Why Your Best Ideas Come When You Stop Trying | Marcus du Sautoy

1. 0:00 – 1:35

   Intro

   1. MSMarcus du Sautoy0:00

      My name's Marcus du Sautoy. I'm a professor of mathematics at the University of Oxford, and also the Simonyi Professor for the Public Understanding of Science. My role is a bridge between the world of academia, where a lot of these things are developed, and society, who are gonna be impacted by these new technologies. In particular, one of the things I've been interested in very much recently is the impact of artificial intelligence. But, you know, we see AI being so successful, we're beginning to wonder, you know, is there anything that it can't do? So I think one thing that people often raise as a thing that surely AI could never do is the idea of creativity. Isn't our creativity somehow a unique expression of what it means to be human? But what you mean by creativity? First sort of creativity is called exploratory creativity. This is kind of taking the rules of the game at the present, trying to understand what more can I do within this kind of rule set? Then you've got what's called combinational creativity. This is finding new things, being creative by combining different areas. But combinational creativity, exploratory creativity, is something that I think an AI will be very good at. What is it that we can do that AI perhaps will always be limited by? The most difficult and the rarest form of creativity is transformational creativity. We're actually quite a lazy species. We're a bit like the lion that sits around all day in the savanna and then just does a short burst in order to capture its prey. I think that actually describes very much how we humans like to approach problems.

2. 1:35 – 2:41

   The Three Levels of Creativity

   1. MSMarcus du Sautoy1:35

      Um, and very often that leads to incredible innovation. Transformational creativity, I think, is a challenge. When I was, uh, at school, I didn't fall in love with mathematics immediately. Um, partly because it focused too much on the kind of technical side of multiplication tables. It just didn't light me up. And then I was very lucky to have a teacher when I was about 12 or 13 that, um, showed me some, kind of the beauty of mathematics, the creative side of mathematics. Perhaps un- unexpected for people to hear, oh, mathematics is a creative subject. People recognize, oh, yeah, it's the language of nature and the language of the sciences. And so if you're doing physics, very often you'll have to use this language. But, but why is it something creative? My teacher showing me how mathematics is bubbling under everything, especially nature. The Fibonacci numbers, 1, 1, 2, 3, 5, 8,

3. 2:41 – 4:37

   Why mathematics is closer to fiction than to science

   1. MSMarcus du Sautoy2:41

      13. You get the next number by adding the two previous numbers together. Now, that's a simple little pattern, but then to start to see, yeah, but this is the key to the way nature grows things. And this is best explained by really pointing out a big difference between mathematics and the other sciences. The other sciences, we're trying to understand the universe around us. We're trying to understand why particular animals evolved in biology, or why the fundamental particles we see which make up the universe. And you might be as creative as you want in the sciences, but it's not particularly helpful if it doesn't match reality. Yet in mathematics, that doesn't matter so much. We're quite interested in worlds which don't have a physical reality. One example is the different sorts of geometries we've created. The ancient Greeks started with Euclidean geometry, which is kind of a flat geometry. But then, you know, mathematicians in the 19th century began to create new geometries where triangles did kind of strange things. Triangles on a sphere add up to more than 180. We have this thing, the hyperbolic geometry, where a saddle or a Pringle crisp, where triangles do different things. So quite often our stories will be about universes that have no physical reality. That sounds very much like a, a novelist or a science fiction writer that goes, "Okay, suppose these are the rules of the game," and then you explore what happened. And so I fell in love with mathematics because of its creative side. But what you mean by creativity? I think there's a lot of concern about is our species, the human species, going to be wiped out or taken over or replaced by artificial intelligence? And I think one thing that people often raise as a thing that surely AI could never do is the idea of creativity. Isn't our creativity somehow a unique expression of what it means to be human? But I think this word creativity is actually quite hard to pin down. So that's kind of the first challenge. If you're going to ask can AI be creative or not,

4. 4:37 – 5:15

   Type 1: Exploratory creativity

   1. MSMarcus du Sautoy4:37

      uh, I think you need a pretty good definition of what creativity is. First sort of creativity is called exploratory creativity. This is kind of taking the rules of the game at the present and sort of pushing that creativity to its extreme, trying to understand what more can I do within this kind of rule set? For example, if you take the music of the Baroque, I would say that Bach was still working within that rule set, but he was just superbly creative in pushing the musical style to its absolute limits, and I would say was a great example of exploratory creativity.

