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Dwarkesh Patel: observation

20 Mar 2026 Dwarkesh Podcast Terence Tao – Kepler, Newton, and the true nature of mathematical discovery

“The ancient Athenians were like, “This can’t be because if the earth is going around the sun, we should see the relative position of the stars change as we’re going around the sun, and the only way that wouldn’t be the case is if they’re so far away that you don’t notice any parallax,” which is actually the correct implication.”

— Dwarkesh Patel

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Speaker
Dwarkesh Patel
Attribution
Verified speaker
Claim type
observation
Recorded
20 Mar 2026
Publisher
Dwarkesh Podcast

Transcript context

…A lot of it’s the test of time. Many great ideas didn’t actually get a great reception at the time they were first proposed. It was only after some other scientists realized that they could take it further and apply them to their own... Deep learning itself was a niche area of AI for a long time. The idea of getting answers entirely through training on data and not through first principles reasoning was very controversial, and it just took a long time before it started bearing fruit. You mentioned the bit. There were other proposals for computer architectures than the zero-one that is universal today. I think there were trits, three-valued logic. In an alternate universe, maybe a different paradigm would have shown up. The transformer, for example, is the foundation of all modern large language models, and it was the first deep learning architecture that really was sophisticated enough to capture language. But it didn’t have to be that way. There could’ve been some other architecture that was the first to do it and once that was adopted, it would become the standard. One reason why it’s hard to assess whether a given idea is going to be fruitful is that it depends on the future. It depends also on the culture and society, which ones get adopted, which ones don’t. The base ten numeral system in mathematics is extremely useful, much better than the Roman numeral system, for instance. But again, there’s nothing special about ten. It’s a system that is useful for us because everyone else uses it. We’ve standardized it. We’ve built all our computers and our number representation systems around it, so we’re stuck with it now. Some people occasionally push for other systems than decimal, but there’s just too much inertia. It’s not something where you can look at any given scientific achievement purely in isolation and give it an objective grade without being aware of the context both in the past and the future. So it may never be something that you can just reinforcement learn the same way that you can for much more localized problems. Often in the history of science when a new theory comes up that in retrospect we realize is correct, it seems to make implications that either make no sense because they’re wrong, and we realize later on why they’re wrong, or they’re correct but seem wildly implausible at the time. As you talked about, Aristarchus had heliocentrism in the third century BC. The ancient Athenians were like, “This can’t be because if the earth is going around the sun, we should see the relative position of the stars change as we’re going around the sun, and the only way that wouldn’t be the case is if they’re so far away that you don’t notice any parallax,” which is actually the correct implication. But there’s times when the implication is incorrect and we just need to graduate to a better level of understanding. Leibniz would chide Newton and disagree with Newton’s theory of gravity on the basis that it implied action at a distance, and they didn’t know the mechanism, and Newton himself was sort of stunned that inertial mass and gravitational mass were the same quantity. All these things later were resolved by Einstein. But it was still progress. So the question for a system of peer review for AI would be: even if you can falsify a theory, how would you notice that it still constitutes progress relative to the thing before? Often, the ultimately correct theory initially is worse in many ways. Copernicus’s theory of the planets was less accurate than Ptolemy’s theory. Geocentrism had been developed for a millennium by that point, and they had made many tweaks and increasingly complicated ad hoc fixes to make it more and more accurate. Copernicus’s theory was a lot simpler but much less accurate. It was only Kepler that made it more accurate than Ptolemy’s theory. Science is always a work in progress. When you only get part of the solution, it looks worse than a theory which is incorrect but somehow has been completed to the point where it kind of answers all the questions. As you say, Newton’s theory had big mysteries. They had the equivalence of mass and action at a distance, which were only resolved with a very conceptually different approach centuries afterwards. Often progress has to be made not by adding more theories, but by deleting some assumptions that you have in your mind. One reason why geocentrism held on for so long is we had this idea that objects naturally want to stay at rest. This is the Aristotelian notion of physics, and so the idea that the Earth was moving… How come we weren’t all falling over? Once you have Newton’s laws of motion—an object in motion remains in motion and so forth—then it makes sense. Conceptually, it’s a very big leap to realize that the Earth is in motion. It doesn’t feel like it’s in motion. The biggest advances, like Darwin’s theory of evolution, is the idea that species are not static. This is not obvious because you don’t see evolution in your lifetime. Well, now we actually can, but it seems permanent and static. Right now we’re going through a cognitive version of the Copernican revolution, where we used to think that human intelligence is the center of the universe, and now we’re seeing that there are very different types of intelligence out there with very different strengths and weaknesses. Our assessment of which tasks require intelligence, which ones don’t, has to be reordered quite a bit. Trying to fit AI into our theories of scientific progress and what is hard and what is easy, we’re struggling quite a lot. We have to ask questions that we’ve never really had to ask before. Or maybe the philosophers had, but now we all have to deal with it.…

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