Better Bounds

I swear this isn’t turning into an AI blog. But did you see the one about the Riemann hypothesis? Someone at Anthropic did something I’m sure they’re all tempted to do, and tried to use an internal version of their Claude AI system to prove the most famous open conjecture in mathematics. It didn’t work, to be clear, and I get the impression they didn’t expect it to. But out of six hundred or so fruitless tries, one attempt did prove a new bound. Previously, mathematicians had been able to prove that at least 41.6% of the zeroes of the Riemann zeta function satisfied the Riemann hypothesis. Now, the new proof shows that at least 67.2% satisfy it. Anthropic’s press release is impressively careful. As someone who’s had to think about how to write content that both excites the public and doesn’t piss off experts too much, they do an admirable job walking that line. They even say, straight-out, “We don’t expect that the techniques Claude used will lead to proving the Riemann hypothesis.”…