AI enters pure mathematics

39:35Um, it's very very cool because I mean it's it's completely obvious I think to everyone who lives under a who does not live under a rock that we are living through one of the most disorienting times in the history of human intellectual life. Okay, this is especially true when it comes to really really hard intellectual disciplines like mathematics because for thousands of years mathematics has been the one domain where human beings can claim something that is very close to absolute certainty. Right? We can say that the act of understanding and the act of proving are one and the same thing. And a mathematical proof it's it's it's been here since the time

40:16of the ancient Greeks with Uklid. It's a certificate of the truth, right? And it's a map as to why something has to be true. And very crucially, for the longest time, it's been something that only human minds can produce. >> Very important point. >> Very important point. It's, you know, we've seen a lot of disciplines fall to computation. Chess >> crazy >> has fallen to computation. The game go has fallen to computation. protein folding has fall into computation and now we are finally seeing the the the the shining city on the hill

40:56which is pure mathematics it is starting to fall right there's crumbles in the infrastructure I just want to briefly note that you know in our time at Princeton some of the smartest people we had the pleasure of being able to be around yeah and breathe the same air that they did were the maths folks. >> Yeah, we're the maths folks. Yeah. >> Like like they >> were a level of smart that is really hard to wrap my own head around. >> Yeah. Yeah. Yeah. Same for me. I mean, I I I took some courses with them, right? And I was just like, I'm going to stick to [laughter] >> I'll stick to the physics department, which is right next door. I took a few

41:37math courses and it was it was extremely fun, but I could just never see myself like being a math major, right? And uh and I mean even in the physics department I was like man what am I doing [laughter] here? But the math the math department was its own little game. And so so this particular story has to do with an AI system. It was used by a researcher at Anthropic