WEBVTT 00:00:00.000 --> 00:00:02.839 Imagine for just a second that you're trying 00:00:02.839 --> 00:00:05.879 to build a functioning spacecraft. Okay a spacecraft. 00:00:06.000 --> 00:00:10.320 Yeah, but here's the catch you Have never seen 00:00:10.320 --> 00:00:12.320 a blueprint You haven't like been taught the 00:00:12.320 --> 00:00:14.720 laws of physics or anything and you're working 00:00:14.720 --> 00:00:18.320 entirely alone in a cave, right? So impossible, 00:00:18.600 --> 00:00:21.019 basically. Exactly. But against all conventional 00:00:21.019 --> 00:00:23.940 logic, the ship you build doesn't just fly. It 00:00:23.940 --> 00:00:27.100 travels faster and further than anything the 00:00:27.100 --> 00:00:29.339 top engineers in the world have ever even conceived 00:00:29.339 --> 00:00:31.920 of. Wow. I mean, it sounds like the origin story 00:00:31.920 --> 00:00:34.780 of like a comic book character or something, 00:00:34.799 --> 00:00:38.020 just a mind operating entirely outside the boundaries 00:00:38.020 --> 00:00:40.600 of human knowledge. It really does. But today, 00:00:40.600 --> 00:00:42.899 we're actually exploring a reality that mirrors 00:00:42.899 --> 00:00:45.740 that exact scenario. Welcome to today's Deep 00:00:45.740 --> 00:00:48.170 Dive. Glad to be here. So we have a massive stack 00:00:48.170 --> 00:00:50.750 of sources today. We're looking at a really comprehensive 00:00:50.750 --> 00:00:54.250 biographical and mathematical overview of Srinivasa 00:00:54.250 --> 00:00:57.450 Ramanujan. Ah yes, a legendary figure. Our mission 00:00:57.450 --> 00:00:59.890 today for you listening is to basically extract 00:00:59.890 --> 00:01:02.270 the ultimate aha moments from a man who, well, 00:01:02.409 --> 00:01:04.189 he essentially pulled advanced mathematics out 00:01:04.189 --> 00:01:06.280 of thin air. He really did. We want to figure 00:01:06.280 --> 00:01:08.640 out what his story reveals about the true nature 00:01:08.640 --> 00:01:11.680 of knowledge and, frankly, genius. Like, how 00:01:11.680 --> 00:01:14.980 does an untrained mind perceive these universal 00:01:14.980 --> 00:01:18.219 truths that experts just, they can't see them? 00:01:18.359 --> 00:01:20.459 It's the ultimate question. Okay, let's unpack 00:01:20.459 --> 00:01:23.219 this. Because to understand how his mind operated, 00:01:23.340 --> 00:01:25.239 we have to look at the environment that forged 00:01:25.239 --> 00:01:27.760 it, right? Definitely. Context is everything 00:01:27.760 --> 00:01:31.500 here. So we are starting in 1887. where in British 00:01:31.500 --> 00:01:34.299 -ruled India, Ramanujan is born into a Tamil 00:01:34.299 --> 00:01:36.459 Brahmin family, and they're living in this small, 00:01:36.739 --> 00:01:40.819 traditional home in Kumbakonam, and they are 00:01:40.819 --> 00:01:43.560 living in deep, deep poverty. Right. I mean, 00:01:43.680 --> 00:01:46.000 the environment was incredibly resource -scarce, 00:01:46.019 --> 00:01:48.459 but the mathematical anomaly that he presented, 00:01:48.799 --> 00:01:50.719 it was just, it was apparent almost immediately. 00:01:50.799 --> 00:01:53.069 Even as a kid, right? Yeah. By the age of 11, 00:01:53.290 --> 00:01:55.430 he had completely exhausted the mathematical 00:01:55.430 --> 00:01:57.609 knowledge of two college students who were renting 00:01:57.609 --> 00:02:00.189 rooms in his family's home. Wait, 11 years old? 00:02:00.450 --> 00:02:04.150 11. And by 13, he had mastered advanced trigonometry 00:02:04.150 --> 00:02:06.670 totally independently. He was already discovering 00:02:06.670 --> 00:02:08.949 complex theorems on his own. Just completely 00:02:08.949 --> 00:02:11.069 disconnected from the global math community. 