WEBVTT 00:00:00.000 --> 00:00:04.240 In 1915, Albert Einstein had this massive problem. 00:00:04.879 --> 00:00:07.320 He had just published his theory of general relativity, 00:00:07.440 --> 00:00:10.800 but it contained this glaring paradox. In certain 00:00:10.800 --> 00:00:13.939 scenarios, energy seemed to just vanish into 00:00:13.939 --> 00:00:16.800 thin air, which breaks the fundamental laws of 00:00:16.800 --> 00:00:19.660 physics. It's a huge issue. Exactly. And to solve 00:00:19.660 --> 00:00:22.460 it, the greatest minds in the world didn't look 00:00:22.460 --> 00:00:25.140 to another famous physicist. They actually had 00:00:25.140 --> 00:00:28.399 to secretly bring in an unpaid, unrecognized 00:00:28.399 --> 00:00:31.070 woman who wasn't even legally allowed to hold 00:00:31.070 --> 00:00:33.729 a university position. It's just wild to think 00:00:33.729 --> 00:00:36.729 about. It really is. Welcome to today's custom 00:00:36.729 --> 00:00:39.770 -tailored deep dive. We are exploring the life 00:00:39.770 --> 00:00:42.409 and work of a historical figure who Albert Einstein, 00:00:42.689 --> 00:00:44.929 Norbert Weiner, and Hermann Weill all described 00:00:44.929 --> 00:00:46.829 as the most important woman in the history of 00:00:46.829 --> 00:00:49.609 mathematics. Her name is Emmy Noether, and we're 00:00:49.609 --> 00:00:51.609 so glad you are here with us to explore her story. 00:00:51.850 --> 00:00:53.670 Yeah, what is so staggering about the source 00:00:53.670 --> 00:00:56.049 material we are synthesizing for you today is 00:00:56.049 --> 00:00:58.350 just the sheer scale of her impact. No, they 00:00:58.350 --> 00:01:00.429 didn't just advance a single field of study. 00:01:00.590 --> 00:01:03.350 No, she didn't. She completely revolutionized 00:01:03.350 --> 00:01:06.530 two entirely different, highly complex branches 00:01:06.530 --> 00:01:08.650 of human knowledge. I mean, we're talking about 00:01:08.650 --> 00:01:11.650 theoretical physics and abstract algebra. OK, 00:01:11.670 --> 00:01:14.290 let's unpack this. Because to understand how 00:01:14.290 --> 00:01:16.409 she reshaped our understanding of the universe, 00:01:16.829 --> 00:01:19.269 we have to look at the incredibly absurd systemic 00:01:19.269 --> 00:01:21.530 roadblocks she had to navigate just to get a 00:01:21.530 --> 00:01:24.340 foot in the door. Yeah, the historical context 00:01:24.340 --> 00:01:27.299 here is crucial. So she was born in 1882 in Erlangen, 00:01:27.500 --> 00:01:29.980 which is a town in Bavaria, to a Jewish family. 00:01:30.000 --> 00:01:33.500 Right. Her father, Max Noether, was actually 00:01:33.500 --> 00:01:36.040 a distinguished mathematician himself. And the 00:01:36.040 --> 00:01:38.040 sources note she was exceptionally clever from 00:01:38.040 --> 00:01:41.319 a young age. There's this great anecdote about 00:01:41.319 --> 00:01:44.260 her rapidly solving a complex brain teaser at 00:01:44.260 --> 00:01:46.739 a children's party. Oh, I love that one. Right. 00:01:47.099 --> 00:01:49.359 But because she was a girl in the late 19th century, 00:01:49.799 --> 00:01:52.400 her intellect was directed entirely toward the 00:01:52.400 --> 00:01:54.540 standard domestic path. Yeah. She was basically 00:01:54.540 --> 00:01:57.799 taught to cook, clean, and play the piano. And 00:01:57.799 --> 00:02:00.040 while the texts mention she didn't particularly 00:02:00.040 --> 00:02:02.219 care for any of those, she did love to dance. 00:02:02.319 --> 00:02:04.739 She really did. She even went so far as to pass 00:02:04.739 --> 00:02:07.239 the official state examinations to teach French 00:02:07.239 --> 00:02:10.419 and English at girls' schools, scoring a very 00:02:10.419 --> 00:02:13.300 good. Which is impressive on its own. For sure. 00:02:13.680 --> 00:02:16.020 But instead of taking that safe, expected route, 00:02:16.340 --> 00:02:20.139 she made a wildly unconventional pivot. She decided 00:02:20.139 --> 00:02:22.340 she wanted to study mathematics at the University 00:02:22.340 --> 00:02:24.819 of Erlangen, Nuremberg. Which, of course, presented 00:02:24.819 --> 00:02:28.039 an immediate systemic wall. Women were legally 00:02:28.039 --> 00:02:30.539 and practically excluded from