1 00:00:00,000 --> 00:00:05,420 A teenage son of a knife grinder invents a method so powerful for designing fortresses 2 00:00:05,420 --> 00:00:09,080 that the French government classifies it as a military secret. 3 00:00:09,740 --> 00:00:13,780 For 15 years, he teaches it only to those with security clearance. 4 00:00:14,420 --> 00:00:16,240 Then, the revolution comes. 5 00:00:16,760 --> 00:00:21,700 And suddenly, this secret becomes the foundation of a new kind of education 6 00:00:21,700 --> 00:00:23,640 that will transform the world. 7 00:00:24,120 --> 00:00:26,940 Last time, we met Pierre-Simon Laplace, 8 00:00:26,940 --> 00:00:32,280 the Newton of France who completed celestial mechanics and founded probability theory. 9 00:00:32,980 --> 00:00:37,660 We saw his demon of perfect determinism and his cool response to Napoleon. 10 00:00:38,300 --> 00:00:39,940 I had no need of that hypothesis. 11 00:00:40,800 --> 00:00:42,400 Welcome back to Men of Mathematics. 12 00:00:43,460 --> 00:00:49,300 Today, we enter the revolutionary era with Gaspar Monge, 13 00:00:49,700 --> 00:00:52,220 the man who invented descriptive geometry, 14 00:00:52,220 --> 00:00:58,140 founded the École Polytechnique, and shaped technical education for centuries to come. 15 00:00:58,640 --> 00:01:06,620 Gaspard Monge was born on May 9, 1746, in Beaune, Burgundy. His father was a knife grinder and 16 00:01:06,620 --> 00:01:12,160 peddler, about as far from the aristocracy as one could be in pre-revolutionary France. 17 00:01:13,080 --> 00:01:18,820 Young Monge showed exceptional ability early. A map of his hometown that he drew at 14 18 00:01:18,820 --> 00:01:25,980 so impressed local officials that they arranged for him to attend a military school in Mezieres. 19 00:01:26,760 --> 00:01:30,980 At the school, Mange was assigned to help draft fortification plans, 20 00:01:31,560 --> 00:01:34,900 work considered beneath the aristocratic officer students. 21 00:01:35,780 --> 00:01:49,340 Asked to design a fortress defense system a task that normally required weeks of calculation Manj developed a graphical method that solved it in hours The officers refused to believe his 22 00:01:49,340 --> 00:01:56,800 solution until they checked every calculation. Then they classified his method as a military 23 00:01:56,800 --> 00:02:04,480 secret. For 15 years, Manj taught his descriptive geometry only to those with security clearance. 24 00:02:04,480 --> 00:02:09,320 It was too valuable for fortress design to risk falling into enemy hands. 25 00:02:09,860 --> 00:02:10,920 What was this secret method? 26 00:02:11,880 --> 00:02:16,340 Mange invented a systematic way to represent three-dimensional objects 27 00:02:16,340 --> 00:02:18,400 using two-dimensional drawings, 28 00:02:18,980 --> 00:02:24,480 using multiple views, plan, and elevation that capture all spatial information. 29 00:02:25,440 --> 00:02:29,940 Before Mange, architects and engineers communicated through perspective drawings 30 00:02:29,940 --> 00:02:31,060 that couldn't be measured. 31 00:02:32,000 --> 00:02:35,700 After Manj, they had a precise language for three-dimensional design. 32 00:02:36,460 --> 00:02:40,900 Every CAD system, every engineering drawing, every architectural blueprint 33 00:02:40,900 --> 00:02:44,620 descends from Manj's descriptive geometry. 34 00:02:45,800 --> 00:02:51,060 Manj's method grew from stereotomy, the ancient art of stone cutting. 35 00:02:51,260 --> 00:02:55,480 How do you cut stones to fit together in arches and vaults? 36 00:02:56,120 --> 00:03:00,740 Each stone must be shaped precisely to bear loads and meet its neighbors. 37 00:03:01,060 --> 00:03:06,100 The Romans knew how to do this through trial and error. 38 00:03:06,100 --> 00:03:08,340 Mange made it mathematical. 39 00:03:08,340 --> 00:03:12,660 In 1781, Mange posed a problem that seemed simple. 40 00:03:12,660 --> 00:03:18,380 Given piles of dirt and holes to fill, what's the cheapest way to move the dirt? 41 00:03:18,380 --> 00:03:30,340 This optimal transport problem has become fundamental to modern mathematics and machine learning It appears in economics for matching supply and demand in image processing for comparing shapes 42 00:03:30,340 --> 00:03:36,340 in machine learning with Wasserstein distances, and in meteorology for tracking air masses. 