00:02:11.509 --> 00:02:14.469 Exactly. Entirely isolated. But the crucial spark, 00:02:14.550 --> 00:02:17.110 the thing that really sets him off, happens when 00:02:17.110 --> 00:02:20.439 he's 16. Yes, the book. Right. He gets his hands 00:02:20.439 --> 00:02:23.319 on this library copy of a book by G .S. Carr. 00:02:23.900 --> 00:02:28.319 It's called A Synopsis of Elementary Results 00:02:28.319 --> 00:02:31.960 in Pure and Applied Mathematics. And the structure 00:02:31.960 --> 00:02:36.219 of that specific book. That is the key that unlocked 00:02:36.219 --> 00:02:39.860 Ramanujan's unorthodox brain. How so? What was 00:02:39.860 --> 00:02:41.960 different about it? Well, it wasn't a standard 00:02:41.960 --> 00:02:44.439 textbook. It didn't walk the reader through the 00:02:44.439 --> 00:02:47.219 logic of how to solve a problem step by step. 00:02:47.219 --> 00:02:49.639 It was essentially just a compilation of about 00:02:49.639 --> 00:02:52.219 5 ,000 theorems with almost no proofs provided. 00:02:52.340 --> 00:02:55.020 Just the answers? Just the final equations, literally. 00:02:55.180 --> 00:02:57.680 Let's cause on that, actually. Because the concept 00:02:57.680 --> 00:03:00.580 of a proof is super foundational here. Oh, absolutely. 00:03:00.900 --> 00:03:03.939 In math, a proof is like the logical scaffolding, 00:03:04.020 --> 00:03:06.139 right? It's the step -by -step argument that 00:03:06.139 --> 00:03:08.919 takes you from a basic assumption to a final, 00:03:09.280 --> 00:03:12.020 undeniable conclusion. Precisely. A proof is 00:03:12.020 --> 00:03:14.060 how a mathematician actually demonstrates that 00:03:14.060 --> 00:03:16.120 their answer is correct. It's the show your work 00:03:16.120 --> 00:03:19.419 part. Exactly. It's show your work scaled up 00:03:19.419 --> 00:03:22.300 to a professional academic level. And Carr's 00:03:22.300 --> 00:03:24.759 book basically stripped all of that away. It 00:03:24.759 --> 00:03:26.919 was just a catalog of final answers. It's like, 00:03:26.919 --> 00:03:28.860 OK, it's like someone trying to become a master 00:03:28.860 --> 00:03:31.400 chef, right? But they're only reading a list 00:03:31.400 --> 00:03:33.900 of ingredients. They never see the recipe steps. 00:03:34.080 --> 00:03:37.479 They never learn what a stole even is. That's 00:03:37.479 --> 00:03:39.460 a great way to put it. You know what the final 00:03:39.460 --> 00:03:41.699 dish is supposed to look and taste like, but 00:03:41.699 --> 00:03:44.460 you have to invent the underlying physics of 00:03:44.460 --> 00:03:47.460 cooking entirely on your own just to recreate 00:03:47.460 --> 00:03:50.659 it. And because he lacked those formal recipes. 00:03:51.069 --> 00:03:54.229 You know the proofs. Ramanujan had to forge his 00:03:54.229 --> 00:03:56.810 own neural pathways to reach those mathematical 00:03:56.810 --> 00:03:58.990 conclusions. He had to rewire his own brain. 00:03:59.270 --> 00:04:01.469 Exactly. He rewired his brain to leap straight 00:04:01.469 --> 00:04:04.389 from the problem to the answer, totally bypassing 00:04:04.389 --> 00:04:06.830 the standard logical stepping stones that every 00:04:06.830 --> 00:04:09.039 formally trained mathematician relies on. Which 00:04:09.039 --> 00:04:12.280 is just wild to think about. And stating incredibly 00:04:12.280 --> 00:04:14.439 complex mathematical results without ever showing 00:04:14.439 --> 00:04:17.100 the derivations, that just became his lifelong 00:04:17.100 --> 00:04:20.000 habit. Which is fascinating, but I mean, it completely 00:04:20.000 --> 00:04:22.579 torpedoed his conventional life. Oh, yeah. It 00:04:22.579 --> 00:04:24.639 was a disaster for his schooling. He becomes 00:04:24.639 --> 00:04:28.199 so intensely focused on this bizarre method of 00:04:28.199 --> 00:04:31.060 independent research that he literally fails 00:04:31.060 --> 00:04:35.360 his college exams. In English, in Sanskrit, in 00:04:35.360 --> 00:04:37.680 physiology. He loses his scholarship. Yeah, he 00:04:37.680 --> 00:04:39.939 actually runs away from home at one point, and 00:04:39.939 --> 00:04:42.899 he's living on the absolute brink of starvation. 