1 00:00:11,040 --> 00:00:12,640 SCIENCE TODAY 2 00:00:12,800 --> 00:00:16,520 You probably wondered why you had to do math 3 00:00:16,680 --> 00:00:19,280 back in the classroom. 4 00:00:19,440 --> 00:00:22,240 On top of it, you thought it was pure boredom. 5 00:00:22,400 --> 00:00:27,280 Well, tonight we're going to try to interest you... 6 00:01:44,760 --> 00:01:48,840 HOW I CAME TO HATE MATH 7 00:02:20,480 --> 00:02:22,600 This is a math nerd. 8 00:02:23,000 --> 00:02:25,320 - A what? - A math nerd. 9 00:02:25,759 --> 00:02:26,759 Too much! 10 00:02:26,760 --> 00:02:28,320 Facebook... What's his name? 11 00:02:29,040 --> 00:02:30,120 Mark Zuckerberg. 12 00:02:30,280 --> 00:02:33,640 In the film it's clear he's weird. He's autistic. 13 00:02:33,800 --> 00:02:35,760 No way! 14 00:02:35,920 --> 00:02:38,040 He just doesn't care about money! 15 00:02:38,200 --> 00:02:41,600 He created Facebook because he's a pro at math, 16 00:02:41,760 --> 00:02:44,880 but is that all he's got on the brain? 17 00:03:09,400 --> 00:03:10,640 C minus... 18 00:03:11,120 --> 00:03:13,720 C, F... 19 00:03:14,120 --> 00:03:15,120 B minus. 20 00:03:15,400 --> 00:03:18,000 Once bad at math always bad at math. 21 00:03:18,160 --> 00:03:19,200 That's for sure! 22 00:03:19,360 --> 00:03:21,160 It's fate. 23 00:03:21,320 --> 00:03:22,600 It's destiny. 24 00:03:22,760 --> 00:03:25,000 Too much value is placed on math. 25 00:03:25,320 --> 00:03:27,600 Parents think it's all-important. 26 00:03:27,760 --> 00:03:29,760 So when kids don't get it, 27 00:03:29,920 --> 00:03:31,440 they think they're dumb. 28 00:03:31,600 --> 00:03:34,720 They get frustrated, feel stuck, 29 00:03:34,880 --> 00:03:36,040 and give up. 30 00:04:32,560 --> 00:04:35,360 A mathematician, as considered by most, 31 00:04:35,520 --> 00:04:38,120 has no imagination. 32 00:04:38,360 --> 00:04:41,040 His thoughts parch the heart. 33 00:04:42,560 --> 00:04:44,040 And he... 34 00:04:44,200 --> 00:04:47,800 Following a line of thought developed in the 18th century, 35 00:04:48,040 --> 00:04:49,240 he's not sensitive. 36 00:04:49,400 --> 00:04:51,400 Take a round of cheese. 37 00:04:51,600 --> 00:04:54,360 You examine its shape, its aroma, etc. 38 00:04:55,040 --> 00:04:58,080 A mathematician is only interested in its shape. 39 00:04:58,240 --> 00:04:59,880 He doesn't see the cheese, 40 00:05:00,040 --> 00:05:02,440 just its circular shape, nothing else. 41 00:05:03,080 --> 00:05:05,720 This extracting parts from reality 42 00:05:06,480 --> 00:05:09,960 is what the mathematician is criticized for. 43 00:05:10,200 --> 00:05:12,240 He doesn't live in the real world. 44 00:05:12,400 --> 00:05:14,240 He's not only useless, 45 00:05:14,400 --> 00:05:16,560 it's worse. 46 00:05:16,720 --> 00:05:20,000 He literally kills reality. By carving it up, 47 00:05:20,880 --> 00:05:22,720 he destroys the world. 48 00:05:22,880 --> 00:05:24,840 Math is the science of death. 49 00:05:25,000 --> 00:05:27,320 Mathematics is serious. It's exact. 50 00:05:27,480 --> 00:05:29,640 It's scientific. It's explicit. 51 00:05:30,000 --> 00:05:31,040 It's frightening. 52 00:05:31,200 --> 00:05:33,720 People make light of it. 53 00:05:33,880 --> 00:05:35,000 They say, 54 00:05:36,200 --> 00:05:39,640 "I might be bad at math, but I'm still cool." 55 00:05:39,800 --> 00:05:43,680 It's amazing how many claim they were last in math. 56 00:05:43,840 --> 00:05:46,080 How could so many be last? 57 00:06:32,400 --> 00:06:36,840 Mathematics is rigorous but also creative. 58 00:06:37,360 --> 00:06:39,880 It's abstract but universal. 59 00:06:40,040 --> 00:06:43,000 It's inegalitarian and democratic. 60 00:06:43,240 --> 00:06:45,360 It's ancient yet always evolving. 61 00:06:45,520 --> 00:06:48,480 It's solitary and collective at once. 62 00:06:48,880 --> 00:06:51,520 It's difficult and super easy. 63 00:06:51,920 --> 00:06:54,600 The words on the left are pretty grim. 64 00:06:54,760 --> 00:06:56,080 Rigorous, abstract, inegalitarian, 65 00:06:56,240 --> 00:06:58,120 ancient, solitary, difficult. 66 00:06:58,280 --> 00:07:01,160 But then there's creative, universal, democratic, 67 00:07:01,320 --> 00:07:04,240 constantly evolving, collective, super easy. 68 00:07:04,880 --> 00:07:06,280 That's way more sexy! 69 00:07:06,440 --> 00:07:08,800 It's still full of pins. 70 00:07:09,360 --> 00:07:11,120 The Queen of Hearts. 71 00:07:12,400 --> 00:07:13,880 It's missing the sleeves. 72 00:07:14,040 --> 00:07:17,200 I love the creative aspect of sewing, 73 00:07:17,360 --> 00:07:20,920 making shapes and playing with them. 74 00:07:21,080 --> 00:07:22,960 It does require a lot of math. 75 00:07:23,120 --> 00:07:25,320 Not that I do it for the math... 76 00:07:26,920 --> 00:07:30,080 but you do have to deal with things like curvature. 77 00:07:30,440 --> 00:07:33,520 For example, I sew for myself, 78 00:07:33,680 --> 00:07:36,400 and I'm not shaped the same as my daughter. 79 00:07:37,640 --> 00:07:40,920 It creates new geometric problems 80 00:07:41,080 --> 00:07:42,760 and it's fun. 81 00:07:45,840 --> 00:07:49,480 Professor of Mathematics 82 00:07:55,800 --> 00:07:58,520 I was called Mr. Math as a kid. 83 00:07:58,680 --> 00:08:01,040 It did go a bit to my head. 84 00:08:01,200 --> 00:08:04,600 I drew graffiti on the walls of the bathroom at home. 85 00:08:05,600 --> 00:08:07,880 Cubic equations and such. 86 00:08:08,040 --> 00:08:09,960 Curious graffiti, for sure. 87 00:08:10,120 --> 00:08:13,280 But they fascinated me. I couldn't solve them. 88 00:08:13,440 --> 00:08:16,320 I asked my teacher to help me 89 00:08:16,480 --> 00:08:17,800 and she never would. 