0:00:01.458,0:00:06.260 Imagine you're in a bar, or a club, 0:00:06.910,0:00:09.591 and you start talking to a girl, 0:00:09.951,0:00:14.542 and after a while this question come up:[br]"So, what do you do for work?" 0:00:14.553,0:00:17.867 And since you think[br]your job is interesting you say: 0:00:17.867,0:00:19.706 "I'm a mathematician." 0:00:19.706,0:00:21.725 (Laughter) 0:00:22.355,0:00:25.617 33.51 % of girls, 0:00:25.617,0:00:26.889 (Laughter) 0:00:26.889,0:00:30.772 in that moment, pretend[br]to get an urgent call and leave. 0:00:30.772,0:00:32.495 (Laughter) 0:00:32.495,0:00:35.806 And 64.69 % of girls 0:00:36.266,0:00:40.077 desperately try to change the topic and leave. 0:00:40.077,0:00:41.269 (Laughter) 0:00:41.269,0:00:44.494 There's 0.8 % made up by your cousin,[br]your girlfriend and your mother, 0:00:44.494,0:00:45.629 (Laughter) 0:00:45.629,0:00:49.694 who know that you work in something weird[br]but don't remember what it is. (Laughter) 0:00:49.694,0:00:52.815 And there is 1 %[br]that actually follows the conversation. 0:00:52.815,0:00:55.080 When that conversation happens, 0:00:55.080,0:00:59.230 at some point, invariably,[br]one of these two phrases come up: 0:00:59.230,0:01:02.575 A: "I was terrible at math,[br]but it wasn't my fault, 0:01:02.575,0:01:05.614 it's that the teacher[br]was horrendous." (Laughter) 0:01:05.614,0:01:08.582 And B: "But what is math really for?" 0:01:08.582,0:01:09.930 (Laughter) 0:01:09.930,0:01:11.955 I'll deal with case B. 0:01:11.955,0:01:13.680 (Laughter) 0:01:13.680,0:01:18.484 When someone asks you what math is for,[br]they're not asking you 0:01:18.484,0:01:21.203 about the application[br]of mathematical science. 0:01:21.203,0:01:22.734 They're asking you: 0:01:22.734,0:01:26.915 "Why did I have to study that bullshit[br]I never used in my life again?" (Laughter) 0:01:26.915,0:01:28.959 That's what they're actually asking. 0:01:28.994,0:01:33.124 So when mathematicians are asked[br]what math is for, 0:01:33.124,0:01:35.404 they tend to split into two groups. 0:01:35.404,0:01:40.739 54.51 % of mathematicians[br]will assume an attacking posture, 0:01:41.609,0:01:46.559 and 44.77 % of mathematicians[br]will take a defensive posture. 0:01:46.559,0:01:50.068 There's a strange 0.8 %,[br]among which I include myself. 0:01:50.068,0:01:52.155 Who are the ones that attack? 0:01:52.155,0:01:54.902 The attacking ones are mathematicians[br]who would tell you: 0:01:54.902,0:01:56.849 "This question makes no sense, 0:01:56.849,0:01:59.597 because mathematics[br]have a meaning on their own-- 0:01:59.597,0:02:02.144 a beautiful edifice with its own logic-- 0:02:02.144,0:02:04.011 and that there's no point 0:02:04.011,0:02:06.688 in constantly searching[br]for all possible applications. 0:02:06.688,0:02:08.847 What's the use of poetry?[br]What's the use of love? 0:02:08.847,0:02:11.908 What's the use of life itself? [br]What kind of question is that?" 0:02:11.908,0:02:13.529 (Laughter) 0:02:13.529,0:02:17.296 Hardy, for instance, is a prime example[br]for this type of attack. 0:02:17.296,0:02:19.652 And those who stand in defense tell you: 0:02:19.652,0:02:24.082 "Even if you don't notice it, buddy,[br]math is behind everything." 0:02:24.082,0:02:25.562 (Laughter) 0:02:25.562,0:02:27.724 They always-- 0:02:27.724,0:02:31.666 always name bridges and computers. 0:02:31.666,0:02:34.041 "If you don't know math,[br]your bridge falls off." 0:02:34.041,0:02:35.566 (Laughter) 0:02:35.566,0:02:38.523 In reality, computers are all about math. 0:02:38.523,0:02:41.008 Now, these guys always happen to tell you 0:02:41.043,0:02:46.050 that behind information security[br]and credit cards are prime numbers. 0:02:46.710,0:02:50.379 These are the answers your math teacher[br]would give you if you asked him-- 0:02:50.379,0:02:52.544 the defensive ones. 0:02:52.544,0:02:54.389 Okay, but, who's right then? 0:02:54.404,0:02:56.990 Those who say math[br]doesn't need to be useful at all, 0:02:56.990,0:02:59.849 or those who say[br]that it's really behind everything? 0:02:59.849,0:03:01.520 Actually, both are right. 