0:00:21.458,0:00:25.831 You can imagine: You're in a bar, [br]or, you know, a disco, 0:00:25.866,0:00:30.645 like that, and you start talking[br]to a girl, and after a while 0:00:30.680,0:00:34.213 this comes up in the conversation:[br]"and what do you do?" 0:00:34.248,0:00:42.045 And as you think your job is interesting[br]you say: "I'm a mathematician." (Laughter) 0:00:42.080,0:00:46.596 33.51 % of girls (Laughter) 0:00:46.631,0:00:52.142 in that moment pretend to get an[br]urgent call and leave. (Laughter) 0:00:52.177,0:01:00.340 And 64.69 % of girls desperately try[br]to change the topic and leave. (Laughter) 0:01:00.375,0:01:05.147 There's a 0.8 % made up by your cousin,[br]your girlfriend and your mother (Laughter) 0:01:05.183,0:01:09.626 that knows you work in something weird but[br]don't remember what (Laughter) 0:01:09.661,0:01:12.515 and there's a 1 % that[br]follows the conversation. 0:01:12.550,0:01:16.155 When that conversation[br]follows, invariably 0:01:16.190,0:01:18.560 in some moment, one of these[br]two phrases shows up: 0:01:18.595,0:01:22.065 A) "I was terrible at math,[br]but it wasn't my fault, 0:01:22.100,0:01:25.274 it's that the teacher[br]was horrendous." (Laughter) 0:01:25.309,0:01:29.253 And B) "But that math thing,[br]what is it for?" (Laughter) 0:01:29.288,0:01:33.289 I'll deal with case B. [br](Laughter) 0:01:33.324,0:01:36.875 When someone asks you what[br]math is for, 0:01:36.910,0:01:40.770 they're not asking you about the[br]applications of mathematical sciences. 0:01:40.805,0:01:43.264 They're asking you:[br]"And why did I have to study 0:01:43.299,0:01:46.272 that bullshit I never used[br]again in my life?" (Laughter) 0:01:46.307,0:01:48.959 That's what they're asking you really. 0:01:48.994,0:01:50.994 Given this, when they ask[br]a mathematician 0:01:51.029,0:01:54.914 what math is for, us[br]mathematicians split in two groups. 0:01:54.949,0:02:00.989 A 54.51 % of mathematicians[br]assumes an attacking posture, 0:02:01.024,0:02:06.109 and a 44.77 % of mathematicians[br]assumes a defensive posture. 0:02:06.144,0:02:09.788 There's a strange 0.8 %,[br]among which I include myself. 0:02:09.824,0:02:11.845 Who are the ones who attack? 0:02:11.880,0:02:14.966 The attacking ones are mathematicians[br]that tell you the question 0:02:15.001,0:02:19.197 makes no sense, because mathematics[br]have their own sense by themselves, 0:02:19.232,0:02:22.229 they're a beautiful edification with[br]its own logic built by itself 0:02:22.264,0:02:26.159 and that there's no use in one always[br]looking after the possible applications. 0:02:26.194,0:02:28.528 What's the use of poetry?[br]What's the use of love? 0:02:28.563,0:02:33.018 What's the use of life itself? [br]What kind of question is that? (Laughter) 0:02:33.053,0:02:37.311 Hardy, for example, is an[br]exponent of this attack. 0:02:37.346,0:02:38.602 And those who stand in [br]defense tell you that 0:02:38.637,0:02:45.068 even if you can't notice, dear,[br]math is behind everything. (Laughter) 0:02:45.103,0:02:50.993 They always name bridges[br]and computers, always. 0:02:51.028,0:02:55.079 If you don't know math,[br]your bridge falls off. (Laughter) 0:02:55.114,0:02:58.193 In reality computers[br]are all about math. 0:02:58.228,0:03:01.008 Now these guys always happen[br]to tell you that behind 0:03:01.043,0:03:05.600 information security and credit[br]cards are prime numbers. 0:03:05.635,0:03:09.989 These are the answers your math teacher[br]will give you if you ask him. 0:03:10.024,0:03:12.829 Those are the defensive ones. 0:03:12.864,0:03:14.389 Okay, but, who's right then? 0:03:14.424,0:03:16.760 Those who say math doesn't need[br]to be useful at all, 0:03:16.795,0:03:18.799 or those who say that it's really[br]behind everything? 0:03:18.834,0:03:21.330 In reality both are right. 0:03:21.365,0:03:25.475 But I told you I'm of that strange 0.8 %[br]that says something else, right? 