get to 100 this way, but it's still cool to get close,
54:19right? Okay. Because it makes us understand a bit more about the function in some sense. >> Part of it part and part of what I've heard people sort of talk about is, you know, as these models begin to connect these ideas that may already exist uh in ways that had not necessarily been connected, folks who are experts and mathematicians deep in these fields will be able to take those ideas as inspirations of oh, let me now think and Mh. >> We now have six forks in the road. I didn't see the six fork in the road because of the fog. >> I can now walk down it because I have the tools to do so. >> Exactly. Exactly. Yeah. So, now let's get into how Claude actually did it. Yep. >> Okay. I've got a few a bit of understanding of how it did it. Okay. Um [snorts] Claude it again tweets. That's
55:00how it they announced I guess that they were doing this right in what appears to be it's like a matter of like 30 hours. They've um they've pushed that bound to 67.2%.
From What Claude Actually Did to the Riemann Hypothesis
Claude takes a real run at the Riemann Hypothesis, forcing us to ask what agentic AI can now do in mathematics, before we open the summer transfer window for America’s scientists.