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

Key Takeaways

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  Long Verification Loops - Scientific breakthroughs like Kepler’s laws often endure decades of 'epistemic hell' where the correct theory initially yields worse predictions than the status quo, requiring human heuristic judgment over simple RL loops.

  “AI makes papers richer and broader, but not deeper.”

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  Breadth Over Depth - While AI currently makes research papers broader and richer by synthesizing vast amounts of information, it has yet to demonstrate the ability to bridge fundamental conceptual gaps that require deep, novel insights.

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  Human-AI Hybridization - The future of mathematics lies in semi-formal languages that allow human intuition to interface with machine rigor, ensuring that humans can still derive understanding from AI-generated solutions.

  “AI makes papers richer and broader, but not deeper.”

Episode Description

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 (https://youtu.be/ztcKyI8_w6k); read the transcript (https://www.dwarkesh.com/p/terence-tao).Sponsors- Jane Street (https://janestreet.com/dwarkesh) 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 (https://x.com/hynwprk/status/2026376546286711206). If you want to try one of these puzzles yourself, there’s one live now at janestreet.com/dwarkesh (https://janestreet.com/dwarkesh).- Labelbox (https://labelbox.com/dwarkesh) 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 (https://labelbox.com/dwarkesh).- Mercury (https://mercury.com/insights) 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 (https://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 (https://www.dwarkesh.com/subscribe?utm_medium=podcast&utm_campaign=CTA_4)