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

EO15:16Added Aug 31, 2026

AI just cracked a mathematical conjecture that had stayed open for decades. It found the counterexample — and still couldn't tell us why it was true.Marcus d...

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  1. Intro

  2. 00:00My name is Marcus Dotoy. I'm a professor
  3. 00:02of mathematics at the University of
  4. 00:03Oxford and also the Simony professor for
  5. 00:06the public understanding [music] of
  6. 00:07science. My role is a bridge between the
  7. 00:10world of academia where a lot of these
  8. 00:12things are developed and society who are
  9. 00:14going to be impacted by these new
  10. 00:16technologies. In particular, one of the
  11. 00:18things I've been interested in very much
  12. 00:20recently is the impact that artificial
  13. 00:22intelligence.
  14. 00:24But, you know, we see AI being so
  15. 00:26successful, we're beginning to wonder,
  16. 00:28you know, is there anything that
  17. 00:29[clears throat] it can't do? And I think
  18. 00:31one thing that people often raise as a
  19. 00:33thing that surely AI could never do is
  20. 00:36the idea of creativity. Isn't our
  21. 00:38creativity somehow a unique expression
  22. 00:40of what it means to be human? But what
  23. 00:43you mean by creativity? First sort of
  24. 00:46creativity is called [music] exploratory
  25. 00:48creativity. This is kind of taking the
  26. 00:50rules of the game at the present [music]
  27. 00:52trying to understand what more can I do
  28. 00:55within this kind of rule [music] set.
  29. 00:57Then you've got what's called
  30. 00:58combinational creativity. This is
  31. 01:01finding new things being creative
  32. 01:02[music] by combining different areas.
  33. 01:05But combinational creativity,
  34. 01:07exploratory creativity is something that
  35. 01:09I think an AI will be very good at. What
  36. 01:11is it that we can do that AI perhaps
  37. 01:14will always be limited by? The most
  38. 01:16difficult and the rarest form of
  39. 01:17creativity is transformational
  40. 01:20creativity. We're actually quite a lazy
  41. 01:22species. We're a bit like the lion that
  42. 01:24sits around all day in the savannah and
  43. 01:26then just does a short burst [music] in
  44. 01:28order to capture its prey. I think
  45. 01:30that's actually describes very much how
  46. 01:32we humans like to approach problems. Um

  47. The Three Levels of Creativity

  48. 01:35[music] and very often that leads to
  49. 01:37incredible innovation. Transformational
  50. 01:40creativity I think is a challenge.
  51. 01:54When I was uh at school, I didn't fall
  52. 01:57in love with mathematics immediately. I
  53. 01:58partly because it focused too much on
  54. 02:01the kind of technical side of
  55. 02:03multiplication tables. It just didn't
  56. 02:05light me up. And then I was very lucky
  57. 02:07to have a teacher when I was about 12 or
  58. 02:0913 that um showed me some kind of the
  59. 02:12beauty of mathematics, the creative side
  60. 02:14of mathematics. Perhaps unexpected for
  61. 02:18people to hear, oh, mathematics is a
  62. 02:19creative subject. People recognize, oh
  63. 02:22yeah, it's the language of nature and
  64. 02:24the language of the sciences. And so if
  65. 02:26you're doing physics, very often you'll
  66. 02:27have to use this language. But but why
  67. 02:29is it something creative? my teacher
  68. 02:32showing me how mathematics is bubbling
  69. 02:35under everything especially nature the
  70. 02:37Fibonacci numbers 1 1 2 3 5 8 13 you get