00:04:43.100 --> 00:04:45.779 His isolation was this profound double -edged 00:04:45.779 --> 00:04:48.420 sword. I mean, on one hand, it caused him immense 00:04:48.420 --> 00:04:50.600 academic failure and physical suffering. Real 00:04:50.600 --> 00:04:52.980 suffering. Yeah. He had no degree, no money, 00:04:53.160 --> 00:04:56.040 no traditional prospects at all. But intellectually, 00:04:56.680 --> 00:04:59.850 his mind just wasn't boxed in. Because he hadn't 00:04:59.850 --> 00:05:02.930 been taught what the academic establishment considered, 00:05:02.930 --> 00:05:05.750 you know, impossible, he wasn't constrained by 00:05:05.750 --> 00:05:07.610 traditional mathematical paradigms. He didn't 00:05:07.610 --> 00:05:09.370 know the rules, so he didn't know he was breaking 00:05:09.370 --> 00:05:12.350 them. Exactly. He was free to explore dimensions 00:05:12.350 --> 00:05:14.870 of numbers that formally trained mathematicians 00:05:14.870 --> 00:05:17.050 wouldn't even think to look at. Which sets up 00:05:17.050 --> 00:05:19.129 this massive collision course because you have 00:05:19.129 --> 00:05:22.069 this isolated college dropout, right? He's working 00:05:22.069 --> 00:05:24.569 as a clerk at the Madras Port Trust for like 00:05:24.569 --> 00:05:27.370 30 rupees a month. doing math on a literal slate 00:05:27.370 --> 00:05:30.610 chalkboard. Right. And he knows he's seeing things 00:05:30.610 --> 00:05:33.029 no one else is seeing. And he desperately needs 00:05:33.029 --> 00:05:35.189 a mathematical peer who can actually read his 00:05:35.189 --> 00:05:38.170 notebooks. So he starts writing letters to British 00:05:38.170 --> 00:05:41.430 academics. And those initial attempts went exactly 00:05:41.430 --> 00:05:44.170 how you might expect. Not well. Not well at all. 00:05:44.250 --> 00:05:47.709 Yeah. He sent his papers to two prominent professors, 00:05:48.110 --> 00:05:51.360 H .F. Baker and E .W. Hobson. and they returned 00:05:51.360 --> 00:05:54.180 his work without a single comment. Just completely 00:05:54.180 --> 00:05:56.259 dismissed him. Totally ignored him. But then 00:05:56.259 --> 00:05:59.720 in January of 1913 he sends a nine -page letter 00:05:59.720 --> 00:06:02.139 packed with unproven theorems to G .H. Hardy 00:06:02.139 --> 00:06:05.470 at Cambridge University. Yes. a major turning 00:06:05.470 --> 00:06:07.990 point. And Hardy is like one of the most prominent 00:06:07.990 --> 00:06:10.250 rigorous mathematicians in the world at this 00:06:10.250 --> 00:06:12.149 time, right? Oh, absolutely. Top of his field. 00:06:12.310 --> 00:06:14.410 So Hardy opens this letter from this unknown 00:06:14.410 --> 00:06:17.649 clerk in India and just sees page after page 00:06:17.649 --> 00:06:20.670 of alien looking formulas, just bizarre assertions 00:06:20.670 --> 00:06:23.250 about infinite series and continued fractions. 00:06:23.709 --> 00:06:25.170 And just to give you a sense of what Hardy was 00:06:25.170 --> 00:06:28.500 actually looking at. A continued fraction is 00:06:28.500 --> 00:06:30.399 a mathematical expression where the denominator 00:06:30.399 --> 00:06:32.600 of a fraction contains another fraction. Okay, 00:06:32.779 --> 00:06:35.019 so a fraction inside a fraction. Right, which 00:06:35.019 --> 00:06:38.209 contains another fraction. potentially go on 00:06:38.209 --> 00:06:40.410 infinitely. That sounds like a nightmare to calculate. 00:06:40.550 --> 00:06:43.529 It is complex. It's a way to represent irrational 00:06:43.529 --> 00:06:46.329 numbers. Numbers that can't be expressed as simple 00:06:46.329 --> 00:06:48.970 fractions like pi with incredible precision. 00:06:49.250 --> 00:06:52.709 Gotcha. But Ramanujan's continued fractions were 00:06:52.709 --> 00:06:56.009 wildly complex. They connected seemingly unrelated 00:06:56.009 --> 00:06:59.149 mathematical concepts in ways that looked almost 00:06:59.149 --> 00:07:02.189 nonsensical to a traditionally trained eye. Okay, 00:07:02.189 --> 00:07:04.050 here's where it gets really interesting though. 