5. 5:15 – 5:44

   Type 2: Combinational creativity

   1. MSMarcus du Sautoy5:15

      Then you've got what's called combinational creativity, and this is one I love using in my own work. I often do it in mathematics because I will go to a seminar, say, in geometry, but I'm a number theorist. So I will see how are they analyzing their structures, and does that give me a new mindset for looking at my area? Very simple example might be, um, fusion cooking, to take the ingredients of, um, Asia, but to cook them in European

6. 5:44 – 6:40

   Type 3: Transformational creativity

   1. MSMarcus du Sautoy5:44

      way. So this is of- often a very fruitful way of finding new things, being creative by combining different areas. The most difficult and the rarest form of creativity is transformational creativity. That's where something seems to come out of nowhere. There's sort of a, you are breaking all of the conventions of the past. And often that's how transformational creativity is done. It'll understand the rules of the past, and it will break something I'd say a lot of the creativity at the beginning of the 20th century is of that type. You've got serialism in music, where suddenly you're throwing away harmonic structure in music and just introducing a 12-tone row. That's really throwing away old structures, but something very interesting and liberating. I think that's the rarest form, and in a way, that's the most challenging for an artificial intelligence because the way AI is creative is it learns on the styles of the past and develops those.

7. 6:40 – 6:58

   How Creative is AI in 2026, Actually?

   1. MSMarcus du Sautoy6:40

      So exploratory creativity is something that, uh, I think an AI will be very good at. Combinational creativity is very good at learning style from one completely different discipline and applying it to another. But transformational creativity, I think, is a challenge.

8. 6:58 – 7:47

   AI cracked a decades-old conjecture

   1. MSMarcus du Sautoy6:58

      Now, how powerful is this tool? Recently, we've had some mathematical challenges which have been open for decades. Suddenly, with the aid of artificial intelligence, we've been able to solve these. But it's interesting that the sort of problem that artificial intelligence is good at is a v- very particular sort. Take the case of this mathematical problem. We had a conjecture that we thought was true. Now, the AI didn't prove that it was true. It did something different. It found a counterexample. It showed it wasn't true. And that's kind of the, the ... Here we see the power of this almost like a telescope. When Galileo got a telescope, that tool allowed us to see deeper into the solar system than we ever had before. We really can regard AI in a

9. 7:47 – 8:20

   AI is a digital telescope, not an artificial brain

   1. MSMarcus du Sautoy7:47

      similar way. It's almost like a digital telescope. It's allowing us to see into the digital world, see patterns emerging. You know, still required very good use of this tool, but it was able to tease out a particular structure that actually contradicted what the conjecture was saying. So I think artificial intelligence is going to be very good, for example, at that. So that's why I often translate artificial intelligence not as artificial intelligence, but augmented intelligence. So I think that's one of its strengths. But there has been example of genuine

10. 8:20 – 9:31

    Move 37: the move every expert called a mistake

    1. MSMarcus du Sautoy8:20

       machine creativity, artificial intelligence which is really changing the landscape. So there's a very famous move now that, say, AlphaGo made in this match that it played against Lee Sedol. It was called Move 37 of game two. That's a very surprising move. I thought it was a mistake. This I would regard as, as genuinely the first kind of sign of creativity in a machine because AlphaGo makes this move very early on in the game and it's a very unconventional move. It's very deep into the board compared to what people traditionally would play at the beginning of the game. So it's a new sort of move, and it was a very surprising move because I remember listening to the, um, commentary of this match on, on YouTube and all of the commentators gasped. I thought it was a quick miss, but, uh, um- A click- And- If we were on my Go- That's right. Right. Yeah ... we'd call it a clicko. They considered it a very bad move because that seems to be very weak to play deep in the board. Yet, by the end of the game, it was this move that, uh, won AlphaGo that second game. So it was incredibly valuable, that move. And this move has genuinely changed the way that humans play the game of Go. You know, you could say, "Oh, is that exploratory creativity 'cause it's just exploring the rules of the game?"

