Inside Claude’s attempt
This chapter sets up Claude's reported attempt at the Riemann Hypothesis by establishing two things that make it unusual: the problem itself is one of the most famous unsolved problems in mathematics, a Millennium Prize problem, and the person who initiated the attempt was Jared Sumner, a software engineer rather than a professional mathematician. Sumner prompted an unreleased version of Claude, and when the model initially refused, he encouraged it with phrases like 'believe in yourself.' The chapter then pivots to introduce the Basel problem as a starting point for explaining what the Riemann Hypothesis actually is.
- Krishna contrasts this with a previously covered result, the Jacobian conjecture counter example, where the human involved was a Princeton and Harvard trained mathematician.
- Anthropic has explicitly stated the version of Claude used is unreleased, which Krishna notes with skepticism about shareholder messaging.
- Krishna recommends the book 'Complex Analysis' by Elias Stein, specifically chapters up to chapter seven minus the Fourier analysis chapter, as the real prerequisite for understanding the Riemann Hypothesis.
- The Basel problem, which Krishna will use as the entry point to the Riemann Hypothesis, was first proposed by Pietro Mengoli in the 1600s.
Transcript
This chapter, from the episode video's captions · 535 words
7:24of the agents that was instrumental in creating this proof. >> Okay. So, we get to kind of see the inside of Claude's mind as it was progressing through this 30 hours of problem solving to get to the Remon hypothesis. >> It's that Pixar movie Inside Out where you get to see where you get to see inside the the thought process, >> dude. Yeah. And and I think I think it's just really cool like how how gran granular we can get here. Okay. So, this is I think crazier than the Jacobian conjecture counter example that we covered. I think two or 3 weeks ago for two reasons. Um the first reason this is the Remon hypothesis. Okay, the Jacobian
8:06conjecture people know about it. I had kind of heard about it. The Remon hypothesis I have been hearing about it since even before I knew anything about complex numbers. It's like Millennium Prize and all this other kind of stuff, right? Um two, the person who initiated this, the human being behind it was not a mathematician. Okay, for the Jacobian conjecture one, um, Alpog was a Princeton and Harvard trained mathematician. This time we've got, um, Jared, we've got, uh, I've got his name right here, Jared Sumner. Okay, he's just a software engineer. Nothing against software engineers, but y'all aren't
8:46mathematicians. Okay, he kind of just prompted the new version of Claude that's unreleased. Anthropic is very clear to say it's unreleased. [laughter] you know, they want their shareholders to be very, very confident of their progress. So, it's an unreleased version of Claude that he prompted with just, "Hey, why don't you take a stab at the Remon hypothesis?" And then when Claude was like, "I'm not going to do that. It's 150-year-old problem that no one solved." He he came back with things like, "Believe in yourself." >> A little bit of do of positive encouragement >> to Claude to an AI >> to an AI. Uh actually what this is okay >> and it's kind of weird that that kind of
9:27worked. So we're going to get into some of that as well. Okay. So first let's go over the reman hypothesis. What is it and why are people obsessed about it? Okay. I could dedicate several 2hour long videos to this thing. Um and truth be told to really understand it you're going to have to go through a book like complex analysis. Again my favorite book that everyone seems to also love as well. complex analysis by Eliasstein. If you go through this book, you got to get to chapter seven to really understand Remon Hypothesis. I think you could skip the chapter on fora analysis because that doesn't really tie into this stuff. But everything else you're going to really need to understand in order to
10:08believe some of the magic that I'm about to tell you, but I'm going to go through kind of a sparknotes version of how you would begin to understand why the Remon hypothesis is so important to solve. Okay, I'm going to begin with the basil problem. This was first proposed by Petro Mangoli in the 1600s.
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.