  71. Why mathematics is closer to fiction than to science

  72. 02:41the next number by adding the two
  73. 02:43previous numbers together and that's a
  74. 02:45simple little pattern but then to start
  75. 02:47to see yeah but this is the key to the
  76. 02:49way nature grows things and
  77. 02:51[clears throat] this is best explained
  78. 02:53by really pointing out a big difference
  79. 02:54between mathematics and the other
  80. 02:56sciences the other sciences we're trying
  81. 02:58to understand the universe around us
  82. 03:00we're trying to understand why
  83. 03:01particular animals evolved in biology or
  84. 03:04why the fundamental particles we see
  85. 03:06which make up the universe and you might
  86. 03:08be as creative as you want in the
  87. 03:09sciences but it's not particularly
  88. 03:11helpful if it doesn't match reality yet
  89. 03:13in mathematics that doesn't matter so
  90. 03:15much we're quite interested in worlds
  91. 03:18which don't have a physical reality one
  92. 03:20example is the different sorts of
  93. 03:22geometries we've created the ancient
  94. 03:25Greeks started with uklidian geometry
  95. 03:27which is kind of a flat geometry but
  96. 03:29then you know mathematician s in the
  97. 03:3119th century began to create new
  98. 03:34geometries where triangles did kind of
  99. 03:36strange things. Triangles on a sphere
  100. 03:38add up to more than 180. We have this
  101. 03:40thing the hyperbolic geometry where a
  102. 03:42saddle or a Pringle crisp where
  103. 03:44triangles do different things. So quite
  104. 03:46often our stories will be about
  105. 03:49universes that have no physical reality.
  106. 03:51That sounds very much like a a novelist
  107. 03:54or a science fiction writer that goes,
  108. 03:56"Okay, suppose these are the rules of
  109. 03:57the game." And then you explore what
  110. 03:59happened. And so I fell in love with
  111. 04:01mathematics because of its creative
  112. 04:04side. But what you mean by creativity? I
  113. 04:08think there's a lot of concern about is
  114. 04:11our species, the human species going to
  115. 04:13be wiped out or taken over or replaced
  116. 04:15by artificial intelligence. And I think
  117. 04:17one thing that people often raise as a
  118. 04:19thing that surely AI could never do is
  119. 04:22the idea of creativity. Isn't our
  120. 04:24creativity somehow a unique expression
  121. 04:26of what it means to be human? But I
  122. 04:29think this word creativity is actually
  123. 04:31quite hard to pin down. So that's kind
  124. 04:32of the first challenge. If you're going
  125. 04:34to ask, can AI be creative or not? I

  126. Type 1: Exploratory creativity

  127. 04:37think you need a pretty good definition
  128. 04:38of what creativity is. First sort of
  129. 04:42creativity is called exploratory
  130. 04:44creativity. This is kind of taking the
  131. 04:46rules of the game at the present and
  132. 04:48sort of pushing that creativity to its
  133. 04:52extreme. Trying to understand what more
  134. 04:54can I do within this kind of rule set.
  135. 04:57For example, if you take the music of
  136. 04:59the Barack, I would say that Bach was
  137. 05:02still working within that rule set, but
  138. 05:05he was just superbly creative in pushing
  139. 05:08the musical style to its absolute
  140. 05:11limits. And I would say was a great
  141. 05:13example of exploratory creativity. Then

  142. Type 2: Combinational creativity

  143. 05:15you've got what's called combinational
  144. 05:17creativity. And this is one I love using
  145. 05:20in my own work. I often do it in
  146. 05:22mathematics because I will go to a
  147. 05:24seminar say in geometry but I'm a number
  148. 05:26theorist. So I will see how are they
  149. 05:30analyzing their structures and does that
  150. 05:32give me a new mindset for looking at my
  151. 05:35area. Very simple example might be um
  152. 05:37fusion cooking to take the ingredients
  153. 05:40of um Asia but to cook them in European

