Big Think Clips - The paradox at the heart of AI and science | Terence Tao

Transcript

0:00 · One analogy I've given in the past is that science is a little bit like going on a hike. You've heard there's some interesting waterfall, some beautiful waterfall out there. So, you decide to to to go hike with some friends to to uh to find it, but you need to make a map. You got lo you get lost a little bit, but maybe while getting lost, you discover something else which is interesting, and you make a note of it. On the way to to this waterfall, you find an even more spectacular waterfall in the distance. you can't get there yet, but maybe some future hiker [music] will figure out a way to get there, too. And so there's there's a whole process to get to your goal, which um is also very valuable.

0:30 · But these tools, these AI tools, they can be like helicopters that will just fly you directly to this waterfall and you can see it and then you fly back, but you learn nothing about how to get there. You you you may not see any other interesting phenomena than the specific thing that you asked for.

0:50 · And so even though technically you achieve your goal much more efficiently, there may be something that that is lost. My name is Terence Tao. I'm a professor of mathematics at the University of California, Los Angeles. And I have a forthcoming book, Six Math Essentials.

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1:23 · To support the media you want to see in the world, go to bigthink.com/membership. [music] And now back to the interview. How AI is changing math and science forever.

1:37 · Science and mathematics has uh changed a lot over the the centuries. Traditionally in science uh the two major paradigms were theory and experiment. um like you would you would create a theory like you know Kepler might create a theory of or how planets move or Newton might create a theory of gravity and then there's this experimental data that you would run an experiment and and see what happens and then you try to see if the theory and the experiment fit. Math was a little different in that it was almost entirely theory. Um there's there are very very few experiments that you would do purely in mathematics.

2:06 · There were a few for example Gaus famously computed the first 100,000 prime numbers and that was a data set that he used to make predictions. he predicted what we now call the prime number theorem. But science and experiment were the two major forms of science.

2:21 · Then later on simulation came along um that you didn't have to run a a big expensive experiment.

2:26 · Sometimes you could just simulate uh let's say um a hurricane in in a supercomput instead of in real life. And then later on big data came along that um rather than than just do a small number of experiments to try to confirm or deny um a specific theory, you could take megabytes or pabytes of data and try to discern patterns, try to extract out laws from just massive data sets. Um and that's a more emerging type of science. But now all these modes of science are being transformed because we now also have AI to to to help us.

3:00 · So so in the past every one of these ways of doing science had to be done by human scientists. You know you had to have someone to perform the experiments or someone to do the theorical calculations or run the simulations um or go through the data and you could use computers for some of that but you have to but even then you have to program the um the data analysis tool or whatever and you still need a lot of expertise.

3:25 · You know, we have automated labs that can that can perform experiments automatically. Um, you can you can get a coding agent to run a simulation for you and you can try to to also run automated data analysis. Um, and increasingly you can also do automated theory. You can take some mathematical problem and ask what are the consequences of these hypotheses and these axioms? What what conclusion should you get? These tools can now be done at scale um much faster. you could potentially run many more theoretical analyses than than any one human scientist could. On the other hand, this is not the only thing that we want. There's value in doing things a slow way, you know.

3:58 · So, a scientist who spending hours and hours working things out on pen and paper uh doing the experiments in the field with with their bare hands and actually debugging the simulations that show up, they often learn a lot of of extra insight beyond just getting the answer that they're trying to seek. And they can find they can discover new phenomena. they can see connections, they can see similarities to some some previous thing that's been studied elsewhere in the literature and they can communicate what what they uh what they are finding to other people.

4:27 · So there is this paradox that on the one hand AI are becoming more powerful and more capable um and and making fewer mistakes and they are ostensively achieving a lot of the goals that we want we think scientists are trying to to to do. They're they're running experiments. They're analyzing data. They're writing papers.

