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

Intro

00:00My name is Marcus Dotoy. I'm a professor of mathematics at the University of Oxford and also the Simony professor for the public understanding [music] of science. My role is a bridge between the world of academia where a lot of these things are developed and society who are going to be impacted by these new technologies.

00:16In particular, one of the things I've been interested in very much recently is the impact that artificial intelligence. But, you know, we see AI being so successful, we're beginning to wonder, you know, is there anything that [clears throat] it can't do?

00:29And 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 [music] exploratory creativity.

00:48This is kind of taking the rules of the game at the present [music] trying to understand what more can I do within this kind of rule [music] set. Then you've got what's called combinational creativity. This is finding new things being creative [music] by combining different areas.

01:05But 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.

01:20We're actually quite a lazy species. We're a bit like the lion that sits around all day in the savannah and then just does a short burst [music] in order to capture its prey. I think that's actually describes very much how we humans like to approach problems.

01:32Um

The Three Levels of Creativity

01:35[music] 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. I partly because it focused too much on the kind of technical side of multiplication tables.

02:03It 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 unexpected for people to hear, oh, mathematics is a creative subject.

02:19People 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 13 you get

Why mathematics is closer to fiction than to science

02:41the next number by adding the two previous numbers together and 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 [clears throat] 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

03:11helpful 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 uklidian geometry which is kind of a flat geometry but then you know mathematician s in the 19th century began to create new geometries where triangles did kind of strange things.

03:36Triangles 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.

03:51That 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?

04:04I 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.

04:22Isn'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? I

Type 1: Exploratory creativity

04:37think 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.

04:57For example, if you take the music of the Barack, 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.

05:13Then

Type 2: Combinational creativity

05:15you'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.

05:35Very simple example might be um fusion cooking to take the ingredients of um Asia but to cook them in European

Type 3: Transformational creativity

05:44way. So this is of 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.

05:59The sort of a you are breaking all of the conventions of the past. And often that's how transformational creativity is done. It will understand the rules of the past and they will break something. I'd say a lot of the creativity at the beginning of the 20th century is of that type.

06:15You'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.

How Creative is AI in 2026, Actually?

06:40So exploratory creativity is [music] something that I think an AI will be very good at. Combinational creativity is very good at learning style from one completely different discipline applying it to another. But transformational creativity I think is a challenge.

AI cracked a decades-old conjecture

06:58Now, how powerful is this tool? Recently, we've had some mathematical challenges which have been open for decades. Certainly, 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 very particular sort.

07:17Take the case of this [clears throat] 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 counter example. It showed it wasn't true. And that's kind of the here we see the power of this almost like a telescope.

07:35When 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

AI is a digital telescope, not an artificial brain

07:47similar 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

Move 37: the move every expert called a mistake

08:20machine creativity artificial intelligence which is really changing the landscape. So there's a very famous move now that Alph Go made in this match that it played against Lisa Doll. It's move 37 of game two. That's a very surprising move. I thought it was a mistake.

08:37This I would regard as as genuinely the first kind of sign of creativity in a machine because Alph Go 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.

08:52So, 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 um a click if we were online go we called it clicko.

09:07They considered 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 won Alph Go that second game. And so it was incredibly valuable that move. And this move has genuinely changed the way that humans play the game of go.

09:25You know, you could say, oh, is that exploratory creativity cuz it's just exploring the rules of the game. But I don't think so. I think you

The local maximum problem

09:32could regard it as transformational creativity because we had certain ways that we thought were good to play the game. And Alph Go 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 [music] to play this game.

09:50But what the AI revealed is okay, that might be a high peak, but it's only what we mathematicians called a local maximum that there's actually a much higher peak if you go down the valley and up the mountain just across the valley. But we couldn't see that cuz it was surrounded by fog in our minds.

10:06And so Al Alph Go has led us to [music] a higher peak. Now you could say, but

Why the credit belongs to the AI, not the coder

10:11hold on. Isn't that just the creativity of the coder who started coding Alph Go? 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. [music] And I think if a human had seen that line of code, it probably would have deleted it thinking that um oh, Alph Go's got gone off in a bad direction.

10:33This is a bad sort of move play that [music] deep in. So I think that 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.

10:51But Alph Go didn't want

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

10:54to play that game of go really wasn't interested. It was us who had the intention to get the thing to play [music] 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 chat GBT you've got to recognize [music] it's really just generating text what's the most probable thing that will follow given my learning process.

11:16So 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 it will suddenly write a novel

What Only Humans Can Do

11:26because it wants to tell you what it's like to be an AI. And that that intention to express itself will be I think an 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 [clears throat] that it can't do?

11:49What 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 savannah and then just does a short burst in order to capture its prey I think that's actually describes very much how we humans like to approach problems um and

12:23[clears throat] 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 I don't want

Gauss as a schoolboy, and the birth of the algorithm

12:35to 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 Friedri Gaus who when he was at school was asked to add up the numbers from 1 to 100.

12:58I 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 1 + 2 that's 3 + 3 is 6 + 4 is 10. That's going to take you forever. But Carrier Gaus, I mean, he was still, I think, 8 years old at the time.

13:16And he he said, "Hold on, there's a much clever way to do this. If you add the first and last number, 1 + 100 is 101. 2 + 99 is 101. 3 + 98 is 101. Oh, great. So, there are 50 pairs of numbers adding up to 101. So, that means the answer is 5,050.

13:34That's was fast, efficient. It's a mentality that I can apply even if the teacher goes, okay, well, you got to do 1 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.

13:50And I think that's that's the real power. And in a way, we're starting [music] 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.

Why AI never bothers to find the shortcut

14:07Early 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 amazing shortcut. The challenge is 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 problem for hours.

14:26We run out of energy. The AI, it still doesn't mind doing things [music] the dumb way. But, you know, going forward that may change. It may be that um human [music] and AI together could well, it can go so much further because we combine our passion for the shortcut, the passion for hold on.

14:45Okay, 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.