Public evidence record
Published podcast speaker
Claim ledger
44 transcript-backed 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.”
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.”
03 / uncertainty
“I don’t know how you can quantify that in such a precise way that you can start doing reinforcement learning.”
04 / belief
“I think one aspect of science is that it’s not just creating a new theory and validating it, but communicating it to others.”
05 / uncertainty
“We don’t know. Some problems have been basically solved by pure brute force. The four color theorem is a famous example.”
06 / 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.”
07 / belief
“On the one hand, I think the type of papers that I would write today, if I had to do them without AI assistance, would definitely take five times longer.”
08 / uncertainty
“You’re trying to climb as many of these cliffs as possible, but it’s in the dark. We don’t know which ones are tall, which ones are short.”
09 / belief
“I think there’ll be a similar thing happening with the hundreds of really prestigious, difficult math problems out there.”
10 / 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.”
11 / 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.”
12 / 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.”
13 / 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.”
14 / prediction
“We don’t even have the paradigms to really take full advantage of it. But we will, and then science will be unrecognizable after that, I think.”
15 / 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.”
16 / 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.”
17 / 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.”
18 / belief
“Maybe if you do math competitions or something, you get a slightly different experience. But I think many people, they don’t find their native math language until very late or usually too late.”
19 / belief
“I think the younger generation is always really creative and enthusiastic and inventive.”
20 / evaluation
“I mean, you can ask some cheater if there’s a specific thing that’s blocking you that some bad case keeps showing up, that for which your tool doesn’t work.”
21 / observation
“You talk to athletes like marathon runners and so forth and they talk about what’s the most important thing, is it the training regimen or the diet and so forth? So much of it is psychology, just tricking yourself to think that the problem is feasible so that you’re motivated to do it.”
22 / belief
“As the unit needle, you can spin it around its center, and I think that gives you a disc of area, I think pi over four.”
23 / belief
“I think the theories that work well, that explain the universe, tend to also involve the same mathematical objects that work well to solve mathematical problems.”
24 / belief
“Yeah, I think mathematics inherently, mathematics is so huge these days that nobody knows all of modern mathematics. And inevitably, we make mistakes and you can’t cover up your mistakes with just bravado because people will ask for your proofs, and if you don’t have the proofs, you don’t have the proofs.”
25 / belief
“I believe so. The history of physics has been out of unification much like mathematics over the years.”
26 / commitment
“Once again, nothing happened. I will move on.” Very occasionally one of these problems or actually solved.”
27 / belief
“There’s the real world, there’s what we observe of the real world, observations, and then our mental models as to how we think the world works.”
28 / belief
“I would definitely not want this to become part of your tenure review or something. But I mean, I think already in enterprise computing, people do use some of these metrics as part of the assessment of performance of an employee.”
29 / belief
“Yeah, so it does keep us honest. It’s not a perfect panacea, but I think we do have more of a culture of admitting error because we’re forced to all the time.”
30 / commitment
“There are simpler versions of the conjecture where we are getting really close. So I think in 10 years we will have many more much closer results, we may not have the whole thing.”
31 / commitment
“Anyway, these are things which I think we will still need even as our tools get better, and you’ll be working with AI supports and so forth.”
32 / uncertainty
“I don’t know how to completely power down the big machine, so it doesn’t interfere the writing of the smaller machine, but everything in principle can happen.”
33 / uncertainty
“If they recognize that there’s a certain technique that can be applied, they will try it. But there are problems which they see and none of their standard techniques obviously applies and the common reaction is than just paralysis, I don’t know what to do.”
34 / belief
“I think the way of colleague might put it is that if you are on the streets of New York and you’re put in a blindfold and you’re put in a car and after some hours the blindfold is off and then you’re in Beijing.”
35 / belief
“We believe the primes behave like a random set. And so the reason why we care about the twin prime conjecture is a test case for whether we can genuinely confidently say with 0% chance of error that the primes behave like a random set.”
36 / evaluation
“Often these models are incorrect, and this causes all kinds of problems. So yeah, to humanize a subject, if you identify a small number of people and say these are representative people of a subject, role models, for example, that has some role, but it can also be too much of it can be harmful because I’ll be the first to say that my own career path is not that of a typical mathematician.”
37 / evaluation
“If viscosity was all there was, then nothing bad would ever happen, but there’s also transport that energy from… in one location of space can get transported because the fluid is in motion to other locations.”
38 / preference
“If I take a set of odd numbers and I flip a coin for each number, and I only keep the numbers for which I got a heads… So I just flip coins, I just randomly take out half the numbers, I keep one half.”
39 / preference
“I spend a lot of time… If there’s a result, I see it in one field, and I like the result, it’s a cool result, but I don’t like the proof, it uses types of mathematics that I’m not super familiar with, I often try to re-prove it myself using the tools that I favor.”
40 / evaluation
“Now I think there’s some more awareness that this systemic risk is actually a much bigger issue, and just because the model is pretty and nice, it may not match reality.”
41 / prediction
“There’s no reason why they should un-mix. But in principle, because of all the collisions between them, there could be some sort of weird conspiracy that maybe there’s a microscopic demon called Maxwell’s Demon that will… every time an oxygen and nitrogen atom collide, they’ll bounce off in such a way that the oxygen sort of drifts onto one side and then nitrogen goes to the other.”
42 / evaluation
“A lot of it is we don’t know how to use these tools, because it’s a paradigm that… We have not had in the past.”
43 / preference
“I mean, I think for some people it’s as a job, you have a problem and if it doesn’t work out, you go on the next one.”
44 / evaluation
“I think hedgehogs and fox… A fox knows many things a little bit, but a hedgehog knows one thing very, very well, and in mathematics, there’s definitely both hedgehogs and foxes, and then there’s people who can play both roles, and I think ideal collaboration, British mathematicians involves very… You need some diversity, like a fox working with many hedgehogs or vice versa, but I identify mostly as a fox, certainly.”