90 00:08:17,960 --> 00:08:21,840 But she did ask me to help her teach the others. 91 00:08:22,000 --> 00:08:24,600 That's when I realized I understood it. 92 00:08:24,760 --> 00:08:26,720 It was easy for me. 93 00:08:26,880 --> 00:08:29,200 That's the way it was. 94 00:08:29,360 --> 00:08:32,320 It was all there, clear as a bell. 95 00:08:32,480 --> 00:08:34,560 But my classmates were lost. 96 00:08:34,720 --> 00:08:38,280 They couldn't visualize objects. Nothing made sense. 97 00:08:38,440 --> 00:08:42,600 They couldn't draw analogies. They had no points of reference. 98 00:08:42,760 --> 00:08:45,120 So trying to come up with images 99 00:08:45,280 --> 00:08:49,520 to explain, demonstrate, help them understand wasn't easy. 100 00:08:49,680 --> 00:08:51,000 I never managed. 101 00:08:51,560 --> 00:08:55,080 It did teach me a lot about life though. 102 00:08:55,360 --> 00:08:57,600 I understood that all of it was hard. 103 00:08:57,960 --> 00:09:02,640 The challenge of knowledge, the challenge of math 104 00:09:02,800 --> 00:09:04,960 is being able to convey and share it. 105 00:09:18,280 --> 00:09:19,880 What a musical entrance... 106 00:09:20,040 --> 00:09:21,040 Not bad, huh? 107 00:09:21,440 --> 00:09:22,440 Hi there! 108 00:09:23,920 --> 00:09:25,920 Advanced Math Class 109 00:09:29,440 --> 00:09:32,160 Like this? Usually a hat is worn... 110 00:09:32,320 --> 00:09:37,040 There's an axis, an ellipse, which takes us back to the subject. 111 00:09:37,200 --> 00:09:39,960 It has two symmetrical axes, a long and a short. 112 00:09:40,120 --> 00:09:42,760 As a rule the long axis of the head 113 00:09:42,920 --> 00:09:45,000 goes in this direction. 114 00:09:45,920 --> 00:09:48,480 We need to remember that mathematics 115 00:09:48,640 --> 00:09:52,040 isn't a single truth or a perfect object 116 00:09:52,600 --> 00:09:55,920 that everyone will fathom or discover in the same manner. 117 00:09:56,640 --> 00:09:58,800 It has a plural meaning. 118 00:09:58,960 --> 00:10:01,680 Each person will interpret it differently. 119 00:10:01,840 --> 00:10:04,080 Okay, 1+1 = 2. 120 00:10:04,240 --> 00:10:07,440 But when you say, 1+1 = 2, what's essential? 121 00:10:07,600 --> 00:10:10,480 The result, the addition, or the 1? 122 00:10:10,640 --> 00:10:12,760 What do I have to do to get 2? 123 00:10:16,320 --> 00:10:19,160 It's difficult to come up with good images, 124 00:10:19,320 --> 00:10:20,560 several images, 125 00:10:21,600 --> 00:10:25,280 so that everyone can relate. 126 00:10:25,520 --> 00:10:28,240 A smile, a grimace. 127 00:10:28,440 --> 00:10:30,240 A smile, and zero. 128 00:10:30,680 --> 00:10:33,040 - Minus 1. - For me, it's zero. 129 00:10:33,200 --> 00:10:34,840 From the top. 130 00:10:35,000 --> 00:10:36,040 One... 131 00:10:37,200 --> 00:10:39,160 one smile, and back at the start. 132 00:10:40,720 --> 00:10:43,720 If we unfold it, it has to be zero... 133 00:10:43,880 --> 00:10:45,960 Don't you see it here? 134 00:10:46,120 --> 00:10:47,960 It's because if here 135 00:10:48,120 --> 00:10:50,360 we continue on, we end up with another. 136 00:10:51,040 --> 00:10:53,560 So it's the same thing above 137 00:10:53,720 --> 00:10:56,680 except the corner is hiding it. 138 00:10:58,760 --> 00:11:01,600 Down below it's there twice. 139 00:11:05,960 --> 00:11:07,680 It counts as one. 140 00:11:07,840 --> 00:11:08,960 And why? 141 00:11:09,120 --> 00:11:12,040 Because what counts isn't necessarily 142 00:11:12,600 --> 00:11:13,640 wthe corner. 143 00:11:13,800 --> 00:11:16,080 You have to make the corners round. 144 00:11:16,240 --> 00:11:18,240 The curve has to be smooth. 145 00:11:18,400 --> 00:11:20,600 Let's start again. One, 146 00:11:20,919 --> 00:11:21,919 two... 147 00:11:21,920 --> 00:11:24,680 Math speaks deeply to who we are. 148 00:11:25,760 --> 00:11:28,960 Words like axis, root, complex number, 149 00:11:29,120 --> 00:11:31,080 imaginary number, negative, 150 00:11:31,440 --> 00:11:32,800 division 151 00:11:32,960 --> 00:11:36,200 also relate to our personal lives. 152 00:11:37,560 --> 00:11:39,880 Okay, no problem. 153 00:11:40,200 --> 00:11:41,200 Bye. 154 00:11:41,360 --> 00:11:42,720 See you Friday. 155 00:11:43,920 --> 00:11:46,000 Bell, you're a sweetie, but stop... 156 00:11:46,320 --> 00:11:49,360 Educational Psychologist in Mathematics 157 00:11:49,640 --> 00:11:52,560 Take a kid who's intelligent, clever, 158 00:11:52,720 --> 00:11:56,480 too smart sometimes for his own good. 159 00:11:56,640 --> 00:11:59,280 When he starts doing math 160 00:11:59,440 --> 00:12:01,560 he suddenly becomes dumb. 161 00:12:01,720 --> 00:12:05,680 It's so hard, it's utterly exhausting. 162 00:12:05,880 --> 00:12:09,160 Then he closes his book and is suddenly full of pep. 163 00:12:09,400 --> 00:12:13,480 It's because doing math demands enormous energy. 164 00:12:13,640 --> 00:12:17,680 In one of his books, a French author wrote, 165 00:12:17,840 --> 00:12:20,600 "I spent two hours not doing my math." 166 00:12:20,760 --> 00:12:24,680 The time spent not doing math is exhausting. 167 00:12:24,840 --> 00:12:28,960 The anxiety of opening your book and not understanding anything. 168 00:12:29,120 --> 00:12:31,600 Feeling that you never will. 169 00:12:31,760 --> 00:12:33,760 Not knowing where to start. The test. 170 00:12:33,920 --> 00:12:38,040 It's terrorizing and completely draining. 