full enrollment 00:02:30.539 --> 00:02:33.120 at universities in Germany at that time. So completely 00:02:33.120 --> 00:02:35.759 shut out. Literally. Yeah. The Academic Senate 00:02:35.759 --> 00:02:38.979 had explicitly declared that mixed sex education 00:02:38.979 --> 00:02:42.360 would, in their words, overthrow all academic 00:02:42.360 --> 00:02:45.860 order. Wow. Overthrow all academic order just 00:02:45.860 --> 00:02:49.280 by being there. Exactly. Consequently, she couldn't 00:02:49.280 --> 00:02:51.599 simply enroll as a student. She had to petition 00:02:51.599 --> 00:02:54.039 individual professors for special unofficial 00:02:54.039 --> 00:02:56.439 permission just to sit in on their classes as 00:02:56.439 --> 00:02:58.620 an auditor. And she just kept showing up. I mean, 00:02:58.919 --> 00:03:00.960 eventually those rigid restrictions loosened 00:03:00.960 --> 00:03:02.840 slightly, allowing her to officially enter the 00:03:02.840 --> 00:03:04.879 university where she became the only woman in 00:03:04.879 --> 00:03:08.180 her school. The only one. Yeah. By 1907, she 00:03:08.180 --> 00:03:10.240 earned her doctorate under a mathematician named 00:03:10.240 --> 00:03:13.340 Paul Gordon, graduating summa cum laude. Great. 00:03:13.500 --> 00:03:16.060 And Gordon was part of a very computational school 00:03:16.060 --> 00:03:19.520 of mathematics. Her thesis under him was incredibly 00:03:19.520 --> 00:03:22.400 dense, culminating in a massive list of over 00:03:22.400 --> 00:03:26.060 300 explicitly worked out mathematical invariants. 00:03:26.379 --> 00:03:29.020 Just page after page of calculations. Exactly. 00:03:29.379 --> 00:03:32.180 And that computational approach is key to understanding 00:03:32.180 --> 00:03:35.280 her later evolution. She spent her early career 00:03:35.580 --> 00:03:38.500 grinding out these highly specific, incredibly 00:03:38.500 --> 00:03:41.560 lengthy mathematical proofs. But her perspective 00:03:41.560 --> 00:03:44.360 was about to shift drastically. Yeah. But first, 00:03:44.539 --> 00:03:47.020 even with a doctorate and a summa cum laude distinction, 00:03:47.479 --> 00:03:49.680 she spent the next seven years working at the 00:03:49.680 --> 00:03:52.020 Mathematical Institute of Arlong and completely 00:03:52.020 --> 00:03:54.699 unpaid. Seven years. Seven years simply because 00:03:54.699 --> 00:03:57.199 of her gender. And I have to point out my absolute 00:03:57.199 --> 00:04:00.039 favorite detail from this era. She later looked 00:04:00.039 --> 00:04:02.580 back at her own computational thesis and those 00:04:02.580 --> 00:04:05.580 early painstaking papers and referred them as 00:04:05.580 --> 00:04:08.900 absolute crap. Yes, I love that detail. It's 00:04:08.900 --> 00:04:10.479 just brilliant. It's like spending years writing 00:04:10.479 --> 00:04:12.599 a dictionary from scratch only to realize later 00:04:12.599 --> 00:04:14.740 you should have just invented the alphabet. That 00:04:14.740 --> 00:04:17.060 is a perfect way to put it. She recognized that 00:04:17.060 --> 00:04:20.240 endlessly computing specific isolated examples 00:04:20.240 --> 00:04:24.199 was the hardest least efficient way to do math. 00:04:24.579 --> 00:04:26.540 And that realization caught the attention of 00:04:26.540 --> 00:04:29.439 two titans of mathematics, David Hilbert and 00:04:29.439 --> 00:04:33.410 Felix Klein. So, in 1915, they invited Noder 00:04:33.410 --> 00:04:35.730 to join the mathematics department at the University 00:04:35.730 --> 00:04:38.370 of Göttingen. Which was huge, right? Oh, massive. 00:04:38.509 --> 00:04:40.509 Yeah. It was essentially the intellectual center 00:04:40.509 --> 00:04:42.649 of the mathematical world at the time. They needed 00:04:42.649 --> 00:04:46.129 her specific expertise in invariant theory, but 00:04:46.129 --> 00:04:49.670 the philosophical faculty at Göttingen vehemently 00:04:49.670 --> 00:04:52.360 objected to her arrival. Naturally. Yeah. They 00:04:52.360 --> 00:04:54.540 asked the administration, quote, What will our 00:04:54.540 --> 00:04:56.519 soldiers think when they return to the university 00:04:56.519 --> 00:04:58.800 and find that they are required to learn at the 00:04:58.800 --> 00:05:01.920 feet of a woman? Ugh. But Hilbert's response 00:05:01.920 --> 00:05:04.420 to that objection is legendary. It really is. 00:05:04.579 --> 00:05:06.939 He basically scolded the faculty, stating on 00:05:06.939 --> 00:05:08.899 the record that the candidate sex was completely 00:05:08.899 --> 00:05:11.160 irrelevant because the university was, quote, 00:05:11.759 --> 00:05:14.139 not a bathhouse. It's such a great comeback. 