0:03:25.510,0:03:29.329 So, go on, ask me[br]what math is for. 0:03:29.364,0:03:32.698 (Audience asks the question) 0:03:32.733,0:03:40.145 Okay! A 76.34 % of people[br]have asked, there's a 23.41 % 0:03:40.180,0:03:44.635 that shut up, and a 0.8 % that[br]I don't know what those guys are doing. 0:03:44.670,0:03:50.883 Well, dear 76.31 %, it's true[br]that math can be 0:03:50.918,0:03:54.605 useless, it's true that it's[br]a beautiful edification, 0:03:54.640,0:03:57.617 a logical one, one probably one of[br]the greatest collective efforts 0:03:57.652,0:04:00.303 the human being has ever made[br]along history. 0:04:00.338,0:04:04.165 But it's also true that there where[br]scientists, where technicians, 0:04:04.200,0:04:09.061 are looking for mathematical theories,[br]models that allow them to advance, 0:04:09.096,0:04:10.193 there they are, in the edification[br]of math, which permeate everything. 0:04:14.034,0:04:16.505 It's true that we have to go[br]somewhat deeper, 0:04:16.541,0:04:17.988 we're going to see what's[br]behind science. 0:04:18.024,0:04:22.288 Science works by intuition,[br]by creativity, and math 0:04:22.323,0:04:25.772 dominate intuition[br]and tame creativity. 0:04:25.807,0:04:30.415 Almost everyone who hasn't heard it before[br]is surprised by the fact that if one took 0:04:30.450,0:04:35.657 a sheet of paper 0.1 mm thick,[br]one of those we use normally, 0:04:35.692,0:04:39.075 big enough, and that I[br]could fold 50 times, 0:04:39.110,0:04:45.395 The thickness of that pile would take up[br]the distance from the Earth to the Sun. 0:04:45.430,0:04:50.196 Your intuition tells you: "Impossible."[br]Do the math and you'll see it's right. 0:04:50.231,0:04:51.845 That's what math is for. 0:04:51.880,0:04:56.067 It true that science, all science,[br]not only has a purpose 0:04:56.102,0:04:59.788 because it makes us understand better[br]the beautiful would we're in. 0:04:59.823,0:05:03.004 And because it does, it helps us[br]avoid the traps 0:05:03.039,0:05:04.799 of this painful world[br]we're in. 0:05:04.834,0:05:08.407 There are sciences that grasp[br]this very application. 0:05:08.442,0:05:10.003 Oncological science, for example. 0:05:10.038,0:05:13.495 And there are others we look[br]from afar, with some jealousy sometimes, 0:05:13.530,0:05:16.044 but knowing we are what supports them. 0:05:16.079,0:05:18.583 All the basic sciences[br]are the support of them, 0:05:18.618,0:05:21.359 and among these is math. 0:05:21.394,0:05:24.726 All that makes science be science[br]is the rigor of math. 0:05:24.761,0:05:29.572 And that rigor belongs to it[br]because its results are eternal. 0:05:29.607,0:05:32.037 Probably you said before,[br]or you were told sometime, 0:05:32.072,0:05:35.478 that diamonds are [br]forever, right? 0:05:35.513,0:05:38.892 It depends on what one[br]understands by forever! 0:05:38.927,0:05:42.569 A theorem, that really[br]is forever! (Laughter) 0:05:42.604,0:05:46.116 The Pythagorean theorem,[br]that is still true 0:05:46.151,0:05:49.221 even if Pythagoras is dead,[br]I'm telling you. (Laughter) 0:05:49.256,0:05:52.876 Even if the world collapsed the[br]Pythagorean theorem would still be true. 0:05:52.911,0:05:58.508 Wherever any two sides and a[br]good hypotenuse get together (Laughter) 0:05:58.543,0:06:08.574 the Pythagorean theorem works[br]to the max. (Applause) 0:06:08.609,0:06:11.997 Well, us mathematicians[br]devote ourselves to making theorems. 0:06:12.032,0:06:15.908 Eternal truths. But it isn't always[br]easy to know what is an 0:06:15.943,0:06:19.205 eternal truth, a theorem, and[br]what is a mere conjecture. 0:06:19.240,0:06:22.834 You need a demonstration. 0:06:22.869,0:06:28.949 For example: imagine you have[br]a big, enormous, infinite field. 0:06:28.984,0:06:32.702 I want to cover it with equal pieces,[br]without leaving any gaps. 0:06:32.737,0:06:34.836 I could use squares, right? 0:06:34.871,0:06:39.542 I could use triangles.[br]Not circles, those leave little gaps. 0:06:39.577,0:06:41.969 Which is the best piece I can use? 0:06:42.004,0:06:46.067 The one that to cover the same surface[br]has the smallest border. 