171 00:12:38,440 --> 00:12:40,680 Math is risky business. 172 00:12:40,840 --> 00:12:43,480 You try to understand, knowing you might fail. 173 00:12:43,640 --> 00:12:46,600 At first, you struggle at it for hours. 174 00:12:47,200 --> 00:12:49,640 Getting it wrong has its reward. 175 00:12:50,320 --> 00:12:53,200 It's the beginning of an idea. You're reasoning. 176 00:12:54,000 --> 00:12:56,720 It's a real adventure, the adventure of math. 177 00:13:00,200 --> 00:13:01,800 The adventure is what comes. 178 00:13:01,960 --> 00:13:04,800 The real work is turning what comes 179 00:13:04,960 --> 00:13:07,880 into something interesting, alive, enriching, 180 00:13:08,040 --> 00:13:09,720 whether it's right or wrong. 181 00:13:18,200 --> 00:13:20,600 So am I a humanoid? 182 00:13:20,760 --> 00:13:22,440 Am I a scientist? 183 00:13:23,720 --> 00:13:25,000 A biologist? 184 00:13:25,160 --> 00:13:26,720 Did I live in New York? 185 00:13:28,200 --> 00:13:29,560 In the 21st century? 186 00:13:30,120 --> 00:13:31,920 Am I Marie Curie? 187 00:13:33,400 --> 00:13:34,520 Not the 20th. 188 00:13:42,640 --> 00:13:44,440 Just one loop on the... 189 00:13:44,840 --> 00:13:46,800 You can do A-C-B like this. 190 00:13:46,960 --> 00:13:50,200 A, C then back to B. 191 00:13:50,360 --> 00:13:51,640 No, it's not B-¹. 192 00:13:51,800 --> 00:13:52,920 That's a C. 193 00:13:53,080 --> 00:13:55,280 This is C-¹, and it goes here. 194 00:13:55,440 --> 00:13:56,800 That's what I did. 195 00:13:57,160 --> 00:13:58,840 - There? - It doesn't work. 196 00:13:59,000 --> 00:14:01,920 In math, you have nothing to lean on. 197 00:14:02,080 --> 00:14:03,640 When you study literature 198 00:14:03,800 --> 00:14:04,880 you have a novel. 199 00:14:05,040 --> 00:14:07,960 The teacher vanishes behind "The Red and the Black." 200 00:14:08,800 --> 00:14:13,760 In math, theorems are difficult to grasp. They're evanescent. 201 00:14:14,760 --> 00:14:17,880 Your math teacher is the incarnation 202 00:14:18,040 --> 00:14:19,880 of mathematics. 203 00:14:20,160 --> 00:14:22,840 I see lots of kids in grade school 204 00:14:24,040 --> 00:14:27,320 who try to add. 3+2... 205 00:14:28,720 --> 00:14:31,640 I watch them finger counting. 206 00:14:31,800 --> 00:14:35,120 They try not to show it. They aren't supposed to. 207 00:14:36,000 --> 00:14:37,600 It's really too bad. 208 00:14:37,760 --> 00:14:42,480 They should use their hands and bodies as support, 209 00:14:42,640 --> 00:14:45,880 even right through high school. 210 00:14:46,040 --> 00:14:48,560 An inflection point is like a toboggan. 211 00:14:48,720 --> 00:14:53,240 A toboggan at first goes increasingly faster. 212 00:14:53,400 --> 00:14:56,320 It gets steeper. It continues the descent, 213 00:14:56,480 --> 00:15:00,120 but towards a much gentler slope. 214 00:15:01,200 --> 00:15:04,520 The moment it stops accelerating 215 00:15:04,680 --> 00:15:06,240 and starts to slow down 216 00:15:06,400 --> 00:15:08,640 is what we call the inflection point. 217 00:15:09,240 --> 00:15:13,400 Then there's a definition based on the second derivative. 218 00:15:13,560 --> 00:15:18,040 But if your body remembers the sensation of riding a toboggan, 219 00:15:18,200 --> 00:15:21,120 the second derivative is easy as Pi. 220 00:15:21,480 --> 00:15:24,000 Each mathematical notion 221 00:15:24,240 --> 00:15:28,520 can be related to a physical experience. 222 00:15:44,280 --> 00:15:45,720 - Goin' well? - Yeah. 223 00:15:48,400 --> 00:15:51,880 The beauty of mathematics lies in those sweet moments 224 00:15:52,040 --> 00:15:53,480 when I suddenly get it. 225 00:15:53,640 --> 00:15:55,840 Now I have the words. 226 00:15:56,000 --> 00:15:58,800 You more or less always understood. 227 00:15:58,960 --> 00:16:03,000 But the road was just so tortuous, you ran out of breath. 228 00:16:03,160 --> 00:16:05,680 It's like climbing a steep mountain face 229 00:16:05,840 --> 00:16:10,120 only to realize how close you are to your starting point. 230 00:16:10,280 --> 00:16:13,560 It's the moment you discover there was a straight path. 231 00:16:13,720 --> 00:16:16,480 Now you can express it. You can convey it. 232 00:16:16,640 --> 00:16:18,800 You can explain it so others understand. 233 00:16:18,960 --> 00:16:20,640 It's an awesome moment. 234 00:16:20,800 --> 00:16:22,800 The beauty of math is that moment 235 00:16:22,960 --> 00:16:26,920 when the words used to describe it flow naturally. 236 00:16:46,120 --> 00:16:49,600 26th International Congress of Mathematicians 237 00:19:38,160 --> 00:19:41,040 When you get the phone call, you go... 238 00:19:41,840 --> 00:19:45,840 You hang up and suddenly wonder if it wasn't a hoax. 239 00:19:46,360 --> 00:19:48,520 The email confirmation comes, 240 00:19:48,680 --> 00:19:49,960 but doubt remains. 241 00:19:50,120 --> 00:19:53,240 Slowly you get other confirmations. 242 00:19:53,400 --> 00:19:55,200 You're told to keep it quiet. 243 00:19:55,360 --> 00:19:59,160 If someone mentions the Fields Medal, you play dumb. 244 00:19:59,400 --> 00:20:02,360 They wish you luck, you thank them. 245 00:20:02,800 --> 00:20:04,160 You can't say anything. 246 00:20:27,120 --> 00:20:30,880 I had a course to prepare. It'll be of a hundred pages. 247 00:20:31,800 --> 00:20:33,680 So I got to writing 248 00:20:33,840 --> 00:20:35,560 but the sources were lacking. 