4:49 · But it may be that it comes at the cost of the AI becomes picks up some skill, but but no human scientist gets any better at doing the science. No human can communicate exactly what just happened and and and why this this scientific discovery is interesting, why this proof is new and and and and what features it has and how it connects. we may have to sort of redesign our um conception of what science is and what we actually want out of science. What exactly is science for and and what are we trying to do? And is there a danger that we are optimizing the wrong thing when we are pointing our AI tools at science?

5:22 · Modern AIs are powered by a a type of algorithm known as machine learning which is trying to predict patterns in data. So a very simple example of machine learning is regression. So if you have some inputs and you some outputs like let's say you observe that if you feed um some animal more food they get they get bigger right so you can plot how much food you give various animals and and you plot their weight or something and you get some dots on on a graph and if you're lucky they will they will fit some line and then um and that line becomes your prediction.

5:56 · So then if you give this dogs this so sort this much food you they would gain this much weight. Now in the real world um you don't always get these nice linear relationships. Often there are many many inputs and there's many many outputs and the relationship can be can be really complicated but sometimes the data has a shape and and um there we now have all kinds of clever ways to kind of detect this shape and try to fit curves to to these input output pairs. What uh large language models which power chat bots and things like that they're just playing the game of naming the next word in a sentence.

6:28 · Roughly speaking, if I say roses are red, violets are blank. What is the next word to fill the sentence? You can probably guess the answer is blue. That's an output. You can imagine this giant plot where the inputs are all these incomplete sentences and the outputs are the words you want to complete and you got all these dots in this high dimensional space and you want to fit some curve to it that will um try to explain what is the most likely word to come out. Sometimes there's more than one answer. Hello, my name is. You know, there could be many many names you could put after the end of the sentence.

6:58 · So, you don't always get a single answer, but you could try to get the most plausible answer. People have tried this and and you know, the the autocomplete feature on your phone does this, you know, like you you text something and it will suggest the next word and sometimes it's kind of right, sometimes it's silly.

7:15 · Once you have any kind of operation like this, it creates some dynamics and you can just keep you know many people have just played on their phone just press autocomplete over and over again and but you get these these gibberish sentences okay um you get monkeys typing on typewriters but the uh the magic of LLMs is that if you um train these LMS on enough data okay so trillions and trillions of data points and you you um you really try to fit as good a curve as possible and this takes like millions and millions of dollars of of computing and months and months of of time, then suddenly uh even when you iterate, it stays coherent.

7:46 · It begins to sound not like monkeys, but it actually sounds like a human uh speaking. And somehow we don't fully understand why that's the case. But what seems to be true is that language like like English or other natural languages contains a lot of hidden patterns that we're not consciously aware of. I mean, we know some of the laws of English. You know, there's laws of grammar and things, but there are there are sort of unspoken, unwritten rules of of language that humans pick up.

8:14 · You know, a human child, even though they're not taught, you know, what a noun is, what a verb is or whatever, they can they can pick up what order uh English words go in. And just by continual exposure to the language, it seems like you can teach these models to also pick up patterns in language to the point where you can give them math questions. the answer to 2 plus three is and they will they will say five. They have been trained to to get the the correct answer to to at least simple math questions.

8:46 · Once you have a little bit of ability to to speak English, you can kind of go in loops and and sort of check your work and make fewer mistakes and you can prompt these models to to to proceed step by step and and and not say something unless it's been double checked and so forth.

9:02 · And so they become a little bit smarter, quote unquote, to the point where they can solve many, many complicated tasks, but they're still just guessing the next word to say. It's not really grounded in any deep understanding of the real world. It's just that they they just have seen the patterns in in the English language or other language that they've absorbed so well that they can mimic people who are speaking uh in intelligent fashion and they can present as being intelligent long enough that they can fool us, but long enough they can actually do useful things.

9:31 · So you know we can now solve certain math problems by asking the LM to provide a proof and sometimes the proof is complete rubbish but if you loop it enough and you have enough checks um you can actually uh start having a positive success rate. Um so it's it's a very strange way of solving problems like it is it is like completely orthogonal to the way we normally think of intelligence as being very grounded methodical thinking first principles. You know, it's like having someone who knows a lot and is bit of slightly drunk and is sort of throwing out ideas, but with enough guidance, uh, you you can actually extract useful output.