11. 9:31 – 10:09

    The local maximum problem

    1. MSMarcus du Sautoy9:31

       But I don't think so. I think you could regard it as transformational creativity because we had certain ways that we thought were good to play the game, and AlphaGo showed us you don't have to stick to that. You can break it and do something quite different. We thought we climbed a mountain peak and we, we knew the top place to play this game. But what the AI revealed is, okay, that might be a high peak, but it's only what we mathematicians call a local maximum, that there's actually a, a much higher peak if you go down the valley and up the mountain just across the valley. But we couldn't see that 'cause it was surrounded by fog in our minds. And so Alf- AlphaGo has led us to a

12. 10:09 – 10:52

    Why the credit belongs to the AI, not the coder

    1. MSMarcus du Sautoy10:09

       higher peak. Now, you could say, "But hold on, isn't that just the creativity of the coder who started coding AlphaGo?" No, I don't think so because this line of code that appeared, this strategy, was not written in by a human. It grew out of the learning process of the code. And I think if a human had seen that line of code, it probably would've deleted it thinking that, um, oh, AlphaGo has gone, gone off in a bad direction. This is a bad sort of move played that deep in. So I think that's really that strategy, those lines of code, play this deep in early on in the game, grew out of the learning process of the code. So I think you should genuinely credit it to the AI and not the human.

13. 10:52 – 11:25

    The one signal that would mean there's a ghost in the machine

    1. MSMarcus du Sautoy10:52

       But AlphaGo didn't want to play that game of Go. It really wasn't interested. It was us who had the intention to get the thing to play the game. AI, we have to recognize, is being created using a lot of statistics. It's a statistical model. What, what's likely? That means something like ChatGPT, you've gotta recognize it's really just generating text. What's the most probable thing that will follow given my learning process? So it can show you that something happens, but not the why. I'm not saying that it won't get to that stage, but at the moment,

14. 11:25 – 12:35

    What Only Humans Can Do

    1. MSMarcus du Sautoy11:25

       it will suddenly write a novel because it wants to tell you what it's like to be an AI and that, that intention to express itself will be, I think, um, our first indication that, you know, oh, maybe there is a ghost in the machine. You know, we see AI being so successful, we're beginning to wonder, you know, is there anything that it can't do? What is it that we can do that AI perhaps will always be limited by? It actually led to me writing one of my books, the book after I wrote about AI and creativity, Better Thinking: The Art of the Shortcut, because I think that one of the things that humans are very good at is when they're faced with a problem, we're actually quite a lazy species. We're a bit like the lion that sits around all day in the savanna and then just does a short burst in order to capture its prey. I think that actually describes very much how we humans like to approach problems. Um, and very often that leads to incredible innovation. We're faced with a problem that just, okay, I can see how to do this by doing a huge amount of laborious donkey work, but

15. 12:35 – 14:07

    Gauss as a schoolboy, and the birth of the algorithm

    1. MSMarcus du Sautoy12:35

       I don't wanna do that. And you sit back and you try and find ... You do some lateral thinking, which is what humans are very good at, and finding some sort of clever way around the problem that you're facing. I think mathematics is developed out of that mentality. I think my favorite example of lazy mind of the mathematician is one about one of my mathematical heroes, Carl Friedrich Gauss, who when he was at school, was asked to add up the numbers from one to 100. I think the teacher thought, "Oh, that'll keep them occupied for ages." Here's a good example of the dumb way. You, you, okay, you start with one plus two plus three plus three is six plus four is 10. That's gonna take you forever. But Carl Friedrich Gauss, I mean, he was still I think eight years old at the time, and he, he said, "Ah, hold on. There's a much cleverer way to do this." If you add the first and last number, one plus 100 is 101, two plus 99 is 101, three plus 98 is 101. Oh, great. So there are 50 pairs of numbers adding up to 101, so that means the answer is 5,050. That's was fast, efficient. It's a mentality that I can apply even if the teacher goes, "Okay, well, you've gotta do one to a million." The laborious way, you'd be there for days trying to do it. But that strategy can be applied however big the number is, and I think that's, that's the real power. And in a way, so we're starting to see where computing emerges from because what you're doing is, is creating an algorithm there. Doesn't matter what number you give me, this algorithm will give you the answer fast and efficiently and correctly.

16. 14:07 – 15:06

    Why AI never bothers to find the shortcut

    1. MSMarcus du Sautoy14:07

       Early coding is all about, okay, you might have very many different numbers in this, but if they all working under the same rule set. So that's a real and amazing shortcut. The challenge is w- would AI come up with these kind of shortcuts? Well, I don't think very often it will because it's got no problem about working incredibly hard, churning through a, a problem for hours. We run out of energy. The AI, it still doesn't mind doing things the dumb way. But, you know, going forward, that may change. It may be that, um, human and AI together could well ... It can go so much further because we combine our passion for the shortcut, the passion for, hold on, okay, you could do that the really long way, but let me introduce a shortcut, and then you, you introduce that into the program and, and then you've got an incredibly efficient combination of, um, the human and the machine. One of my central messages is to remember that artificial intelligence is not a competitor. It's a collaborator.

Episode duration: 15:17