00:05:14.779 --> 00:05:17.860 But despite Hilbert's forceful defense, the systemic 00:05:17.860 --> 00:05:21.170 barriers largely held firm. For her first four 00:05:21.170 --> 00:05:24.209 years at Guttigen, Nother possessed no official 00:05:24.209 --> 00:05:26.930 academic title, and she still wasn't paid a salary. 00:05:27.610 --> 00:05:30.110 Unbelievable. Yeah. She was forced to deliver 00:05:30.110 --> 00:05:33.009 her lectures under Hilbert's name, acting on 00:05:33.009 --> 00:05:36.120 paper as his assistant. But she didn't just survive 00:05:36.120 --> 00:05:38.699 this environment. Almost immediately upon arriving, 00:05:38.939 --> 00:05:41.279 she tackled that massive looming problem for 00:05:41.279 --> 00:05:43.620 Einstein that we mentioned earlier. The energy 00:05:43.620 --> 00:05:46.560 paradox. Exactly. Solving the energy conservation 00:05:46.560 --> 00:05:49.220 paradox in general relativity would define her 00:05:49.220 --> 00:05:52.259 first major era of work. So to understand the 00:05:52.259 --> 00:05:54.959 problem she solved, we have to look at how general 00:05:54.959 --> 00:05:58.430 relativity changed physics. Einstein proposed 00:05:58.430 --> 00:06:00.730 that gravity wasn't just a pull between objects. 00:06:01.029 --> 00:06:02.810 Right, it was something more fundamental. Yeah, 00:06:02.829 --> 00:06:05.189 it was the actual warping and curving of space 00:06:05.189 --> 00:06:07.730 -time itself. But when physicists applied traditional 00:06:07.730 --> 00:06:10.290 mathematics to this warping space -time, it looked 00:06:10.290 --> 00:06:12.410 like energy was occasionally being created or 00:06:12.410 --> 00:06:15.149 destroyed. Which is a huge red flag. Totally. 00:06:15.509 --> 00:06:17.750 That broke the law of conservation of energy, 00:06:18.170 --> 00:06:21.329 which is a foundational tiller of physics. Hilbert 00:06:21.329 --> 00:06:25.000 and Klein brought Noether in. specifically to 00:06:25.000 --> 00:06:27.139 analyze the mathematical architecture of this 00:06:27.139 --> 00:06:30.680 problem. And in 1918, she resolved it by proving 00:06:30.680 --> 00:06:33.779 what is now universally known as Noether's theorem. 00:06:34.259 --> 00:06:36.759 Okay, let's break that theorem down because the 00:06:36.759 --> 00:06:39.040 formal definition states that a conservation 00:06:39.040 --> 00:06:42.699 law is associated with any differentiable symmetry 00:06:42.699 --> 00:06:45.379 of a physical system. That is a mouthful. It 00:06:45.379 --> 00:06:47.439 really is. It's an incredibly heavy string of 00:06:47.439 --> 00:06:50.100 words for you, the listener, to visualize. Right. 00:06:50.220 --> 00:06:51.860 Well, if we connect this to the bigger picture, 00:06:52.139 --> 00:06:55.079 let's simplify the concept of symmetry. Think 00:06:55.079 --> 00:06:57.259 of a symmetry as a fundamental feature of a physical 00:06:57.259 --> 00:07:00.180 system that remains completely unchanged even 00:07:00.180 --> 00:07:02.160 when you shift it or transform it. Okay, tracking 00:07:02.160 --> 00:07:04.120 with you. No, they're mathematically proved. 00:07:04.350 --> 00:07:06.550 that if the laws governing a physical experiment 00:07:06.550 --> 00:07:09.209 work the exact same way today as they will tomorrow, 00:07:09.509 --> 00:07:11.850 which is called time symmetry, then the total 00:07:11.850 --> 00:07:14.470 energy within that system must absolutely be 00:07:14.470 --> 00:07:16.970 conserved. Got it. Furthermore, if the experiment 00:07:16.970 --> 00:07:19.629 works the exact same way, regardless of which 00:07:19.629 --> 00:07:22.129 direction it's facing, which is rotational symmetry, 00:07:23.110 --> 00:07:25.829 then angular momentum must be conserved. So they 00:07:25.829 --> 00:07:29.050 are linked. Exactly. She proved that the conservation 00:07:29.050 --> 00:07:31.449 laws of physics aren't just arbitrary rules we 00:07:31.449 --> 00:07:33.850 observed and wrote down. They are the direct 00:07:33.980 --> 00:07:37.379 inescapable mathematical consequence of the symmetries 00:07:37.379 --> 00:07:40.680 in nature. The sources offer a fantastic analogy 00:07:40.680 --> 00:07:44.420 to help ground this. Picture a jagged asteroid 00:07:44.420 --> 00:07:47.060 tumbling through deep space. The asteroid itself 00:07:47.060 --> 00:07:49.980 is completely asymmetric. It's a lumpy, irregular 00:07:49.980 --> 00:07:53.279 rock. But Noether's theorem isn't concerned with 00:07:53.279 --> 00:07:55.699 the shape of the rock. It focuses on the physical 00:07:55.699 --> 00:07:58.100 laws governing the space the rock is moving through. 00:07:58.100 --> 00:07:59.980 Right, the environment. Because the laws of physics 00:07:59.980 --> 00:08:02.699 are rotationally symmetric, meaning empty space 00:08:02.699 --> 00:08:05.790 doesn't have a preferred direction. up or down, 00:08:05.910 --> 00:08:07.970 the angular momentum of that tumbling asteroid 00:08:07.970 --> 00:08:10.670 is strictly conserved. And here's where it gets 00:08:10.670 --> 00:08:12.949 really interesting. Oh, this is the best part. 00:08:13.490 --> 00:08:15.610 No other figured out that in Einstein's general 00:08:15.610 --> 00:08:18.810 relativity, space -time is warping, meaning time 00:08:18.810 --> 00:08:21.490 symmetry is locally broken. Therefore, energy 00:08:21.490 --> 00:08:23.870 doesn't have to be conserved locally, but it 00:08:23.870 --> 00:08:27.050 is conserved globally across the universe. She 00:08:27.050 --> 00:08:29.810 essentially saved general relativity. Handing 00:08:29.810 --> 00:08:32.470 Albert Einstein the mathematical proof that validated 00:08:32.470 --> 00:08:35.919 his greatest theory, would be the crowning achievement 00:08:35.919 --> 00:08:38.500 of anyone's lifetime. I mean, most scientists 00:08:38.500 --> 00:08:41.360 would build an entire career on that single theorem. 00:08:41.799 --> 00:08:44.159 Absolutely. Noether, however, recognized that 00:08:44.159 --> 00:08:46.720 the same structural bird's -eye view she applied 00:08:46.720 --> 00:08:49.779 to physical symmetries could be used to completely 00:08:49.779 --> 00:08:52.879 dismantle and rebuild the very rules of mathematics 00:08:52.879 --> 00:08:55.240 itself. Wait, let me push back on this on behalf 00:08:55.240 --> 00:08:57.580 of the listener for a second. Up to this point, 00:08:57.820 --> 00:08:59.860 mathematics, even at its highest levels, was 00:08:59.860 --> 00:09:02.899 highly computational. Very much so. Like, if 00:09:02.899 --> 00:09:05.500 you look at Paul Gordon's era, the focus was 00:09:05.500 --> 00:09:08.200 on grinding out massive proofs and finding specific 00:09:08.200 --> 00:09:11.120 invariants. Isn't math supposed to be about calculating 00:09:11.120 --> 00:09:13.649 actual numbers and finding specific answers? 00:09:13.710 --> 00:09:15.470 That's how a lot of people viewed it. So why 00:09:15.470 --> 00:09:17.850 does moving away from specific examples to pure 00:09:17.850 --> 00:09:21.330 abstraction make her so revolutionary? This raises 00:09:21.330 --> 00:09:23.809 an important question about how we define progress 00:09:23.809 --> 00:09:27.350 in mathematics. Noether developed a uniquely 00:09:27.350 --> 00:09:30.330 conceptual style of working, what in German is 00:09:30.330 --> 00:09:33.610 called Begrifflich Mathematik. Conceptual mathematics? 00:09:33.889 --> 00:09:36.690 Exactly. The Dutch mathematician B. L. van der 00:09:36.690 --> 00:09:39.210 Worden, who worked closely with her, explained 00:09:39.210 --> 00:09:42.129 it perfectly. He noted that her dieting maxim 00:09:42.129 --> 00:09:45.029 was that relationships between numbers only become 00:09:45.029 --> 00:09:47.389 fully productive when they are isolated from 00:09:47.389 --> 00:09:49.649 particular objects and made into universally 00:09:49.649 --> 00:09:52.649 valid concepts. So she was essentially stripping 00:09:52.649 --> 00:09:55.330 the specific numbers out of the math to find 00:09:55.330 --> 00:09:57.889 the architectural blueprints underneath. Precisely. 