10:05 · It's not the most advanced mathematics out there actually. Um, but you give it a lot of data and a lot of time and a lot of other band-aids and things and it actually works pretty well. I find that some of the debate on AI's uh role in in science and other disciplines is we often default to a one-dimensional view of

10:27 · thinking like this. there's there's easy tasks and and and hard tasks and very hard tasks and and and humans are can can do tasks up to a certain level and AIs can do task to a certain level and so which one is which one is better that's kind of a one dimensional way of thinking but what I found uh when when sort of working with AIS and and comparing their way of solving problems to humans way of solving problems is that they are really quite complimentary human experts um uh will will focus on depth you know so like a human mathematician which will solve thousands and thousands of problems they can work on.

10:59 · But they will pick one or two problems that they think are are difficult but not so difficult that they're impossible but they're difficult enough that the the exercise of trying to make a bit of progress towards them will reveal all kinds of insights that they can share and maybe their students or some other collaborators or or other people can build upon what they do. When we point the AIS at really difficult problems where none of the standard techniques apply, they are still very very bad. I mean they're just randomly guessing but they excel at breath.

11:26 · So if you if you point them at a thousand problems um of various difficulties now some may be just too hard but there will be some which actually are within reach of existing methods and there's some method out there in the literature which will solve your problem or maybe you have to combine together two separate methods and it's just that there there's just not enough human experts to look at all these problems and the human experts that do look at these problems they may not realize that there was this obscure paper from a journal um in 1970 that actually has the key idea that will solve this problem.

11:58 · They don't have the patience or the time to sort of go through all the different combinations of how which technique might work on which problem. But the AIS, you know, they will somewhat randomly they will take sort of educated guesses as to what techniques might work for a problem and some of them will be stupid and but some of them might work and through all these combinations we're finding that sometimes they can catch they can catch a solution that that the rest of all the humans have missed. Occasionally the consensus the conventional wisdom on of of the experts is wrong.

12:28 · You know that we all think that that a problem has a positive answer but actually the has a negative answer and we just didn't look at the negative case too much because we thought everyone thought that the the answer was was true but an AI may not have that preconception. So uh sometimes the AI just serves as an independent pair of eyes. And so some problems that we thought were very difficult had a surprisingly simple solution which in retrospect we should have as maybe we should have gotten ourselves to. They're beginning to become successful at when you point them at a very broad range of problems and they solve some percentage of them. Like maybe you point them at a thousand problems and they solve 5% those problems.

13:02 · That's still 50 problems solved. you can already have tools that in some sense outperform humans mathematicians by raw number of problems solved. Um now the 50 problems that get solved may not be the 50 problems that you most want solved.

13:17 · They could be 50 random problems. Um but still it it is it is very impressive. What I think we will have to do as a profession is find ways to um to incorporate this new capability to to solve some problems at broad scales um and somehow figure out how to to to make that mesh with our existing capability to solve a few deep problems very slowly. Kepler's story of how he found his famous laws of motion is a is a fascinating one. It shows how important the process is.

13:50 · Kepler learned of Capernacus' theory of the motion of the planets. And Capernacus had roughly worked out how far the Earth was from the sun, how far Mars was and so forth. And Kepler noticed that the ratios of these um orbits looked a little bit like the like certain ratios that showed him in geometry.

14:05 · And so eventually he proposed that actually if you take spheres one sphere for every planet and he had six planets known at the time that he could inscribe five platonic solids you like a dodiced and a cube and a tetrahedrron and so forth between these six spheres and he thought it would get a perfect fit and this explained the shape of the solar system in terms of the five solars. This was his beautiful geometric idea.

14:26 · It was only after he managed to get his hands on some really high quality um observational data of Tao Brahi which he had to fight for actually and possibly even steal and he tried to fit it his theory to this this data and he found that it didn't actually quite fit that with the precision that Tao's data um offered he could not quite get these spheres to fit and in fact he discovered from that process that the the orbit of Mars and Earth could not be circles at all that there had to be some other shape. He spent many years um figuring out what to do.