00:07:04.069 --> 00:07:05.970 I have to push back on this narrative a bit. 00:07:06.319 --> 00:07:08.300 Because something doesn't add up for me. Sure, 00:07:08.420 --> 00:07:11.139 what is it? If this letter was just nine pages 00:07:11.139 --> 00:07:14.720 of alien equations with zero proofs, why didn't 00:07:14.720 --> 00:07:16.980 Hardy just throw it in the trash like Baker and 00:07:16.980 --> 00:07:19.800 Hobson did? That's a fair point. Right! Like, 00:07:20.000 --> 00:07:22.060 in a pre -internet era, how does a Cambridge 00:07:22.060 --> 00:07:24.259 professor distinguish a once -in -a -century 00:07:24.259 --> 00:07:27.939 genius from a random person writing literal gibberish? 00:07:28.079 --> 00:07:29.980 That is actually the pivotal question of this 00:07:29.980 --> 00:07:32.259 entire story. Because it just seems so unlikely 00:07:32.259 --> 00:07:34.800 that he would even read it. Well, Hardy didn't 00:07:34.800 --> 00:07:37.800 just blindly trust the alien equations. He needed, 00:07:38.120 --> 00:07:42.300 um... A Rosetta Stone, basically. An anchor of 00:07:42.300 --> 00:07:44.120 credibility. Oh, okay. So there was something 00:07:44.120 --> 00:07:46.839 familiar in there. Exactly. Amidst all the wildly 00:07:46.839 --> 00:07:50.379 unfamiliar theorems, Hardy recognized a few formulas. 00:07:50.699 --> 00:07:54.459 Like what? Specifically, he saw a result concerning 00:07:54.459 --> 00:07:56.980 the convergence of a certain series that had 00:07:56.980 --> 00:07:59.040 already been determined by a mathematician named 00:07:59.040 --> 00:08:03.120 G. Bauer back in 1859. And Ramoujian had just 00:08:03.120 --> 00:08:06.000 independently rediscovered it. Yes. He rediscovered 00:08:06.000 --> 00:08:08.439 it entirely on his own. So because Ramanujan 00:08:08.439 --> 00:08:12.240 got that one obscure known theorem correct, it 00:08:12.240 --> 00:08:14.939 validated all the rest of the crazy stuff. It 00:08:14.939 --> 00:08:17.420 provided the context Hardy needed to trust the 00:08:17.420 --> 00:08:19.360 unknown. You know, Hardy realized that no one 00:08:19.360 --> 00:08:21.439 could accidentally stumble onto Bauer's theorem 00:08:21.439 --> 00:08:23.579 while just writing gibberish. That makes a lot 00:08:23.579 --> 00:08:25.660 of sense. As Hardy later concluded regarding 00:08:25.660 --> 00:08:28.040 those wildly unfamiliar continued fractions, 00:08:28.360 --> 00:08:30.920 he said they, quote, must be true because if 00:08:30.920 --> 00:08:33.679 they were not true, no one would have the imagination 00:08:33.679 --> 00:08:36.350 to invent them. Wow. If they weren't true, no 00:08:36.350 --> 00:08:38.110 one would have the imagination to invent them. 00:08:38.289 --> 00:08:40.009 That's a brilliant way to look at it. It really 00:08:40.009 --> 00:08:42.929 is. So Hardy is convinced. He knows he's holding 00:08:42.929 --> 00:08:45.769 lightning in a bottle here. But to do anything 00:08:45.769 --> 00:08:48.649 with it, Ramanujan has to cross the globe to 00:08:48.649 --> 00:08:52.570 Cambridge. Which was a massive monumental hurdle. 00:08:52.710 --> 00:08:55.450 Right. Because of his background. Ramanujan's 00:08:55.450 --> 00:08:58.309 orthodox Brahmin upbringing strictly forbade 00:08:58.309 --> 00:09:01.009 overseas travel. I mean, crossing the ocean meant 00:09:01.009 --> 00:09:03.970 losing his caste. It wasn't just a longboat ride. 00:09:04.009 --> 00:09:07.009 It was a huge cultural taboo. He only agreed 00:09:07.009 --> 00:09:09.570 to leave for England after his mother had this 00:09:09.570 --> 00:09:12.049 vivid dream, right? Where the family goddess 00:09:12.049 --> 00:09:15.409 Namajiri commanded her not to stand in her son's 00:09:15.409 --> 00:09:18.330 way. That's the story. And when he finally arrives 00:09:18.330 --> 00:09:20.350 in Cambridge, we see this incredible collision 00:09:20.350 --> 00:09:23.580 of two Brilliant, but fundamentally opposite 00:09:23.580 --> 00:09:26.659 minds. I can only imagine. Ramanujan was deeply 00:09:26.659 --> 00:09:29.360 religious. He relied almost exclusively on intuition. 