00:09:58.009 --> 00:10:01.190 Instead of proving a theorem for a specific polynomial, 00:10:01.750 --> 00:10:03.870 she looked for the underlying structural rules 00:10:03.870 --> 00:10:06.909 that governed all polynomials. This led to her 00:10:06.909 --> 00:10:09.129 revolutionary work with mathematical structures 00:10:09.129 --> 00:10:12.549 called rings and ideals. Think of a ring not 00:10:12.549 --> 00:10:15.269 as a physical shape, but as a defined universe 00:10:15.269 --> 00:10:17.669 of numbers where you can add, subtract, and multiply 00:10:17.669 --> 00:10:20.240 like the integers on a clock face. But division 00:10:20.240 --> 00:10:22.460 might not work perfectly without leaving remainders. 00:10:22.480 --> 00:10:25.159 Okay, I can picture that. Noether wasn't interested 00:10:25.159 --> 00:10:27.639 in computing the specific numbers inside that 00:10:27.639 --> 00:10:30.120 universe. She was mapping the laws governing 00:10:30.120 --> 00:10:33.039 the universe itself. And mapping those laws led 00:10:33.039 --> 00:10:35.539 to her elegant use of something called the ascending 00:10:35.539 --> 00:10:38.240 chain condition, which feels like a vital piece 00:10:38.240 --> 00:10:40.940 of this puzzle. It is the bedrock of her algebraic 00:10:40.940 --> 00:10:44.240 work. The ascending chain condition deals with 00:10:44.240 --> 00:10:47.129 nested sets of mathematical ideals. Think of 00:10:47.129 --> 00:10:49.470 them like Russian nesting dolls of equations, 00:10:49.850 --> 00:10:51.830 one fitting inside the other. OK, the nesting 00:10:51.830 --> 00:10:53.870 dolls. Yeah. In order to prove that in certain 00:10:53.870 --> 00:10:56.950 mathematical structures, this chain of nested 00:10:56.950 --> 00:11:00.429 ideals cannot go on infinitely, it must eventually 00:11:00.429 --> 00:11:03.549 terminate. You hit a solid foundation. So by 00:11:03.549 --> 00:11:05.909 proving that the chain eventually stops, she 00:11:05.909 --> 00:11:08.149 demonstrated that no matter how deep you go into 00:11:08.149 --> 00:11:10.690 these mathematical structures, you won't fall 00:11:10.690 --> 00:11:13.460 forever. You hit a floor. And knowing that floor 00:11:13.460 --> 00:11:16.100 exists allowed mathematicians to confidently 00:11:16.100 --> 00:11:18.759 build entirely new theoretical architectures 00:11:18.759 --> 00:11:22.200 on top of it. Mathematical objects that satisfy 00:11:22.200 --> 00:11:24.879 this foundational condition are now literally 00:11:24.879 --> 00:11:29.080 named no theory in inner honor. Today, mathematicians 00:11:29.080 --> 00:11:32.100 work with no theory in rings, no theory in modules, 00:11:32.720 --> 00:11:35.259 and no theory in spaces. So what does this all 00:11:35.259 --> 00:11:38.820 mean? By working strictly with these vast abstractions, 00:11:39.100 --> 00:11:41.299 she essentially handed future mathematicians 00:11:41.299 --> 00:11:44.200 the skeleton key to abstract algebra. She really 00:11:44.200 --> 00:11:46.080 did. You created a framework that allowed them 00:11:46.080 --> 00:11:49.000 to solve entirely new classes of problems without 00:11:49.000 --> 00:11:51.919 getting dogged down in endless computation. And 00:11:51.919 --> 00:11:54.080 what I find so compelling is that this massive 00:11:54.080 --> 00:11:57.620 shift toward the conceptual disability to look 00:11:57.620 --> 00:12:00.080 past superficial details to find the universal 00:12:00.080 --> 00:12:03.460 truth underneath extended perfectly to how she 00:12:03.500 --> 00:12:05.700 interacted with the people around her. Oh, absolutely. 00:12:05.879 --> 00:12:07.860 Her mind was constantly living in the abstract 00:12:07.860 --> 00:12:10.419 clouds, but her heart was fiercely dedicated 00:12:10.419 --> 00:12:12.820 to the students in front of her. The historical 00:12:12.820 --> 00:12:15.200 accounts highlight a fascinating dichotomy in 00:12:15.200 --> 00:12:17.879 her personality. She had an incredibly eccentric 00:12:17.879 --> 00:12:20.580 presence and a total lack of vanity. Totally 00:12:20.580 --> 00:12:23.139 unpretentious. Yeah. The sources describe her 00:12:23.139 --> 00:12:25.799 speaking very quickly during lectures, frequently 00:12:25.799 --> 00:12:29.110 abandoning her lesson plans entirely. Her classes 00:12:29.110 --> 