0:03:01.520,0:03:03.183 But remember I told you 0:03:03.183,0:03:06.726 I belong to that strange 0.8 %[br]claiming something else. 0:03:06.726,0:03:09.929 So, go ahead, ask me what math is for. 0:03:09.929,0:03:12.858 Audience: What is math for? 0:03:12.858,0:03:17.183 Okay, so 76.34 % of you[br]asked the question, 0:03:17.783,0:03:20.720 23.41 % didn't say anything, 0:03:20.720,0:03:22.127 and 0.8 %-- 0:03:22.127,0:03:24.675 not sure what those guys were doing. 0:03:24.675,0:03:26.985 Well, dear 76.31 % 0:03:29.035,0:03:32.815 it's true that math can be useless, 0:03:32.815,0:03:35.685 it's true that it's[br]a beautiful edification, a logical one, 0:03:35.685,0:03:38.537 probably one[br]of the greatest collective effort 0:03:38.537,0:03:40.633 the human race[br]has ever achieved in history. 0:03:40.633,0:03:42.732 But it's also true that there, 0:03:42.732,0:03:47.331 where scientists and technicians[br]are looking for mathematical theories 0:03:47.331,0:03:49.641 that allow them to advance, 0:03:49.641,0:03:53.708 they are in the edification of math,[br]which permeates everything. 0:03:53.708,0:03:56.585 It's true that we have to go[br]somewhat deeper, 0:03:56.585,0:03:58.308 to see what's behind science. 0:03:58.308,0:04:01.858 Science is based on intuition, creativity. 0:04:02.348,0:04:05.772 Math dominates intuition[br]and tames creativity. 0:04:06.747,0:04:09.437 Almost every person[br]who hasn't heard this before 0:04:09.437,0:04:11.647 is surprised when they hear 0:04:11.647,0:04:16.187 that a 0.1 mm thick sheet of paper--[br]one that we normally use-- 0:04:16.187,0:04:19.505 is big enough, that if you fold 50 times, 0:04:19.505,0:04:25.205 the thickness of that pile would take up[br]the distance from the Earth to the Sun. 0:04:25.600,0:04:28.201 Your intuition tells you it's impossible. 0:04:28.201,0:04:30.622 Do the math and you'll see it's right. 0:04:30.622,0:04:33.135 That's what math is for. 0:04:33.135,0:04:36.917 It's true that the main purpose[br]of science, of all types of science, 0:04:36.917,0:04:40.288 is to make us better understand[br]the beautiful world we live in. 0:04:40.288,0:04:41.669 And because it does so, 0:04:41.669,0:04:45.179 it can help us avoid the traps[br]of this painful world we live in. 0:04:45.179,0:04:48.657 There are sciences[br]that grasp this very application. 0:04:48.657,0:04:50.413 Oncological science, for example. 0:04:50.413,0:04:53.905 And there are others we look at from afar,[br]with jealousy sometimes, 0:04:53.905,0:04:56.464 but knowing we are what supports them. 0:04:56.464,0:04:59.213 All the basic sciences[br]are the support of them, 0:04:59.213,0:05:01.649 and among these is math. 0:05:01.649,0:05:05.366 All that makes science, science,[br]is the rigor of math. 0:05:05.366,0:05:10.062 And that rigor belongs to it[br]because the results are eternal. 0:05:10.062,0:05:12.757 You probably said or were told[br]at some point, 0:05:12.757,0:05:15.708 that diamonds are forever, right? 0:05:17.178,0:05:19.392 It depends on[br]what you understand by "forever"! 0:05:19.392,0:05:21.883 A theorem-- that really is forever! 0:05:21.883,0:05:23.134 (Laughter) 0:05:23.134,0:05:26.486 The Pythagorean theorem is still true 0:05:26.486,0:05:29.431 even though Pythagoras is dead,[br]I'm telling you. (Laughter) 0:05:29.431,0:05:30.946 Even if the world collapsed 0:05:30.946,0:05:33.391 the Pythagorean theorem[br]would still be true. 0:05:33.391,0:05:37.452 Wherever any two sides[br]and a good hypotenuse get together 0:05:37.452,0:05:38.673 (Laughter) 0:05:38.673,0:05:41.364 the Pythagorean theorem[br]works at its the max. 0:05:41.364,0:05:44.355 (Applause) 0:05:48.785,0:05:52.407 Well, us mathematicians devote ourselves[br]to come up with theorems. 0:05:52.407,0:05:54.143 Eternal truths. 0:05:54.143,0:05:58.139 But it isn't always easy to know[br]what an eternal truth, a theorem, is 0:05:58.139,0:06:00.045 compared to a mere conjecture. 0:06:00.045,0:06:02.834 You need demonstration. 0:06:02.869,0:06:04.596 For example, 0:06:04.596,0:06:09.423 imagine you have a big,[br]enormous, infinite field. 0:06:09.423,0:06:13.132 I want to cover it with equal pieces,[br]without leaving any gaps. 0:06:13.132,0:06:15.256 I could use squares, right? 0:06:15.256,0:06:19.222 I could use triangles.