  154. Type 3: Transformational creativity

  155. 05:44way. So this is of a very fruitful way
  156. 05:48of finding new things being creative by
  157. 05:50combining different areas. The most
  158. 05:53difficult and the rarest form of
  159. 05:54creativity is transformational
  160. 05:57creativity. That's where something seems
  161. 05:59to come out of nowhere. The sort of a
  162. 06:01you are breaking all of the conventions
  163. 06:03of the past. And often that's how
  164. 06:06transformational creativity is done. It
  165. 06:07will understand the rules of the past
  166. 06:09and they will break something. I'd say a
  167. 06:11lot of the creativity at the beginning
  168. 06:12of the 20th century is of that type.
  169. 06:15You've got serialism in music where
  170. 06:17suddenly you're throwing away harmonic
  171. 06:20structure in music and just introducing
  172. 06:22a 12 tone row. That's really throwing
  173. 06:25away old structures. But something very
  174. 06:28interesting and liberating. I think
  175. 06:30that's the rarest form and in a way
  176. 06:32that's the most challenging for an
  177. 06:33artificial intelligence because the way
  178. 06:36AI is creative is it learns on the
  179. 06:38styles of the past and develops those.

  180. How Creative is AI in 2026, Actually?

  181. 06:40So exploratory creativity is [music]
  182. 06:42something that I think an AI will be
  183. 06:43very good at. Combinational creativity
  184. 06:45is very good at learning style from one
  185. 06:48completely different discipline applying
  186. 06:49it to another. But transformational
  187. 06:51creativity I think is a challenge.

  188. AI cracked a decades-old conjecture

  189. 06:58Now, how powerful is this tool?
  190. 07:00Recently, we've had some mathematical
  191. 07:03challenges which have been open for
  192. 07:05decades. Certainly, with the aid of
  193. 07:07artificial intelligence, we've been able
  194. 07:10to solve these. But it's interesting
  195. 07:12that the sort of problem that artificial
  196. 07:15intelligence is good at is a very
  197. 07:17particular sort. Take the case of this
  198. 07:19[clears throat] mathematical problem. We
  199. 07:21had a conjecture that we thought was
  200. 07:23true. Now, the AI didn't prove that it
  201. 07:25was true. It did something different. It
  202. 07:27found a counter example. It showed it
  203. 07:29wasn't true. And that's kind of the here
  204. 07:33we see the power of this almost like a
  205. 07:35telescope. When Galileo got a telescope,
  206. 07:38that tool allowed us to see deeper into
  207. 07:41the solar system than we ever had
  208. 07:43before. We really can regard AI in a

  209. AI is a digital telescope, not an artificial brain

  210. 07:47similar way. It's almost like a digital
  211. 07:49telescope. It's allowing us to see into
  212. 07:51the digital world, see patterns
  213. 07:53emerging. you know still required very
  214. 07:56good use of this tool but it was able to
  215. 07:57tease out a particular structure that
  216. 08:00actually contradicted what the
  217. 08:02conjecture was saying so I think
  218. 08:04artificial intelligence is going to be
  219. 08:06very good for example at that so that's
  220. 08:08why I often translate artificial
  221. 08:10intelligence not as artificial
  222. 08:11intelligence but augmented intelligence
  223. 08:13so I think that's one of its strengths
  224. 08:16but there has been example of genuine

  225. Move 37: the move every expert called a mistake

  226. 08:20machine creativity artificial
  227. 08:22intelligence which is really changing
  228. 08:24the landscape. So there's a very famous
  229. 08:26move now that Alph Go made in this match
  230. 08:29that it played against Lisa Doll. It's
  231. 08:32move 37 of game two.
  232. 08:33That's a very surprising move.
  233. 08:35I thought it was a mistake.
  234. 08:37This I would regard as as genuinely the
  235. 08:39first kind of sign of creativity in a
  236. 08:42machine because Alph Go makes this move
  237. 08:44very early on in the game and it's a
  238. 08:46very unconventional move. It's very deep
  239. 08:48into the board compared to what people
  240. 08:50traditionally would play at the
  241. 08:52beginning of the game. So, it's a new
  242. 08:53sort of move and it was a very
  243. 08:55surprising move because I remember
  244. 08:57listening to the um commentary of this
  245. 08:59match on on YouTube and all of the
  246. 09:01commentators gasped.
  247. 09:02I thought it was a quick miss but um
  248. 09:04a click if we were online go we called
  249. 09:06it clicko.
  250. 09:07They considered a very bad move because
  251. 09:10that seems to be very weak to play deep
  252. 09:12in the board. Yet by the end of the game
  253. 09:15it was this move that won Alph Go that
  254. 09:18second game. And so it was incredibly
  255. 09:20valuable that move. And this move has
  256. 09:22genuinely changed the way that humans
  257. 09:25play the game of go. You know, you could
  258. 09:27say, oh, is that exploratory creativity
  259. 09:29cuz it's just exploring the rules of the
  260. 09:30game. But I don't think so. I think you