43 00:03:37,360 --> 00:03:43,380 Monge also contributed to the study of curved surfaces. He investigated the lines of curvature 44 00:03:43,380 --> 00:03:49,140 on surfaces, special curves that point in the directions of maximum and minimum bending. 45 00:03:49,980 --> 00:03:54,040 This work influenced Gauss's later development of differential geometry. 46 00:03:54,660 --> 00:03:59,940 The French Revolution swept away the old order, including the old educational system. 47 00:04:00,720 --> 00:04:05,900 In 1794, the revolutionary government needed to train engineers fast. 48 00:04:06,500 --> 00:04:09,860 Mange was called upon to help create a new kind of school. 49 00:04:09,860 --> 00:04:13,800 The Ecole Polytechnique was revolutionary in its approach. 50 00:04:14,740 --> 00:04:16,740 Science taught through rigorous mathematics. 51 00:04:17,680 --> 00:04:18,900 No distinction by birth. 52 00:04:19,620 --> 00:04:21,000 Talent was all that mattered. 53 00:04:21,860 --> 00:04:24,940 Practical applications alongside pure theory. 54 00:04:25,720 --> 00:04:27,280 The blackboard method of teaching. 55 00:04:28,560 --> 00:04:32,560 The Ecole produced an extraordinary concentration of mathematical talent. 56 00:04:33,380 --> 00:04:35,040 Cauchy for rigorous analysis. 57 00:04:35,620 --> 00:04:38,480 Fourier for the heat equation and Fourier series. 58 00:04:39,040 --> 00:04:41,320 Poisson for probability and physics, 59 00:04:41,820 --> 00:04:43,480 Carnot for thermodynamics, 60 00:04:44,040 --> 00:04:45,520 Fresnel for wave optics, 61 00:04:45,980 --> 00:04:48,080 and Coriolis for rotating systems. 62 00:04:49,060 --> 00:04:51,760 French mathematics dominated the early 19th century, 63 00:04:52,240 --> 00:04:54,320 largely because of Mange's institution. 64 00:04:55,220 --> 00:04:57,320 Mange accompanied Napoleon to Egypt 65 00:04:57,320 --> 00:04:59,220 as part of the scientific expedition. 66 00:04:59,980 --> 00:05:14,740 He helped found the Institut d and contributed to the Description de l the massive survey that sparked European fascination with ancient Egypt Napoleon trusted Mange like few others 67 00:05:15,560 --> 00:05:21,840 Gaspard Mange rose from poverty to transform technical education. His descriptive geometry 68 00:05:21,840 --> 00:05:27,500 gave engineers a precise language for three-dimensional design. His optimal transport 69 00:05:27,500 --> 00:05:34,000 problem continues to generate research today. His École Polytechnique became the model for 70 00:05:34,000 --> 00:05:38,480 technical schools worldwide, and he did it all while remaining devoted to Napoleon, 71 00:05:39,000 --> 00:05:44,960 a loyalty that would cost him everything. After Waterloo, the restored monarchy stripped 72 00:05:44,960 --> 00:05:51,200 Mange of his honors and expelled him from the Institut de France. His health broke. 73 00:05:52,160 --> 00:05:57,080 When he died in 1818, the government forbade students from attending his funeral. 74 00:05:57,500 --> 00:06:00,440 they came anyway. As E.T. Bell wrote, 75 00:06:01,100 --> 00:06:06,020 Manj was one of those rare spirits who excel both as creators and as teachers. 76 00:06:06,940 --> 00:06:09,440 His influence on French mathematics was profound. 77 00:06:10,100 --> 00:06:15,820 Next time on Men of Mathematics, we meet Joseph Fourier, the orphan who conquered heat. 78 00:06:16,020 --> 00:06:21,660 From revolutionary politics to Egyptian deserts to the mathematics of heat conduction, 79 00:06:22,240 --> 00:06:26,960 Fourier discovered that any periodic function can be broken into simple waves. 80 00:06:27,500 --> 00:06:32,280 His series changed mathematics, physics, and engineering forever. 81 00:06:33,160 --> 00:06:36,100 Thank you for joining us on this journey through mathematical history. 82 00:06:36,700 --> 00:06:42,320 If you appreciate the mind that gave us modern technical drawing, subscribe and hit the notification 83 00:06:42,320 --> 00:06:46,580 bell. New episodes release every week. I'll see you next time.