14:58 · I think I I don't know how long he held on to this this theory of of the platonic solids and you can see in his writings he tried many other things. He tried to to make the circles off center and at some point he landed on the ellipse and then suddenly everything fit.

15:14 · It does show that there is an interplay between theory and experiment. You know that that you can pose a theory if it doesn't fit the data it's it it may not be a good theory. But um it's it's more complicated than that too. Before Kepler, one of the criticisms of Capernacus's theory was that already Capernacus acknowledged that that his measurements were worse than the best predictions available at the time. So the best models were the geocentric models which had been developed by the Greeks and then by the Arabs and Indians.

15:41 · There were many many adjustments and fine-tuning and they had a very very precise model that could predict in a very complicated way where all the planets would be. uh and Kepler Capernacus's model was worse. Just knowing agreement of data is not necessarily um the the only metric. It was only after Kepler found his his revised model where the orbits were not circles but ellipses that the heliocentric model became more accurate than the geocentric model. What this tells you is that is that science is um you can't always get instant feedback as to whether you've solved a scientific problem or not.

16:16 · If Kepler and and Copernicus had AIS and they asked them to predict a model for for for the universe, it could be that the AIs that generated the correct ketocentric model would be discarded because initially their predictions were not as good as as as the geocentric ones. It takes time to really digest all these theories and see how they fit with everything else that we know about planets and motion and gravity and everything.

16:43 · One concern actually is that AI are too fast. there's a danger that these AIs will do what's called overfitting and and create a very complicated model which is not which has nothing to do with what's actually going on but just fits your data extremely extremely well um but it doesn't extrapolate beyond that that that data set how we incorporate AI into the scientific discovery process will be uh a challenge it can certainly accelerate individual steps of of the process you know you can make experimentation faster um you can you can write code faster you can write your papers faster but size as a may not necessarily accelerate just because every single component gets faster.

17:18 · There is a danger that that we will optimize uh the wrong thing when we when we point AI at science and we will on paper get all these amazing successes and but find out that science is not actually advancing as it in the way that it used to. But we will find out it's still better to have these tools than not have them. But we're still learning how to use them most efficiently. Part of what we do is is we solve problems and and we we try to find solutions to problems and and and prove things. Uh and proofs go through a certain life cycle. First of all, you have to to to generate a proof for a solution. And this used to be quite hard.

17:50 · But but some of the proofs that you generate are incorrect. Um so then you have to to verify them, check which one check that is correct. Uh and that also used to be quite tedious. But both of these of these tasks are becoming more and more automated. So we we begin to see more and more proposed solutions to various problems and many of them are actually correct but proofs are also getting longer. Uh and when when when they're written by AIs they are often not very pleasant to read.

18:16 · An AI generated proof might might spend a lot of time talking about something very trivial and spend very little time talking about the most interesting portion of of of the paper. I think because the AI can't distinguish sort of what is hard what is difficult because by brute force everything takes the same amount of time for them. A human who has sort of naturally had to struggle at the most difficult step of a paper would naturally spend a lot of time on that step. And so you need to write out the paper in a proof in a way that it reads well and it can be explained to other people.

18:45 · And then other people have to get excited by it. they they they they have to accept it as oh this is really interesting that this this will help me solve my own problems or it really um clarifies why this phenomenon was true that it has to be accepted and this is where we we tra traditionally have the peer review process where we we send papers to referees and if the referees are are excited by this result then

19:13 · um the paper gets accepted but you know there could be papers that are technically they are correct and and they are readable and fine but but they could answering a question that no one cares about. And then finally, it needs to be sort of completely polished and put into textbooks and and taught to students. And often the first version of a proof is not suitable for writing on textbooks.