  261. The local maximum problem

  262. 09:32could regard it as transformational
  263. 09:34creativity because we had certain ways
  264. 09:37that we thought were good to play the
  265. 09:39game. And Alph Go showed us you don't
  266. 09:42have to stick to that. You can break it
  267. 09:43and do something quite different. We
  268. 09:45thought we climbed a mountain peak and
  269. 09:47we we knew the top place [music] to play
  270. 09:50this game. But what the AI revealed is
  271. 09:52okay, that might be a high peak, but
  272. 09:54it's only what we mathematicians called
  273. 09:56a local maximum that there's actually a
  274. 09:58much higher peak if you go down the
  275. 10:00valley and up the mountain just across
  276. 10:02the valley. But we couldn't see that cuz
  277. 10:04it was surrounded by fog in our minds.
  278. 10:06And so Al Alph Go has led us to [music]
  279. 10:08a higher peak. Now you could say, but

  280. Why the credit belongs to the AI, not the coder

  281. 10:11hold on. Isn't that just the creativity
  282. 10:13of the coder who started coding Alph Go?
  283. 10:16No, I don't think so. Because this line
  284. 10:18of code that appeared, this strategy was
  285. 10:21not written in by a human. It grew out
  286. 10:24of the learning process of the code.
  287. 10:26[music] And I think if a human had seen
  288. 10:27that line of code, it probably would
  289. 10:29have deleted it thinking that um oh,
  290. 10:31Alph Go's got gone off in a bad
  291. 10:33direction. This is a bad sort of move
  292. 10:35play that [music] deep in. So I think
  293. 10:37that really that strategy, those lines
  294. 10:40of code play this deep in early on in
  295. 10:42the game grew out of the learning
  296. 10:44process of the code. So I think you
  297. 10:46should genuinely credit it to the AI and
  298. 10:51not the human. But Alph Go didn't want

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

  300. 10:54to play that game of go really wasn't
  301. 10:55interested. It was us who had the
  302. 10:58intention to get the thing to play
  303. 11:00[music] the game. AI we have to
  304. 11:02recognize is being created using a lot
  305. 11:05of statistics. It's a statistical model.
  306. 11:07What what's likely that means something
  307. 11:10like chat GBT you've got to recognize
  308. 11:12[music] it's really just generating text
  309. 11:14what's the most probable thing that will
  310. 11:16follow given my learning process. So it
  311. 11:18can show you that something happens but
  312. 11:21not the why. I'm not saying that it
  313. 11:23won't get to that stage but at the
  314. 11:24moment it will suddenly write a novel

  315. What Only Humans Can Do

  316. 11:26because it wants to tell you what it's
  317. 11:28like to be an AI. And that that
  318. 11:30intention to express itself will be I
  319. 11:32think an our first indication that you
  320. 11:35know oh maybe there is a ghost in the
  321. 11:37machine.
  322. 11:43You know we see AI being so successful
  323. 11:46we're beginning to wonder you know is
  324. 11:47there anything [clears throat] that it
  325. 11:49can't do? What is it that we can do that
  326. 11:51AI perhaps will always be limited by? It
  327. 11:55actually led to me writing one of my
  328. 11:57books. the book after I wrote about AI
  329. 11:59and creativity better thinking the art
  330. 12:01of the shortcut because I think that one
  331. 12:03of the things that humans are very good
  332. 12:06at is when they're faced with a problem
  333. 12:08we're actually quite a lazy species
  334. 12:10we're a bit like the lion that sits
  335. 12:12around all day in the savannah and then
  336. 12:14just does a short burst in order to
  337. 12:16capture its prey I think that's actually
  338. 12:18describes very much how we humans like
  339. 12:21to approach problems um and
  340. 12:23[clears throat] very often that leads to
  341. 12:25incredible innovation we're faced with a
  342. 12:27problem that just okay I can see how to
  343. 12:30do this by doing a huge amount of
  344. 12:32laborious donkey work but I don't want