249 00:20:35,720 --> 00:20:38,320 I had to rework this, rewrite that. 250 00:20:38,480 --> 00:20:42,160 Articles needed reworking. I ended up rewriting everything. 251 00:20:42,320 --> 00:20:44,720 It's the book that's in command. 252 00:20:44,880 --> 00:20:46,880 If the chapter doesn't sing, 253 00:20:47,040 --> 00:20:50,320 if that little voice says "no," you rework it. 254 00:20:50,480 --> 00:20:52,520 Over and over again. 255 00:20:52,680 --> 00:20:56,960 After years, days and nights of work 256 00:20:57,120 --> 00:21:00,000 it's there. It's finally done. 257 00:21:00,600 --> 00:21:02,320 I worked on this thing 258 00:21:03,680 --> 00:21:06,480 sometimes morning and night. 259 00:21:06,640 --> 00:21:09,720 The first time I sat down to reread it, 260 00:21:09,880 --> 00:21:12,280 make corrections and polish it up, 261 00:21:12,440 --> 00:21:14,480 I took advantage of my vacation. 262 00:21:14,640 --> 00:21:17,280 My family left on a trip and I stayed home. 263 00:21:17,960 --> 00:21:19,520 I went to the marketplace, 264 00:21:19,720 --> 00:21:22,360 bought a bunch of vegetables, 265 00:21:22,520 --> 00:21:24,600 and made a big pot of soup. 266 00:21:24,760 --> 00:21:27,360 I ate it for a full week. 267 00:21:27,520 --> 00:21:30,240 Not to mention bread. Bread is absolutely vital. 268 00:21:30,400 --> 00:21:32,120 I read all day. 269 00:21:32,280 --> 00:21:34,960 I'd get up in the morning, read and revise 270 00:21:35,120 --> 00:21:36,800 until I went to bed. 271 00:21:36,960 --> 00:21:38,320 I did that for a week. 272 00:21:38,480 --> 00:21:41,360 To achieve good results that's what is necessary. 273 00:22:11,600 --> 00:22:13,000 In the history of mathematics 274 00:22:13,160 --> 00:22:15,360 there's one award that stands apart. 275 00:22:15,520 --> 00:22:16,680 Jean-Pierre Bourguignon, Institute of Advanced Scientific Studies (IHES) 276 00:22:16,840 --> 00:22:18,440 It celebrates youth. 277 00:22:18,600 --> 00:22:21,680 Recipients of the Fields Medal must be under 40. 278 00:22:21,840 --> 00:22:23,600 The prize money isn't large, 279 00:22:23,760 --> 00:22:26,640 characteristic of how mathematicians operate. 280 00:22:26,800 --> 00:22:29,240 And in the field of study 281 00:22:29,400 --> 00:22:31,280 it's the most prestigious award. 282 00:25:03,040 --> 00:25:06,120 Mathematics is too often reduced to calculations. 283 00:25:06,280 --> 00:25:09,320 Even if they play an important role, 284 00:25:09,480 --> 00:25:13,720 mathematics is the largest manufacturer of concepts in the world. 285 00:25:14,040 --> 00:25:17,800 In the 20th century the field of mathematics exploded. 286 00:25:17,960 --> 00:25:21,880 In 1900, research mathematicians 287 00:25:22,040 --> 00:25:24,040 numbered around 150 in the world. 288 00:25:24,200 --> 00:25:26,800 Today there are 80,000! 289 00:25:26,960 --> 00:25:30,040 And they each produce about one theorem a year. 290 00:25:32,240 --> 00:25:36,240 It's just full of overflowing, abundant activity. 291 00:25:36,400 --> 00:25:40,200 It's essential to bring attention to this movement. 292 00:27:28,240 --> 00:27:32,040 Inaugural Address 293 00:28:04,280 --> 00:28:09,080 Mathematician/Funder of Renaissance Technologies 294 00:29:55,800 --> 00:29:59,440 Julia Robinson Mathematics Festival 295 00:32:23,040 --> 00:32:24,520 It's often ideological. 296 00:32:24,680 --> 00:32:27,640 Those involved often have biased opinions, 297 00:32:27,800 --> 00:32:29,360 which are hard to change. 298 00:32:29,520 --> 00:32:32,120 When we teach kids 299 00:32:32,480 --> 00:32:35,920 we shouldn't have biased opinions or preconceived ideas. 300 00:32:36,560 --> 00:32:38,400 It's surprising when you think 301 00:32:38,560 --> 00:32:43,040 how little our brains have evolved over the millenniums. 302 00:32:43,760 --> 00:32:45,000 Take a child... 303 00:32:45,840 --> 00:32:49,320 What he learns at the beginning of his experience 304 00:32:49,480 --> 00:32:52,600 isn't necessarily technology-dependant. 305 00:32:52,760 --> 00:32:55,720 We should already have found better, 306 00:32:55,880 --> 00:32:59,400 the best methods for teaching how to read and count. 307 00:33:00,120 --> 00:33:03,400 Yet no one can agree. That isn't normal. 308 00:33:03,560 --> 00:33:06,320 Yes, things are changing in high school curriculum. 309 00:33:06,480 --> 00:33:10,320 We have to adapt to advances in science and technology. 310 00:33:10,480 --> 00:33:12,440 But for kids, we should've found 311 00:33:12,600 --> 00:33:15,240 the miracle method on which everyone agrees. 312 00:33:16,000 --> 00:33:18,680 2 plus 2 still equals 4. 313 00:33:18,840 --> 00:33:22,360 We have to be able to educate children 314 00:33:22,800 --> 00:33:27,080 who, in some twenty years, will become active citizens. 315 00:33:27,240 --> 00:33:31,400 We need to anticipate what life will be like for them. 316 00:33:32,480 --> 00:33:35,640 We live in a changing world. A world of progress. 317 00:33:38,560 --> 00:33:41,080 A world that is often violent and cruel. 318 00:33:41,360 --> 00:33:44,040 An uncertain world where people kill and die. 319 00:33:44,200 --> 00:33:45,800 Where children suffer. 320 00:33:47,640 --> 00:33:49,960 This world will soon be theirs. 321 00:33:50,120 --> 00:33:53,360 We must adapt education to the world of tomorrow. 322 00:33:53,760 --> 00:33:56,800 The recently proposed reform has caused reaction. 323 00:33:57,040 --> 00:34:01,280 Modern mathematics, the reform that has confused 324 00:34:01,440 --> 00:34:03,200 students and parents alike. 