[br]Not circles, those leave little gaps. 0:06:19.777,0:06:22.004 Which is the best piece I can use? 0:06:22.004,0:06:26.687 The one that covers the same surface[br]has the smallest border. 0:06:26.687,0:06:31.396 In the year 300, Pappus of Alexandria[br]said the best is to use hexagons, 0:06:31.396,0:06:33.243 just like bees do. 0:06:33.243,0:06:34.990 But he didn't demonstrate it. 0:06:34.990,0:06:37.688 The guy said, "Hexagons, great![br]Let's go with hexagons!" 0:06:37.688,0:06:40.656 He didn't demonstrate it,[br]he stayed in a conjecture. 0:06:40.656,0:06:42.334 "Hexagons!" 0:06:42.334,0:06:45.964 And the world, as you know,[br]split into pappists and anti-pappists, 0:06:45.964,0:06:49.713 until 1700 years later-- 0:06:49.713,0:06:51.892 1700 years later-- 0:06:51.892,0:06:56.497 in 1999 Thomas Hales demonstrated 0:06:57.047,0:07:02.001 that Pappus and the bees were right,[br]the best was to use hexagons. 0:07:02.001,0:07:03.823 And that became a theorem,[br]the honeycomb theory, 0:07:03.858,0:07:05.993 that will be true forever[br]forever and ever, 0:07:06.028,0:07:09.224 for longer than any diamond[br]you may have. (Laughter) 0:07:09.259,0:07:11.683 But what happens if we go to 3 dimensions? 0:07:11.718,0:07:17.352 If I want to fill the space, with equal[br]pieces, without leaving any gaps, 0:07:17.387,0:07:18.998 I can use cubes, right? 0:07:19.033,0:07:23.019 Not spheres, those leave little gaps.[br](Laughter) 0:07:23.054,0:07:25.587 What is the best piece[br]I can use? 0:07:25.622,0:07:30.562 Lord Kelvin, the one of the Kelvin degrees[br]and all said, he said 0:07:30.597,0:07:38.139 that the best was to use a[br]truncated octahedron (Laughter) 0:07:38.174,0:07:49.069 that as you all know (Laughter)[br]is this thing over here! (Applause) 0:07:49.104,0:07:53.853 Come on! Who doesn't have a truncated[br]octahedron at home? (Laughter) 0:07:53.888,0:07:56.659 Even if it's plastic. Kid, bring[br]the truncated octahedron, we have guests. 0:07:56.694,0:08:01.243 Everybody has one! (Laughter)[br]But Kelvin didn't demonstrate it. 0:08:01.278,0:08:05.670 He stayed in a conjecture,[br]Kelvin's conjecture. 0:08:05.705,0:08:12.357 The world, as you know, split between[br]kelvinists and anti-kelvinists (Laughter) 0:08:12.392,0:08:18.823 until a hundred-and-something years later,[br]a hundred-and-something years later, 0:08:18.859,0:08:23.672 someone found a better structure. 0:08:23.707,0:08:28.626 Weaire and Phelan, Weaire and Phelan[br]found this little thing over here, 0:08:28.661,0:08:34.714 (Laughter) this structure they put the[br]imaginative name of 0:08:34.749,0:08:38.732 the Weaire-Phelan structure. (Laughter) 0:08:38.768,0:08:41.188 It seems like a strange thing[br]but it isn't that strange, 0:08:41.224,0:08:42.799 it's also present in nature. 0:08:42.835,0:08:47.399 It's very curious that this structure,[br]because of its geometric properties, 0:08:47.434,0:08:51.012 was used to build[br]the swimming building 0:08:51.047,0:08:53.824 in the Beijing Olympic Games. 0:08:53.859,0:08:57.089 There Michael Phelps won[br]8 gold medals, and became 0:08:57.124,0:08:59.645 the best swimmer of all times. 0:08:59.680,0:09:03.036 Well, of all times[br]until someone better comes along, no? 0:09:03.071,0:09:05.666 As it happens to the[br]Weaire-Phelan structure, 0:09:05.701,0:09:08.473 it's the best until something better[br]shows up. 0:09:08.508,0:09:12.645 But be careful, because this one[br]really has the opportunity, 0:09:12.680,0:09:17.775 that if a hundred-and-something years[br]pass, even if it's in 1700 years, 0:09:17.810,0:09:23.603 someone demonstrates that this[br]is the best piece possible. 0:09:23.638,0:09:27.898 And then it will be a theorem,[br]a truth forever, forever and ever. 0:09:27.933,0:09:31.552 For longer than any diamond. 0:09:31.587,0:09:39.835 So, well, if you want to tell someone[br]you'll love them forever (Laughter) 0:09:39.870,0:09:42.289 you can give them a diamond,[br]but if you want to tell them 0:09:42.324,0:09:47.933 that you'll love them forever and ever,[br]give them a theorem! (Laughter) 0:09:47.968,0:09:53.126 However, you'll have to demonstrate, 0:09:53.161,0:09:56.105 that your love doesn't stay a conjecture. 0:09:56.140,0:09:59.963 (Applause) 0:10:01.998,0:10:04.875 Thank you.