19:33 · It often is is done in a very inefficient way and is is not the the ordering of steps is not quite logical. There's a certain digestion process where where someone has to spend a lot of time thinking very hard to what is completely the the right way to organize to edit the paper to sort of flow in the same way. a little bit like how you would you would edit a documentary or a movie.

19:52 · And so what we're finding is that AI tools are accelerating the early stages of this process, but not the late stages. We're now generating many proofs. We are verifying a bunch of them, but the pace of understanding them and putting them into the final textbook form is still done by humans. Um and in fact we're now experiencing what you might call proof indigestion where suddenly there's lots and lots of pending uh solutions to problems that should be understood and should be go into textbooks but they just we're just flooded now with with too many of them and we have to pick and we have to triage and this is something that has never had to happen before.

20:26 · Um it used to be that solutions came out so rarely that um if a solution to a major problem got got solved. All the experts would sort of drop everything and read it and and try to digest it as quickly as possible because it was so rare and so valuable that it was worth doing. And now we're just getting flooded with with all these possible solutions. I myself, you know, I've had to stop trying to stay current with all the latest developments in in in my in in my field. Sometimes there's just so much going on. I I can't promise now to read every single development that that that shows up.

20:56 · I mean, this was already beginning to be a problem even before AI, but AI has really accelerated the sheer volume of of content being generated. And so, we're going to need much better curation and uh and filtering.

21:12 · It's a good problem to have. I mean, it's like it's better to have a to have too much food, more food than you can eat than than not enough food to eat. But it is still a problem. AIS have become increasingly capable in mathematics. for people like me who have been following the developments for the last three years.

21:28 · Um there's been a kind of steady progression, you know, so four years ago they could solve middle school math problems and then they could solve high school math problems and then uh high school Olympia level problems and then um some problems you like graduate student um level qualifying exam problems and then they're starting to solve a few of the the minor um unsolved problems that maybe someone like Paul Erdish would have proposed but no one really looked at. So it's a lot of low hanging fruit. And then just recently there's been one or two occasions where they they managed to solve some problems that people actually really did try very hard to solve.

22:02 · Somehow collectively the humans all had were taking the wrong turn and the AIS which had a different set of biases had managed to cobble together um a solution which was quite clever and has been quite um has already had some impact. there's been some nearby problems to the union distance problem for instance which have not also been solved by humans who have adapted the uh the AI's technique. I found that quite exciting. Uh so I think for some my colleagues it was very concerning especially if they hadn't been following the previous developments and and and not realizing that this was where they were at.

22:35 · If a colleague had only seen say what chatp could do in 2023 and if you asked it a difficult math question then it would give you complete rubbish and they they are quite different now. And it's still fundamentally the same technology, but but they have found ways to reduce the error rate and and become genuinely useful. Now, it's still unclear how replicatable this is. Many of these achievements um they're done by private companies. They they not disclosing how much resources they spent to to use. I mean, is it was it $100,000 a commute computer? Was it a million dollars? We don't really know.

23:07 · And we don't know their success rate. um was this problem that they solved the only problem that they looked at or did they look at 10 problems? They look at 100 problems. While the results are impressive, um we don't have enough data to to really gauge whether this will become a completely regular occurrence going forward or whether it's only if you spend $100,000 over several months with a team of 10 people that you can get results like this.

23:33 · And maybe it's only 1% of all problems that we care about are immunable to this method. uh yeah we don't know but there are efforts to more properly benchmark in a scientific way. The most recent of these challenges is called the first proof challenge.

23:49 · They tested the latest models against a test set of 10 research level questions and the best models could do like five or six out of 10 of these sort of medium level difficulty math problems which already had a solution but the solution was kept secret that I think there's a lot of routine tasks tasks that we we do every day as a as a as in our research that some percentage of those can now be done by by AIS it could be expensive many of of these tools they require say a couple hundred dollars to run to before they can get a solution and sometimes they fail.