325 00:34:03,360 --> 00:34:05,760 Modern mathematics should provide us 326 00:34:05,920 --> 00:34:07,680 with a universal tool 327 00:34:07,840 --> 00:34:11,680 that will enable us to adapt to new situations. 328 00:34:13,520 --> 00:34:17,120 In the '70s there was a desire to modernize 329 00:34:17,280 --> 00:34:18,520 and industrialize France. 330 00:34:18,680 --> 00:34:21,040 To do that we needed engineers, 331 00:34:21,200 --> 00:34:24,040 more than the number graduating from university. 332 00:34:24,200 --> 00:34:25,680 Historian of Mathematics 333 00:34:25,840 --> 00:34:30,120 We needed a large pool of them. Mathematics was considered the means 334 00:34:30,280 --> 00:34:32,520 by which to train them. 335 00:34:33,400 --> 00:34:36,160 It was the baby boom, the population had soared. 336 00:34:37,000 --> 00:34:38,480 The birthrate had risen, 337 00:34:38,920 --> 00:34:42,040 and classes were filled to the brim. 338 00:34:42,440 --> 00:34:45,440 The problem was how to offer opportunity 339 00:34:45,600 --> 00:34:47,000 to everyone. 340 00:34:49,240 --> 00:34:52,080 The modern mathematics reform 341 00:34:52,240 --> 00:34:53,840 was thought to be 342 00:34:54,000 --> 00:34:58,000 the most effective means to teach the masses. 343 00:34:58,160 --> 00:35:00,880 Access to mathematical knowledge 344 00:35:01,040 --> 00:35:04,600 was thought to be something natural to man, 345 00:35:05,000 --> 00:35:09,200 while literary knowledge, theater, poetry, music 346 00:35:09,360 --> 00:35:12,280 was learned socially. 347 00:35:13,080 --> 00:35:16,000 This viewpoint was not entirely sound 348 00:35:16,160 --> 00:35:18,160 but it was workable. 349 00:35:20,600 --> 00:35:22,920 First, programs were revised. 350 00:35:23,080 --> 00:35:26,600 Mathematics had to be conceived differently. 351 00:35:26,760 --> 00:35:30,200 Mathematics is a logical, clear, distinct process 352 00:35:30,400 --> 00:35:34,840 and was thus deemed the "least worst" means of selection. 353 00:35:41,440 --> 00:35:43,160 The math curriculum was inspired 354 00:35:43,320 --> 00:35:47,720 by the work of top mathematicians who had influenced their era. 355 00:35:48,960 --> 00:35:51,200 It was a group of mathematicians, 356 00:35:51,360 --> 00:35:56,040 young professors who would get together 357 00:35:58,080 --> 00:35:59,680 and prepare their courses. 358 00:35:59,840 --> 00:36:02,880 "Let's work up next year's courses." 359 00:36:03,040 --> 00:36:06,720 Before they knew it, they were rewriting mathematics. 360 00:36:11,840 --> 00:36:13,840 It was a time in the field 361 00:36:14,000 --> 00:36:17,120 where some order needed to be restored. 362 00:36:17,280 --> 00:36:21,200 Notations needed reviewing, interdisciplinary relations assessed. 363 00:36:21,360 --> 00:36:24,280 They had to start from scratch, and it took years. 364 00:36:24,440 --> 00:36:26,960 This group of mathematicians 365 00:36:27,120 --> 00:36:30,440 published under the pseudonym Nicolas Bourbaki. 366 00:36:30,680 --> 00:36:35,240 Though it started in France, within a few years 367 00:36:35,400 --> 00:36:37,840 it had become a worldwide movement. 368 00:36:38,000 --> 00:36:40,200 It was quite a phenomenon. 369 00:36:40,360 --> 00:36:44,920 Conferences were held on "modern math" 370 00:36:45,080 --> 00:36:47,080 in South-East Asia, 371 00:36:47,440 --> 00:36:48,640 in Brazil, 372 00:36:49,480 --> 00:36:53,400 and, of course, "new math" in England and the United States. 373 00:36:53,640 --> 00:36:55,760 Yes, it was new mathematics, 374 00:36:56,560 --> 00:36:58,200 with an emphasis on modern. 375 00:36:58,360 --> 00:37:01,880 In other words, mathematics truly of the time. 376 00:37:04,040 --> 00:37:08,160 The modern mathematics reform echoed, in the events of May '68, 377 00:37:08,320 --> 00:37:11,960 the demands for more freedom in the classroom. 378 00:37:12,120 --> 00:37:15,480 People felt they had been liberated 379 00:37:15,640 --> 00:37:17,200 from so many constraints, 380 00:37:17,360 --> 00:37:19,880 especially those of authority. 381 00:37:20,080 --> 00:37:24,360 They were breaking with a restrictive culture 382 00:37:24,560 --> 00:37:26,960 that had so encumbered them 383 00:37:27,120 --> 00:37:29,480 and didn't allow them 384 00:37:29,920 --> 00:37:32,400 to be truly themselves. 385 00:37:50,840 --> 00:37:54,120 I was at school during the reform and loved it. 386 00:37:54,600 --> 00:37:58,080 It created a real opening, which was fabulous. 387 00:37:58,240 --> 00:38:01,240 It led to a generation of mathematicians 388 00:38:01,400 --> 00:38:03,800 with the highest qualifications 389 00:38:03,960 --> 00:38:06,560 and a solid foundation. 390 00:38:06,720 --> 00:38:07,840 It's true. 391 00:38:08,000 --> 00:38:10,280 But generations since 392 00:38:10,440 --> 00:38:13,480 have been either disgusted or overwhelmed, 393 00:38:13,640 --> 00:38:16,640 when they could've learned math, 394 00:38:16,800 --> 00:38:19,840 or at least not rejected it. 395 00:38:20,000 --> 00:38:23,960 That's truly sad. It's still a heavy price to pay. 396 00:38:24,120 --> 00:38:28,760 A number of politicians and journalists were so traumatized 397 00:38:28,920 --> 00:38:31,720 they still can't say they enjoy math. 398 00:38:32,080 --> 00:38:35,960 If you don't get it, you're in trouble. 399 00:38:36,160 --> 00:38:38,160 You're not doing any more calculations? 400 00:38:38,320 --> 00:38:40,600 We don't know how to do them anymore. 401 00:38:40,760 --> 00:38:43,800 Calculations with decimals, numerals, division... 