0:06:46.102,0:06:51.056 Pappus of Alexandria, in the year 300[br]said the best was to use hexagons, 0:06:51.091,0:06:54.569 like bees do.[br]But he didn't demonstrate it! 0:06:54.604,0:06:57.538 The guy said "hexagons, great,[br]come on, hexagons, let's go with it!" 0:06:57.573,0:07:01.288 He didn't demonstrate it, he stayed[br]in a conjecture, he said "Hexagons!" 0:07:01.323,0:07:05.394 And the world, as you know, split into[br]pappists and anti-pappists, 0:07:05.429,0:07:11.195 until 1700 years later,[br]1700 years later, 0:07:11.230,0:07:17.212 in 1999 Thomas Hales[br]demonstrated that Pappus 0:07:17.247,0:07:21.321 and the bees were right,[br]the best was to use hexagons. 0:07:21.356,0:07:23.823 And that became a theorem,[br]the honeycomb theory, 0:07:23.858,0:07:25.993 that will be true forever[br]forever and ever, 0:07:26.028,0:07:29.224 for longer than any diamond[br]you may have. (Laughter) 0:07:29.259,0:07:31.683 But what happens if we go to 3 dimensions? 0:07:31.718,0:07:37.352 If I want to fill the space, with equal[br]pieces, without leaving any gaps, 0:07:37.387,0:07:38.998 I can use cubes, right? 0:07:39.033,0:07:43.019 Not spheres, those leave little gaps.[br](Laughter) 0:07:43.054,0:07:45.587 What is the best piece[br]I can use? 0:07:45.622,0:07:50.562 Lord Kelvin, the one of the Kelvin degrees[br]and all said, he said 0:07:50.597,0:07:58.139 that the best was to use a[br]truncated octahedron (Laughter) 0:07:58.174,0:08:09.069 that as you all know (Laughter)[br]is this thing over here! (Applause) 0:08:09.104,0:08:13.853 Come on! Who doesn't have a truncated[br]octahedron at home? (Laughter) 0:08:13.888,0:08:16.659 Even if it's plastic. Kid, bring[br]the truncated octahedron, we have guests. 0:08:16.694,0:08:21.243 Everybody has one! (Laughter)[br]But Kelvin didn't demonstrate it. 0:08:21.278,0:08:25.670 He stayed in a conjecture,[br]Kelvin's conjecture. 0:08:25.705,0:08:32.357 The world, as you know, split between[br]kelvinists and anti-kelvinists (Laughter) 0:08:32.392,0:08:38.823 until a hundred-and-something years later,[br]a hundred-and-something years later, 0:08:38.859,0:08:43.672 someone found a better structure. 0:08:43.707,0:08:48.626 Weaire and Phelan, Weaire and Phelan[br]found this little thing over here, 0:08:48.661,0:08:54.714 (Laughter) this structure they put the[br]imaginative name of 0:08:54.749,0:08:58.733 the Weaire-Phelan structure. (Laughter) 0:08:58.768,0:09:01.189 It seems like a strange thing[br]but it isn't that strange, 0:09:01.224,0:09:02.800 it's also present in nature. 0:09:02.835,0:09:07.399 It's very curious that this structure,[br]because of its geometric properties, 0:09:07.434,0:09:11.012 was used to build[br]the swimming building 0:09:11.047,0:09:13.824 in the Beijing Olympic Games. 0:09:13.859,0:09:17.089 There Michael Phelps won[br]8 gold medals, and became 0:09:17.124,0:09:19.645 the best swimmer of all times. 0:09:19.680,0:09:23.036 Well, of all times[br]until someone better comes along, no? 0:09:23.071,0:09:25.666 As it happens to the[br]Weaire-Phelan structure, 0:09:25.701,0:09:28.473 it's the best until something better[br]shows up. 0:09:28.508,0:09:32.645 But be careful, because this one[br]really has the opportunity, 0:09:32.680,0:09:37.775 that if a hundred-and-something years[br]pass, even if it's in 1700 years, 0:09:37.810,0:09:43.603 someone demonstrates that this[br]is the best piece possible. 0:09:43.638,0:09:47.898 And then it will be a theorem,[br]a truth forever, forever and ever. 0:09:47.933,0:09:51.552 For longer than any diamond. 0:09:51.587,0:09:59.835 So, well, if you want to tell someone[br]you'll love them forever (Laughter) 0:09:59.870,0:10:02.289 you can give them a diamond,[br]but if you want to tell them 0:10:02.324,0:10:07.933 that you'll love them forever and ever,[br]give them a theorem! (Laughter) 0:10:07.968,0:10:13.126 However, you'll have to demonstrate, 0:10:13.161,0:10:16.105 that your love doesn't stay a conjecture. 0:10:16.140,0:10:19.963 (Applause) 0:10:21.998,0:10:24.875 Thank you.