00:12:32.049 were so spontaneous, dense, and intense that 00:12:32.049 --> 00:12:34.649 they often alienated casual observers. People 00:12:34.649 --> 00:12:37.029 just couldn't keep up. Right. People would drop 00:12:37.029 --> 00:12:39.909 in to audit her class, become completely overwhelmed 00:12:39.909 --> 00:12:42.090 by the abstraction, and leave in frustration 00:12:42.090 --> 00:12:44.360 after half an hour. But the students who stayed 00:12:44.360 --> 00:12:46.720 her devoted followers, who became known as the 00:12:46.720 --> 00:12:50.500 Nowher Boys, absolutely worshipped her. I love 00:12:50.500 --> 00:12:52.480 the contradiction in how she taught. It's very 00:12:52.480 --> 00:12:55.320 striking. On one hand, she was dubbed a severe 00:12:55.320 --> 00:12:59.019 critic. She demanded absolute mathematical accuracy 00:12:59.019 --> 00:13:01.559 from her students and could be incredibly blunt 00:13:01.559 --> 00:13:03.820 if your logic was flawed. She didn't hold back. 00:13:03.960 --> 00:13:06.620 Not at all. But on the other hand, she was deeply 00:13:06.620 --> 00:13:09.840 nurturing. There's a wonderful story where the 00:13:09.840 --> 00:13:12.340 university building was locked down for a state 00:13:12.340 --> 00:13:14.779 holiday. Oh, I know this one. Yeah, so instead 00:13:14.779 --> 00:13:17.279 of canceling class, she simply gathered her students, 00:13:17.759 --> 00:13:19.500 walked them out through the woods, and continued 00:13:19.500 --> 00:13:22.240 lecturing at a local coffee house. That's just 00:13:22.240 --> 00:13:26.240 so her. She was also entirely unconcerned with 00:13:26.240 --> 00:13:30.580 societal norms or traditional appearances. Olgotowski 00:13:30.580 --> 00:13:32.779 Todd, another distinguished mathematician of 00:13:32.779 --> 00:13:35.720 the era, recalled a luncheon where Noether was 00:13:35.720 --> 00:13:38.039 so wholly engrossed in discussing a mathematical 00:13:38.039 --> 00:13:41.919 concept that she was gesticulating wildly, spilling 00:13:41.919 --> 00:13:44.480 her food down her dress and simply wiping it 00:13:44.480 --> 00:13:46.879 off with a napkin, completely unperturbed. Just 00:13:46.879 --> 00:13:49.620 totally focused on the math. Exactly. She didn't 00:13:49.620 --> 00:13:52.080 care about the spilled food or the stairs. She 00:13:52.080 --> 00:13:54.460 only cared about the purity of the ideas being 00:13:54.460 --> 00:13:56.639 discussed. And she didn't care who got the credit 00:13:56.639 --> 00:13:59.019 for those ideas either. That is perhaps her most 00:13:59.019 --> 00:14:01.220 remarkable trait in the highly competitive world 00:14:01.220 --> 00:14:04.440 of high -level academia. She was completely un 00:14:04.440 --> 00:14:07.600 -egotistical. Which is rare. Very. She frequently 00:14:07.600 --> 00:14:09.519 allowed her students and colleagues to claim 00:14:09.519 --> 00:14:12.159 credit for her own original ideas to help them 00:14:12.159 --> 00:14:15.419 build their careers. Her spontaneous, rapid -fire 00:14:15.419 --> 00:14:18.139 discussions in class directly formed the foundational 00:14:18.139 --> 00:14:21.100 basis for major, field -defining textbooks, like 00:14:21.100 --> 00:14:23.220 Van der Weerden's Modern Algebra. She was just 00:14:23.220 --> 00:14:25.100 happy the work was getting out there. Right. 00:14:25.240 --> 00:14:27.820 She didn't seek the spotlight. She viewed mathematics 00:14:27.820 --> 00:14:31.379 as a collaborative pursuit of truth. That unshakable, 00:14:31.460 --> 00:14:34.179 nurturing spirit, her focus purely on truth and 00:14:34.179 --> 00:14:36.899 community, remained her ultimate armor when the 00:14:36.899 --> 00:14:39.200 political climate around her turned incredibly 00:14:39.200 --> 00:14:43.379 dark. As we move into the 1930s, the world she 00:14:43.379 --> 00:14:45.759 helped build in Germany was violently disrupted. 00:14:46.000 --> 00:14:48.980 It was. In 1933, the Nazi government came to 00:14:48.980 --> 00:14:51.600 power in Germany. One of the administration's 00:14:51.600 --> 00:14:53.679 earliest sweeping actions was the passage of 00:14:53.679 --> 00:14:56.039 the law for the restoration of the professional 00:14:56.039 --> 00:14:58.779 civil service. Right. The text notes that this 00:14:58.779 --> 00:15:01.039 law systematically dismissed Jews and politically 00:15:01.039 --> 00:15:03.120 suspects employees from all government jobs, 00:15:03.519 --> 00:15:06.399 which explicitly included university professorships. 