402 00:38:43,960 --> 00:38:45,760 I'm completely lost. 403 00:38:45,920 --> 00:38:48,360 The big problem is the language. 404 00:38:48,520 --> 00:38:51,680 Math terms are super complicated. 405 00:38:51,840 --> 00:38:55,280 Math has become so abstract, it's a joke. 406 00:38:55,440 --> 00:38:58,360 The new definition of a straight line 407 00:38:58,520 --> 00:38:59,520 makes no sense. 408 00:38:59,800 --> 00:39:02,640 You learn it by heart and mindlessly recite it. 409 00:39:02,800 --> 00:39:04,360 You get the gist of it, 410 00:39:04,520 --> 00:39:07,000 but the terms are incomprehensible. 411 00:39:07,200 --> 00:39:10,800 Even parents have to go back to school. 412 00:39:11,440 --> 00:39:13,800 95 percent of parents 413 00:39:14,080 --> 00:39:17,040 can't make sense of the new textbooks. 414 00:39:19,200 --> 00:39:22,880 Kindergarteners were told not to finger-count. 415 00:39:23,040 --> 00:39:25,560 They had to identify commonalities between... 416 00:39:26,080 --> 00:39:27,760 3 isn't the number anymore. 417 00:39:27,920 --> 00:39:31,640 It's 3 shoes, 3 pants, 3 crayons. 418 00:39:31,880 --> 00:39:34,560 And the link between them? The number 3! 419 00:39:34,720 --> 00:39:38,360 Except kids already know what the number 3 is. 420 00:39:38,680 --> 00:39:39,680 Likewise, 421 00:39:40,840 --> 00:39:43,200 you don't draw a line 422 00:39:43,360 --> 00:39:47,480 because the act of drawing has been corrupted by the senses. 423 00:39:47,640 --> 00:39:49,680 It needs to be defined abstractly. 424 00:39:49,840 --> 00:39:53,280 The idea behind the reform was 425 00:39:53,440 --> 00:39:56,000 to make kids understand before actually drawing. 426 00:39:56,160 --> 00:39:59,400 Understand first then feel, and only then. 427 00:39:59,760 --> 00:40:02,080 On top of it, teachers hadn't been trained. 428 00:40:02,240 --> 00:40:06,600 At the time there was a shortage of high school teachers 429 00:40:06,760 --> 00:40:11,240 so we had to hire teachers from grade school 430 00:40:11,480 --> 00:40:15,520 who hadn't studied science at college. 431 00:40:15,680 --> 00:40:17,520 They were good teachers 432 00:40:17,680 --> 00:40:20,760 but had no scientific basis. 433 00:40:20,920 --> 00:40:25,040 And they were supposed to teach this new math 434 00:40:25,200 --> 00:40:29,200 with its extreme level of abstraction. 435 00:40:29,360 --> 00:40:33,840 So as not lose grip, they went strictly by the book. 436 00:40:34,000 --> 00:40:35,360 They understood nothing. 437 00:40:35,520 --> 00:40:38,920 - So their students didn't either? - Exactly. 438 00:40:39,200 --> 00:40:40,880 Teaching methods changed. 439 00:40:41,040 --> 00:40:43,440 Completely. I was a teacher back then. 440 00:40:43,600 --> 00:40:46,480 It helped me improve my teaching skills. 441 00:40:46,800 --> 00:40:50,120 How have kids reacted to the changes? 442 00:40:50,280 --> 00:40:53,240 They love their new math lessons. 443 00:40:53,400 --> 00:40:54,960 They can't wait for class. 444 00:40:55,120 --> 00:40:57,880 They don't get tired during the lesson. 445 00:40:58,040 --> 00:40:59,040 It's a game. 446 00:40:59,200 --> 00:41:01,720 It's quite amusing to read 447 00:41:02,400 --> 00:41:04,880 the modern mathematics textbooks. 448 00:41:05,520 --> 00:41:09,520 The explanations kept getting longer. 449 00:41:09,680 --> 00:41:15,560 They had to learn to "speak well" even if it concerned mathematics. 450 00:41:15,720 --> 00:41:17,480 That hadn't been planned. 451 00:41:25,560 --> 00:41:29,240 What was supposed to be a sphere of creativity and freedom 452 00:41:29,400 --> 00:41:32,080 became something that petrified everyone. 453 00:41:32,240 --> 00:41:35,520 "I don't understand anything. I'm completely lost." 454 00:41:35,680 --> 00:41:40,040 It created bewilderment instead of creativity, 455 00:41:40,200 --> 00:41:45,360 like a rabbit caught in headlights. "What's this truck going to do to me?" 456 00:41:45,520 --> 00:41:48,240 A school curriculum 457 00:41:48,400 --> 00:41:50,800 can't be conceived on paper. 458 00:41:50,960 --> 00:41:53,080 It has to be tested. 459 00:41:55,400 --> 00:41:58,480 You have to experiment when it comes to child education. 460 00:41:58,640 --> 00:42:01,160 You first test a program, see how kids fare 461 00:42:01,320 --> 00:42:03,120 then go from there. 462 00:42:03,280 --> 00:42:09,240 We're limited in our understanding of how the brain works. 463 00:42:09,400 --> 00:42:11,960 All we can do is experiment. 464 00:42:12,560 --> 00:42:16,200 Modern mathematics was full of honorable intentions. 465 00:42:16,360 --> 00:42:20,640 It was developed by the best mathematicians of the day. 466 00:42:20,800 --> 00:42:24,160 It just wasn't the right reform at the right time. 467 00:42:40,520 --> 00:42:42,120 Nowadays, 468 00:42:42,280 --> 00:42:45,840 people use the word "Bourbakist" as an insult. 469 00:42:46,000 --> 00:42:47,880 A kind insult, it you will. 470 00:42:48,320 --> 00:42:51,320 "You're abstract. What are you, a Bourbakist?" 471 00:42:51,480 --> 00:42:54,440 For a time people criticized Bourbaki, 472 00:42:54,600 --> 00:42:57,640 but now I think there's a general consensus 473 00:42:57,800 --> 00:43:01,400 that Bourbaki had a big impact on mathematics. 474 00:43:01,560 --> 00:43:03,720 There's no denying or idealizing it. 475 00:43:03,880 --> 00:43:05,400 It was a milestone. 