24:22 · They they spend all this compute and and they end up with with nothing useful. We are seeing now in programming that many expert programmers are reporting that their ability to write code has increased by a factor of five or 10 or 100 with these with these tools but they are also they can they can feel themselves learn losing the ability to code by hand and sometimes they cannot review the code that that that comes out of these agents. There's a trade-off you know speed and is not everything. I very much like the collaborative aspect of mathematics.

24:47 · I didn't realize was so important until relatively late in my career that uh like a lot of the mathematics I've learned I I learned after grad school by by working with uh with mathematicians and and and scientists in different fields. I teach them what I know, they teach me what what what they know and I become much broader as as a as as a result. When you're working with a collaborator that you've been working with a long time, um there's a point where you become almost mentally attuned.

25:15 · Perhaps you've been familiar, like if it's a really close friend or family member that you talk to for a long time, sometimes you can complete each other's sentences. You know what the other person's going to say? And you can sometimes get that when you collaborate. You can you can throw out an idea and before you even finish the sentence, the other person gets it and and can run with it. People have tried to use AIS like this and AIS they are you can't converse with them.

25:37 · Of course they make mistakes sometimes they they sometimes will be psychopantic and and only tell you what what you want to hear but also the interactions right now with these tools are kind of personal like I've tried to collaborate with people um in person and also have an AI present but breaks up the rhythm. these these tools they don't they're not really conversational like not as fluid conversation as as as as they

26:07 · are with human collaborators yet. uh maybe they will get they will get there until recently they don't learn from your conversations you know so with a collaborator when when you you know you can resume the next day you can pick up very quickly and sometimes even for a call that you haven't met for years you can pick up some very old threads AIS have a certain amount of context and they can remember some things and and they can record they can make notes and kind of simulate this memory but you can't attune uh to an AI the same way that you can to a really close collaboration Yet I actually don't use these tools so much for the actual problem solving process.

26:39 · I found to date that these tools are much better at secondary tasks like like doing literature searches or or checking a proof or writing some code, proof reading uh something that I wrote to see if there's any opportunity to make things a little bit tighter. I find, yeah, the rhythm of of working with an AI is not quite the the rhythm I I prefer working with a human collaborator, but that could just be the the current state of current technology. Maybe in the future AIS will be much more conversational and and much more human to interact with.

27:17 · So we're at a somewhat risky point in in sort of the uh the structure of of funding the scientific enterprise in general because on the one hand these tools are allowing us to create the outputs of science or what seems to be the outputs of science at at a much accelerated rate but it could come at the cost of of nurturing our seed corn for the next generation of scientists. For example, there there is a real concern that um the training problems that we give our graduate students to work on to as as their as their first projects to to get a little bit of of of recognition and and and career training and experience.

27:51 · These are the types of problems which now AIs can um they can replicate many of the papers. But if you replace the grad students by by these AIs, you know, the AIS will will generate these grad student level papers, but then we won't get the next generation of of of students. But if we if we don't continue this process of digesting, you know, all this AI output to build the next base of knowledge for the next generation of humans and AIs to to build upon that, we may end up stagnating as as as a a scientific society.

28:17 · You know, that we we'll be able to optimize everything that we can we can do with our current technology, but we may not actually develop really original new ideas anymore. we will need to to really um

28:34 · have a much more open discussion about what basic science is and what is useful for and why it's important to still have curiositydriven re research. why we still need a community of of of of humans to explore things sometimes slowly, sometimes, you know, in in in ways that are not as efficient as the latest model AIS and also the um the insights that that we that we we we gain. I think um we should share them more and we should do more outreach to to the general public.

29:03 · I think the general public today, you know, they can see the visible outputs of science. you know, they have a cell phone, they have the internet, they they they have GPS or whatever. Many people, they they don't see the um the whole process and and how a basic understanding of math and science actually makes the world around them a lot less scary and just a a lot a lot clearer.

29:23 · I think a lot of people now are just living in in a state of anxiety. The world is so complicated.

29:29 · We haven't emphasized these sort of softer values of science as much as sort of the hard you know like um technological outputs and things but science does add a certain amount of clarity to to to one's thinking and you know these are valuable things and they need to be supported.

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