00:15:06.679 --> 00:15:08.620 No, that was targeted on multiple fronts. Oh, 00:15:08.879 --> 00:15:10.639 so. Well, she was dismissed due to her Jewish 00:15:10.639 --> 00:15:12.960 ancestry. And additionally, student leaders had 00:15:12.960 --> 00:15:14.860 submitted complaints regarding her status as 00:15:14.860 --> 00:15:18.220 a quote, Marxist leaning Jewish. This was owing 00:15:18.220 --> 00:15:20.960 to her previous academic visits to Moscow and 00:15:20.960 --> 00:15:23.600 her known pacifist social democratic leanings. 00:15:23.840 --> 00:15:25.600 And just to be clear to you listening, we are 00:15:25.600 --> 00:15:27.620 impartially reporting the facts from the source 00:15:27.620 --> 00:15:31.090 material here. The reality is she had given her 00:15:31.090 --> 00:15:33.889 entire life to elevating her country's academic 00:15:33.889 --> 00:15:37.070 prestige, only to be cast out in an instant based 00:15:37.070 --> 00:15:39.870 on these targeted laws. Yeah. Yet the sources 00:15:39.870 --> 00:15:42.269 note she accepted the decision with remarkable 00:15:42.269 --> 00:15:45.429 calmness. While others around her were understandably 00:15:45.429 --> 00:15:48.549 panicking, the mathematician Herman Weil observed 00:15:48.549 --> 00:15:51.330 that neither became a moral solace amidst the 00:15:51.330 --> 00:15:53.750 hatred and despair. She really was a pillar for 00:15:53.750 --> 00:15:56.049 them. She simply kept teaching. She gathered 00:15:56.049 --> 00:15:58.250 students in her own apartment to continue their 00:15:58.250 --> 00:16:01.110 discussion. on class field theory. There is one 00:16:01.110 --> 00:16:03.389 detail from this period that perfectly captures 00:16:03.389 --> 00:16:06.269 her focus. One of her students actually showed 00:16:06.269 --> 00:16:08.629 up to her apartment for a lesson wearing the 00:16:08.629 --> 00:16:12.549 uniform of the Nazi Sturmabteilung, the SA paramilitary 00:16:12.549 --> 00:16:14.970 organization. Unbelievable. Another was reportedly 00:16:14.970 --> 00:16:17.970 completely unfazed by his uniform. She let him 00:16:17.970 --> 00:16:20.509 in, taught the mathematics as usual, and later 00:16:20.509 --> 00:16:22.649 even laughed about the sheer absurdity of the 00:16:22.649 --> 00:16:25.049 situation. Her focus remains strictly on the 00:16:25.049 --> 00:16:26.610 mathematics and the people who wanted to learn 00:16:26.610 --> 00:16:28.990 it, regardless of the terror outside her door. 00:16:29.710 --> 00:16:32.309 But ultimately, remaining in Germany became physically 00:16:32.309 --> 00:16:35.690 and professionally impossible. Yes. She was forced 00:16:35.690 --> 00:16:38.649 into exile, leaving behind her home, her native 00:16:38.649 --> 00:16:41.029 language, and the mathematical center she had 00:16:41.029 --> 00:16:44.340 spent decades building. She found refuge in the 00:16:44.340 --> 00:16:47.480 United States, accepting a position at Bryn Mawr 00:16:47.480 --> 00:16:50.500 College in Pennsylvania. A fresh start. Exactly. 00:16:51.059 --> 00:16:53.440 There, she formed a new group of dedicated female 00:16:53.440 --> 00:16:56.080 researchers, sometimes referred to as the Nother 00:16:56.080 --> 00:16:58.559 Girls. She also secured a lecturing position 00:16:58.559 --> 00:17:00.960 at the Institute for Advanced Study in Princeton. 00:17:01.340 --> 00:17:04.680 Though ever the astute and blunt observer, she 00:17:04.680 --> 00:17:06.799 sharply noted that she wasn't truly welcome at 00:17:06.799 --> 00:17:08.890 Princeton University itself. referring to it 00:17:08.890 --> 00:17:11.490 as a men's university where nothing female was 00:17:11.490 --> 00:17:14.029 admitted. She called it like she saw it. Always. 