476 00:43:10,120 --> 00:43:13,120 The idea behind it was to convey 477 00:43:13,280 --> 00:43:15,840 a maximum of knowledge to a maximum of kids. 478 00:43:16,880 --> 00:43:20,960 But trends in math curriculum sort of betrayed the spirit of math. 479 00:43:21,240 --> 00:43:23,320 It became hard, 480 00:43:23,480 --> 00:43:27,560 severe, too abstract, completely based on objects... 481 00:43:30,800 --> 00:43:32,680 independent of human beings. 482 00:43:43,000 --> 00:43:45,400 Bit by bit, the idea of mathematics 483 00:43:45,560 --> 00:43:49,240 as profitable, as functional prevailed. 484 00:43:49,560 --> 00:43:50,920 Obviously, 485 00:43:51,080 --> 00:43:53,120 Clemenceau High School Principal 486 00:43:53,280 --> 00:43:55,760 science majors are eclipsing all the others. 487 00:43:58,520 --> 00:44:02,360 It's terrible to see math being used as an assessment tool, 488 00:44:03,440 --> 00:44:06,680 when many kids will never become scientists. 489 00:44:08,320 --> 00:44:12,560 Since science is considered "the" field of study today, 490 00:44:12,720 --> 00:44:15,880 landing a prestigious position is all but guaranteed. 491 00:44:16,040 --> 00:44:20,840 Students major in math, even those graduating with a BA. 492 00:44:57,280 --> 00:44:59,920 SCIENCE OF EDUCATION RESEARCHER 493 00:45:54,160 --> 00:45:57,400 MSRI Director 494 00:49:12,440 --> 00:49:15,400 Mathematical Research Institute of Oberwolfach 495 00:49:15,560 --> 00:49:16,560 Germany 496 00:49:46,600 --> 00:49:50,600 Director 497 00:54:49,640 --> 00:54:51,120 Research can't be just summoned up. 498 00:54:51,280 --> 00:54:56,040 You must rely on initiatives and the competence of experts. 499 00:54:56,360 --> 00:54:59,160 There are those who suddenly have an idea. 500 00:54:59,320 --> 00:55:03,000 They set it out. But no, it doesn't work. 501 00:55:03,160 --> 00:55:05,000 The second time, it's still no. 502 00:55:05,160 --> 00:55:07,960 The third time, yes! It finally works. 503 00:55:09,400 --> 00:55:13,120 People have a hard time understanding creativity. 504 00:55:14,040 --> 00:55:17,960 Artists function differently. They explore the unknown. 505 00:55:23,760 --> 00:55:25,760 It's hard to find the right problem. 506 00:55:25,920 --> 00:55:28,840 Those of no interest come by the dozen. 507 00:55:29,000 --> 00:55:32,880 Asking the right question is a big chunk of the work. 508 00:55:33,120 --> 00:55:35,640 It's the path taken that's important. 509 00:55:35,800 --> 00:55:38,640 And there isn't one unique path. 510 00:55:39,400 --> 00:55:41,640 Sometimes you find a shortcut, 511 00:55:41,920 --> 00:55:43,960 a really simple shortcut. 512 00:55:44,120 --> 00:55:47,600 Not as simple as an exercise, but close. 513 00:55:48,480 --> 00:55:50,400 It's much less important. 514 00:55:50,560 --> 00:55:52,080 The proof is simpler, 515 00:55:52,240 --> 00:55:56,320 but a complex proof is much more profound and rich. 516 00:56:31,040 --> 00:56:33,680 The mathematical result is important, 517 00:56:33,840 --> 00:56:36,800 but the proof is often just as important. 518 00:56:36,960 --> 00:56:38,280 So is the approach, 519 00:56:39,160 --> 00:56:43,240 the arguments used, the interdisciplinary connections, 520 00:56:43,400 --> 00:56:45,440 the developed theories, the tools. 521 00:56:46,360 --> 00:56:49,240 A new way of seeing things, new connections. 522 00:56:49,760 --> 00:56:53,520 They all lead to other ideas, other avenues, other techniques. 523 00:56:54,320 --> 00:56:56,720 And this requires a lot of time. 524 00:57:01,320 --> 00:57:04,200 In order to discover new fields of application, 525 00:57:04,360 --> 00:57:07,360 or radically new concepts and phenomena, 526 00:57:07,520 --> 00:57:10,480 highly developed research is required. 527 00:57:11,040 --> 00:57:12,640 Unfortunately... 528 00:57:12,960 --> 00:57:16,760 When we realized research, apart from the rising costs, 529 00:57:16,920 --> 00:57:20,840 was having an impact, 530 00:57:21,000 --> 00:57:25,840 and that science and industry were now connected through high-technology, 531 00:57:26,000 --> 00:57:28,920 people said, "We're there. 532 00:57:29,080 --> 00:57:31,640 "We're now one. We'll draw the consequences, 533 00:57:31,800 --> 00:57:34,560 "and now function like companies." 534 00:57:34,720 --> 00:57:36,200 That's a big mistake. 535 00:57:36,480 --> 00:57:39,960 "We finance you, so we want to know what you're doing. 536 00:57:40,120 --> 00:57:42,080 "We'll decide what you work on." 537 00:57:42,280 --> 00:57:44,720 That's blatant abuse of power. 538 00:57:44,880 --> 00:57:48,120 It kills the process we should be defending. 539 00:57:48,360 --> 00:57:50,360 All countries do it except... 540 00:57:50,640 --> 00:57:51,640 China. 541 00:57:51,800 --> 00:57:53,200 The total counterexample. 542 00:57:53,360 --> 00:57:55,960 The Chinese understood they couldn't meet 543 00:57:56,120 --> 00:58:00,360 the expected levels of performance and development 544 00:58:00,520 --> 00:58:03,320 without massively increasing pure research. 545 00:58:03,480 --> 00:58:06,200 They'll have a labor shortage in 25 to 30 years. 546 00:58:06,360 --> 00:58:09,160 They'll need to produce high value-added products 547 00:58:09,320 --> 00:58:13,120 in order for the country to survive. 548 00:58:13,280 --> 00:58:15,800 They recognized in order to achieve that 549 00:58:15,960 --> 00:58:18,840 they'd need highly developed fundamental research. 