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Dwarkesh Podcast / episode intelligence

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

20 Mar 2026 25 published claims 2 attributable people

Speakers in the public record

Claim mix

belief 6prediction 6uncertainty 4evaluation 3recommendation 2preference 2observation 1commitment 1

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The useful parts, with receipts.

25 published records

01 / evaluation

He had some preconceived theories first. It seems like this is less and less the way we make progress, just because the data is so much more massive and useful.

“He had some preconceived theories first. It seems like this is less and less the way we make progress, just because the data is so much more massive and useful.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

02 / evaluation

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.

“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.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

04 / recommendation

One takeaway I had from reading and watching your stuff on the cosmic distance ladder… By the way, I highly recommend people watch your series with 3Blue1Brown on the cosmic distance ladder.

“One takeaway I had from reading and watching your stuff on the cosmic distance ladder… By the way, I highly recommend people watch your series with 3Blue1Brown on the cosmic distance ladder.”
Speaker
Dwarkesh Patel
Publisher
Dwarkesh Podcast

06 / belief

I feel like a big crux in these conversations about how good AI will be for science is, I think you said this, that they’re using existing techniques and modifying them.

“I feel like a big crux in these conversations about how good AI will be for science is, I think you said this, that they’re using existing techniques and modifying them.”
Speaker
Dwarkesh Patel
Publisher
Dwarkesh Podcast

08 / evaluation

Eventually, we’ve systematically mapped out what doesn’t work and what does work, and we can see a path forward, but it’s evolving with our discussion.

“Eventually, we’ve systematically mapped out what doesn’t work and what does work, and we can see a path forward, but it’s evolving with our discussion.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

09 / belief

Whereas with research, the reason we care about solving the Millennium Prize Problems is that presumably that in the process of solving them, we discover new mathematical objects or new techniques that advance our civilization’s understanding of mathematics.

“Whereas with research, the reason we care about solving the Millennium Prize Problems is that presumably that in the process of solving them, we discover new mathematical objects or new techniques that advance our civilization’s understanding of mathematics.”
Speaker
Dwarkesh Patel
Publisher
Dwarkesh Podcast

12 / observation

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.

“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.”
Speaker
Dwarkesh Patel
Publisher
Dwarkesh Podcast

14 / belief

Suppose the AI figures it out, and latent in the Lean is some brand-new construction which, if we realized its significance, we would be able to apply in all these different situations.

“Suppose the AI figures it out, and latent in the Lean is some brand-new construction which, if we realized its significance, we would be able to apply in all these different situations.”
Speaker
Dwarkesh Patel
Publisher
Dwarkesh Podcast

16 / commitment

One big question I have is how plausible is it that if we just keep training AIs—they get better and better at solving problems in Lean—that they will continue to solve more and more impressive problems, and then we will be surprised at how little insight we got from some Lean solution to proving the Riemann hypothesis or something.

“One big question I have is how plausible is it that if we just keep training AIs—they get better and better at solving problems in Lean—that they will continue to solve more and more impressive problems, and then we will be surprised at how little insight we got from some Lean solution to proving the Riemann hypothesis or something.”
Speaker
Dwarkesh Patel
Publisher
Dwarkesh Podcast

17 / prediction

I think we would very rapidly abandon any cryptography based on the primes, because if there was one pattern that we didn’t know about, there are probably more, and these patterns can lead to exploits in crypto.

“I think we would very rapidly abandon any cryptography based on the primes, because if there was one pattern that we didn’t know about, there are probably more, and these patterns can lead to exploits in crypto.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

18 / prediction

I think within a decade, a lot of things that math students currently do—what we spend the bulk of our time doing and a lot of stuff we put in our papers today—can be done by AI.

“I think within a decade, a lot of things that math students currently do—what we spend the bulk of our time doing and a lot of stuff we put in our papers today—can be done by AI.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

19 / preference

If there was some semi-formal framework where this could be done semi-automatically in a way that isn’t easily hackable... It’s really important with these formal proof assistants that there are no backdoors or exploits you can use to somehow get your certified proof without actually proving it, because reinforcement learning is just so good at finding these backdoors.

“If there was some semi-formal framework where this could be done semi-automatically in a way that isn’t easily hackable... It’s really important with these formal proof assistants that there are no backdoors or exploits you can use to somehow get your certified proof without actually proving it, because reinforcement learning is just so good at finding these backdoors.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

20 / prediction

I think AI-type tools will actually revolutionize the experimental side of math, where you don’t care so much about individual problems and the process of solving them, but you want to gather large-scale data about what things work and what things don’t.

“I think AI-type tools will actually revolutionize the experimental side of math, where you don’t care so much about individual problems and the process of solving them, but you want to gather large-scale data about what things work and what things don’t.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

22 / preference

When there are holes in the argument where none of the things are working, then what do you do? They can suggest random things, but often I find that trying to chase them down to make them work, and finding they don’t work, wastes more time than it saves.

“When there are holes in the argument where none of the things are working, then what do you do? They can suggest random things, but often I find that trying to chase them down to make them work, and finding they don’t work, wastes more time than it saves.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

23 / prediction

I think in the future, there will be entire professions of mathematicians who might take a giant Lean-generated proof and do some ablation on it, trying to remove parts of it and find more elegant ways.

“I think in the future, there will be entire professions of mathematicians who might take a giant Lean-generated proof and do some ablation on it, trying to remove parts of it and find more elegant ways.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast

24 / prediction

I think AI has driven the cost of idea generation down to almost zero, in a very similar way to how the internet drove the cost of communication down to almost zero.

“I think AI has driven the cost of idea generation down to almost zero, in a very similar way to how the internet drove the cost of communication down to almost zero.”
Speaker
Terence Tao
Publisher
Dwarkesh Podcast
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