00:17:14.250 --> 00:17:16.490 She spent roughly a year and a half in the United 00:17:16.490 --> 00:17:19.069 States enjoying a supportive environment and 00:17:19.069 --> 00:17:21.269 fully absorbing herself and her favorite subjects, 00:17:21.950 --> 00:17:23.930 but tragically her life and her work were cut 00:17:23.930 --> 00:17:27.869 short in 1935. She was only 53 years old. It 00:17:27.869 --> 00:17:30.890 was incredibly sudden. Doctors had found a pelvic 00:17:30.890 --> 00:17:33.230 tumor, and during the subsequent surgery, they 00:17:33.230 --> 00:17:35.670 discovered an ovarian cyst the size of a large 00:17:35.670 --> 00:17:39.049 cantaloupe. Just massive. Yeah. And for a few 00:17:39.049 --> 00:17:41.589 days post -operation, she seemed to be recovering 00:17:41.589 --> 00:17:44.710 normally. But then she suffered a sudden, severe 00:17:44.710 --> 00:17:48.009 circulatory collapse. Her temperature skyrocketed, 00:17:48.049 --> 00:17:52.170 and she passed away on April 14, 1935. So fast. 00:17:52.470 --> 00:17:54.730 Following her death, her ashes were buried under 00:17:54.730 --> 00:17:57.990 the cloistered walkway of Bryn Mawr's old library. 00:17:58.329 --> 00:18:00.630 The outpouring of grief and profound respect 00:18:00.630 --> 00:18:02.650 from the global scientific community was just 00:18:02.650 --> 00:18:04.789 immense. Albert Einstein wrote a letter to the 00:18:04.789 --> 00:18:07.089 New York Times publicly stating that she was 00:18:07.089 --> 00:18:09.730 the most significant creative mathematical genius 00:18:09.730 --> 00:18:11.750 produced since the higher education of women 00:18:11.750 --> 00:18:14.630 began. That is high praise and as we reflect 00:18:14.630 --> 00:18:16.690 on this deep dive with you today it is vital 00:18:16.690 --> 00:18:19.230 to remember exactly why Emmy Noether's legacy 00:18:19.230 --> 00:18:21.970 matters so profoundly to our modern world. It 00:18:21.970 --> 00:18:24.230 affects everything. It really does whether we 00:18:24.230 --> 00:18:27.769 are theoretical physicists calculating the conservation 00:18:27.769 --> 00:18:30.250 of energy and momentum, or computer scientists 00:18:30.250 --> 00:18:33.230 utilizing complex algorithms based on noetherian 00:18:33.230 --> 00:18:35.890 rings to secure data, we are literally speaking 00:18:35.890 --> 00:18:38.710 her language. We owe her so much. By stripping 00:18:38.710 --> 00:18:41.170 away the superficial numbers to look at the invisible 00:18:41.170 --> 00:18:43.650 architecture underneath, she created shortcuts 00:18:43.650 --> 00:18:45.769 to understanding the universe that have saved 00:18:45.769 --> 00:18:48.829 modern scientists lifetimes of work. The source 00:18:48.829 --> 00:18:52.089 material details how her theorem explicitly connected 00:18:52.089 --> 00:18:54.690 physical symmetry to universal conservation laws. 00:18:55.180 --> 00:18:58.380 But what's truly mind -bending is where her mathematical 00:18:58.380 --> 00:19:00.500 framework takes us tomorrow. I know. It's wild 00:19:00.500 --> 00:19:02.900 to think about. The source material shows how 00:19:02.900 --> 00:19:05.339 Noether proved that the profound symmetries of 00:19:05.339 --> 00:19:08.400 nature dictate its universal laws. But if we 00:19:08.400 --> 00:19:11.220 look at her own life, it was fiercely asymmetric. 00:19:11.220 --> 00:19:14.539 Right. She faced immense systemic bias. She was 00:19:14.539 --> 00:19:16.839 excluded because she was a woman, exiled because 00:19:16.839 --> 00:19:19.640 she was Jewish. Yet she still managed to gift 00:19:19.640 --> 00:19:23.160 humanity with universal truths. It makes you 00:19:23.160 --> 00:19:25.880 wonder. What other profound symmetries or universal 00:19:25.880 --> 00:19:28.839 truth in our own world are we missing today simply 00:19:28.839 --> 00:19:31.039 because we continue to exclude certain perspectives 00:19:31.039 --> 00:19:33.799 from the conversation? That is a brilliant thought 00:19:33.799 --> 00:19:36.559 to leave you with. Sometimes to truly see the 00:19:36.559 --> 00:19:38.720 hidden architecture of the universe, you have 00:19:38.720 --> 00:19:41.380 to look past the rigid computational rules we've 00:19:41.380 --> 00:19:43.599 created for ourselves. Thank you for joining 00:19:43.599 --> 00:19:46.019 us on this custom tailored deep dive into the 00:19:46.019 --> 00:19:48.539 extraordinary mind of Emmy Noether. Keep questioning 00:19:48.539 --> 00:19:50.339 the structure of things and we'll see you next 00:19:50.339 --> 00:19:50.519 time.