  345. Gauss as a schoolboy, and the birth of the algorithm

  346. 12:35to do that and you sit back and you try
  347. 12:37and find you do some lateral thinking
  348. 12:38which is what humans are very good at
  349. 12:40and finding some sort of clever way
  350. 12:42around the problem that you're facing I
  351. 12:44think mathematics is developed out of
  352. 12:47that mentality I think my favorite
  353. 12:49example of lazy mind of the
  354. 12:52mathematician is one about one of my
  355. 12:54mathematical heroes Carl Friedri Gaus
  356. 12:56who when he was at school was asked to
  357. 12:58add up the numbers from 1 to 100. I
  358. 13:00think the teacher thought, "Oh, that'll
  359. 13:02keep them occupied for ages." Here's a
  360. 13:04good example of the dumb way. You you
  361. 13:06okay, you start with 1 + 2 that's 3 + 3
  362. 13:08is 6 + 4 is 10. That's going to take you
  363. 13:11forever. But Carrier Gaus, I mean, he
  364. 13:14was still, I think, 8 years old at the
  365. 13:16time. And he he said, "Hold on, there's
  366. 13:17a much clever way to do this. If you add
  367. 13:20the first and last number, 1 + 100 is
  368. 13:22101. 2 + 99 is 101. 3 + 98 is 101. Oh,
  369. 13:28great. So, there are 50 pairs of numbers
  370. 13:30adding up to 101. So, that means the
  371. 13:32answer is 5,050.
  372. 13:34That's was fast, efficient. It's a
  373. 13:37mentality that I can apply even if the
  374. 13:40teacher goes, okay, well, you got to do
  375. 13:411 to a million. The laborious way, you'd
  376. 13:44be there for days trying to do it. But
  377. 13:47that strategy can be applied however big
  378. 13:50the number is. And I think that's that's
  379. 13:51the real power. And in a way, we're
  380. 13:53starting [music] to see where computing
  381. 13:56emerges from because what you're doing
  382. 13:58is is creating an algorithm there.
  383. 14:00Doesn't matter what number you give me,
  384. 14:02this algorithm will give you the answer
  385. 14:04fast and efficiently and correctly.

  386. Why AI never bothers to find the shortcut

  387. 14:07Early coding is all about okay, you
  388. 14:09might have very many different numbers
  389. 14:11in this, but if they all working under
  390. 14:13the same rule set, so that's a real
  391. 14:15amazing shortcut. The challenge is would
  392. 14:17AI come up with these kind of shortcuts?
  393. 14:20Well, I don't think very often it will
  394. 14:22because it's got no problem about
  395. 14:24working incredibly hard, churning
  396. 14:26through a problem for hours. We run out
  397. 14:28of energy. The AI, it still doesn't mind
  398. 14:31doing things [music] the dumb way. But,
  399. 14:33you know, going forward that may change.
  400. 14:35It may be that um human [music] and AI
  401. 14:38together could well, it can go so much
  402. 14:40further because we combine our passion
  403. 14:42for the shortcut, the passion for hold
  404. 14:45on. Okay, you could do that the really
  405. 14:46long way, but let me introduce a
  406. 14:48shortcut. And then you you introduce
  407. 14:50that into the program and and then
  408. 14:52you've got an incredibly efficient
  409. 14:54combination of um the human and the
  410. 14:56machine. One of my central messages is
  411. 14:59to remember that artificial intelligence
  412. 15:02is not a competitor, it's a
  413. 15:05collaborator.