550 00:58:19,040 --> 00:58:21,600 However there is a consequence to this. 551 00:58:21,760 --> 00:58:26,080 Most scientists are passionate about what they do. 552 00:58:26,240 --> 00:58:30,400 Take away their freedom, tell them what to do every morning 553 00:58:30,560 --> 00:58:31,960 and they'll up and leave. 554 00:58:32,120 --> 00:58:36,080 Researchers aren't well paid, though I'm not complaining. 555 00:58:36,240 --> 00:58:38,880 But most scientists are highly competent. 556 00:58:39,040 --> 00:58:42,240 If they want to make money, they'll go elsewhere. 557 00:58:42,400 --> 00:58:45,480 To get the most creative to stay leave them alone. 558 00:58:46,080 --> 00:58:48,960 Institute of Advanced Scientific Studies (IHES), Bures-sur-Yvette, France 559 01:03:31,080 --> 01:03:34,640 Mathematics works well with music and mountains. 560 01:03:34,800 --> 01:03:37,440 Mathematics, mountain, music. M-M-M. 561 01:03:56,480 --> 01:03:58,960 Alain, is your sense of orientation good? 562 01:05:35,200 --> 01:05:41,560 Computational Science Researcher 563 01:09:40,400 --> 01:09:45,520 We live in a world saturated with massive, complex data. 564 01:09:45,680 --> 01:09:48,240 Any two individuals in the world 565 01:09:48,400 --> 01:09:50,680 are connected by a chain of acquaintances. 566 01:09:50,840 --> 01:09:53,920 This is known as discrete mathematics. 567 01:09:55,280 --> 01:09:57,800 Everything today is done through data analysis. 568 01:09:57,960 --> 01:09:59,720 Google's search engine 569 01:09:59,880 --> 01:10:04,160 is a mathematical algorithm worth 200 billion dollars. 570 01:10:14,520 --> 01:10:17,120 Cryptography Laboratory 571 01:15:13,360 --> 01:15:17,760 Olivier, help Alexis out so he doesn't break anything. 572 01:18:24,440 --> 01:18:27,400 Mathematicians remained craftsmen for a long time. 573 01:18:27,560 --> 01:18:31,800 But the social impact of what they are now doing 574 01:18:31,960 --> 01:18:35,120 is a radical shift. 575 01:18:37,160 --> 01:18:40,480 Many hadn't much considered scientific responsibility. 576 01:18:40,640 --> 01:18:44,280 They thought they lived in a world a bit apart. 577 01:18:44,440 --> 01:18:46,800 They'd never had to choose, like some, 578 01:18:46,960 --> 01:18:50,440 whether or not to join the Manhattan Project 579 01:18:50,600 --> 01:18:53,200 and help in the making of the atomic bomb. 580 01:18:53,520 --> 01:18:56,760 Suddenly there was a whole branch of mathematics 581 01:18:56,920 --> 01:19:01,440 that found itself at the heart of economic activity, 582 01:19:01,600 --> 01:19:05,800 an economic activity that was having a massive global impact. 583 01:19:05,960 --> 01:19:07,720 Financial mathematics. 584 01:19:28,800 --> 01:19:31,400 Professor of Financial Mathematics 585 01:21:18,880 --> 01:21:22,520 The sophistication of the mathematics changed abruptly. 586 01:21:22,680 --> 01:21:27,200 You now had mathematical products, like you have chemical products. 587 01:21:27,360 --> 01:21:32,400 Banks were making a number of new offers. 588 01:21:33,400 --> 01:21:39,440 New products, new ways of developing financing operations, 589 01:21:40,480 --> 01:21:43,560 new profit-sharing plans. 590 01:21:43,720 --> 01:21:46,480 Schemes that hadn't existed before. 591 01:21:46,640 --> 01:21:48,520 These were new products 592 01:21:48,680 --> 01:21:54,680 whose very existence depended on new mathematics. 593 01:24:19,440 --> 01:24:21,400 Most models used by the banks 594 01:24:21,800 --> 01:24:23,960 are based on random variables. 595 01:24:24,120 --> 01:24:26,960 These models were built on statistical data 596 01:24:27,120 --> 01:24:30,320 in order to calibrate the parameters. 597 01:24:33,000 --> 01:24:37,000 Most of these banks, in feverish competition with each other, 598 01:24:37,160 --> 01:24:38,480 never shared information. 599 01:24:39,040 --> 01:24:42,360 From a scientific viewpoint, it was crucial 600 01:24:42,520 --> 01:24:45,960 to have at one's disposal a vast pool of data. 601 01:24:46,120 --> 01:24:47,840 And that was non-existent 602 01:24:48,120 --> 01:24:52,520 because each bank jealously guarded its own information. 603 01:33:51,040 --> 01:33:54,080 LaPlace said that if we knew everything 604 01:33:54,240 --> 01:33:55,960 we could predict everything. 605 01:33:57,800 --> 01:33:58,800 In the end, 606 01:33:58,920 --> 01:34:02,760 our inclination for breaking "nature" down 607 01:34:02,920 --> 01:34:04,360 into forms and numbers, 608 01:34:04,520 --> 01:34:08,240 drawing conclusions, even predicting destiny 609 01:34:08,640 --> 01:34:10,720 dates back to antiquity. 610 01:34:10,880 --> 01:34:12,520 It's in our nature. 611 01:34:15,080 --> 01:34:18,120 But it's important to learn to live fortuitously, 612 01:34:18,280 --> 01:34:19,560 with uncertainty, 613 01:34:19,720 --> 01:34:23,000 and to master it, to actually live it. 614 01:34:27,880 --> 01:34:31,200 Our fascination with scientism has wreaked havoc. 615 01:34:31,360 --> 01:34:33,480 "Science can solve everything." 616 01:34:33,640 --> 01:34:36,600 Philosophically speaking, that's unacceptable. 617 01:34:36,760 --> 01:34:39,320 Science doesn't have all the answers. 618 01:34:40,640 --> 01:34:42,920 What science can give us 619 01:34:43,080 --> 01:34:46,640 is the capacity to turn doubt into a virtue. 620 01:34:47,280 --> 01:34:49,560 We all must doubt when it's appropriate, 621 01:34:49,720 --> 01:34:53,640 but we can find certitude even in moments of doubt. 622 01:38:45,880 --> 01:38:47,880 Subtitles by Theresa Murphy 623 01:38:48,040 --> 01:38:49,880 Subtitling: C.M.C. - Paris 9999 00:00:0,500 --> 00:00:2,00 www.moviesubtitles.org