Terence Tao – Kepler, Newton, and the true nature of mathematical discovery

The Lunar Society: Read the notes at at podcastnotes.org. Don't forget to subscribe for free to our newsletter, the top 10 ideas of the week, every Monday --------- We begin the episode with the absolutely ingenious and surprising way in which Kepler discovered the laws of planetary motion.People sometimes say that AI will make especially fast progress at scientific discovery because of tight verification loops.But the story of how we discovered the shape of our solar system shows how the verification loop for correct ideas can be decades (or even millennia) long.During this time, what we know today as the better theory can actually make worse predictions.And the reasons it survives this epistemic hell is some mixture of judgment and heuristics that we don’t even understand well enough to actually articulate, much less codify into an RL loop. Hope you enjoy!Watch on YouTube; read the transcript.Sponsors- Jane Street loves challenging my audience with different creative puzzles. One of my listeners, Shawn, solved Jane Street’s ResNet challenge and posted a great walk-through on X. If you want to try one of these puzzles yourself, there’s one live now at janestreet.com/dwarkesh.- Labelbox can get you rubric-based evals, no matter your domain. These rubrics allow you to give your model feedback on all the dimensions you care about, so you can train how it thinks, not just what it thinks. Whatever you’re focused on—math, physics, finance, psychology or something else—Labelbox can help. Learn more at labelbox.com/dwarkesh.- Mercury just released a new feature called Insights. Insights summarizes your money in and out, showing you your biggest transactions and calling out anything worth paying attention to. It’s a super low-friction way to stay on top of your business. Learn more at mercury.com/insights.Timestamps(00:00:00) – Kepler was a high temperature LLM(00:11:44) – How would we know if there’s a new unifying concept within heaps of AI slop?(00:26:10) – The deductive overhang(00:30:31) – Selection bias in reported AI discoveries(00:46:43) – AI makes papers richer and broader, but not deeper(00:53:00) – If AI solves a problem, can humans get understanding out of it?(00:59:20) – We need a semi-formal language for the way that scientists actually talk to each other(01:09:48) – How Terry uses his time(01:17:05) – Human-AI hybrids will dominate math for a lot longer Get full access to Dwarkesh Podcast at www.dwarkesh.com/subscribe