00:09:29.779 --> 00:09:32.139 He famously stated, an equation for me has no 00:09:32.139 --> 00:09:34.419 meaning unless it expresses a thought of God. 00:09:34.720 --> 00:09:37.320 A thought of God, wow. Yeah. He claimed to have 00:09:37.320 --> 00:09:39.720 literal visions of blood drops, and he'd see 00:09:39.720 --> 00:09:42.480 the goddess Namajiri unfolding scrolls of complex 00:09:42.480 --> 00:09:45.059 mathematical content right before his eyes. And 00:09:45.059 --> 00:09:47.399 then sitting across the desk from him is G. H. 00:09:47.500 --> 00:09:51.039 Hardy. The exact opposite. Literally. A staunch 00:09:51.039 --> 00:09:53.759 atheist and what his peers called an apostle 00:09:53.759 --> 00:09:56.860 of proof. Yes. For Hardy, mathematical rigor 00:09:56.860 --> 00:10:00.039 was the only religion. If you couldn't prove 00:10:00.039 --> 00:10:03.480 it step by step, it wasn't mathematics. So the 00:10:03.480 --> 00:10:06.059 cultural and philosophical friction there was 00:10:06.059 --> 00:10:09.539 just intense. I mean, Hardy was constantly trying 00:10:09.539 --> 00:10:12.500 to teach Ramanujan the formal math he had missed, 00:10:12.899 --> 00:10:15.720 like how to actually write a proof. Without destroying 00:10:15.720 --> 00:10:18.159 his natural intuition, I assume. Exactly. That 00:10:18.159 --> 00:10:21.080 was the delicate balance. It's like, OK, it's 00:10:21.080 --> 00:10:24.589 like taking a completely self -taught. wildly 00:10:24.589 --> 00:10:27.009 brilliant jazz improviser, someone who plays 00:10:27.009 --> 00:10:30.289 entirely by ear, and forcing them to jam with 00:10:30.289 --> 00:10:33.210 a strict sheet music only classical conductor. 00:10:33.370 --> 00:10:35.350 That's a perfect analogy. The jazz player is 00:10:35.350 --> 00:10:37.230 just feeling the music, jumping straight to the 00:10:37.230 --> 00:10:39.070 climax of the song, and the classical conductor 00:10:39.070 --> 00:10:41.070 is shouting, wait, what time signature is this? 00:10:41.110 --> 00:10:42.570 You have to write down the notes so the rest 00:10:42.570 --> 00:10:44.570 of the orchestra can play along. If we connect 00:10:44.570 --> 00:10:47.610 this to the bigger picture. Progress often requires 00:10:47.610 --> 00:10:49.710 this exact kind of friction. I know you mean. 00:10:50.090 --> 00:10:52.909 Well intuition needs rigor to become universally 00:10:52.909 --> 00:10:56.370 applicable. You need both. Yeah. And their collaboration 00:10:56.370 --> 00:10:59.289 on the partition function is the absolute perfect 00:10:59.289 --> 00:11:01.070 example of this. Okay, let's break that down 00:11:01.070 --> 00:11:02.990 for the listener because the partition function 00:11:02.990 --> 00:11:04.970 sounds super intimidating. It does sound technical. 00:11:05.110 --> 00:11:07.149 But if I'm reading the sources correctly, a partition 00:11:07.149 --> 00:11:09.490 is just figuring out how many ways you can add 00:11:09.490 --> 00:11:12.830 up whole numbers to get a specific target number. 00:11:13.210 --> 00:11:15.330 That's it. Exactly. It's actually very simple 00:11:15.330 --> 00:11:17.750 at its core. Take the number four. Okay, four. 00:11:17.789 --> 00:11:20.389 You can make four by just having four. Right. 00:11:20.570 --> 00:11:23.389 Or three plus one. Right. Or two plus two. Exactly. 00:11:23.610 --> 00:11:25.509 Or two plus one plus one. Or one plus one plus 00:11:25.509 --> 00:11:27.470 one plus one. So the number of partitions for 00:11:27.470 --> 00:11:30.250 four is five. Yep. That seems really simple. 00:11:30.610 --> 00:11:33.450 It is simple until the numbers get bigger. By 00:11:33.450 --> 00:11:36.289 the time you reach the number 200, the number 00:11:36.289 --> 00:11:39.929 of partitions explodes to nearly four. trillion 00:11:39.929 --> 00:11:43.009 ways. Four trillion just for the number 200. 00:11:43.110 --> 00:11:45.409 Almost four trillion, yeah. And mathematicians 00:11:45.409 --> 00:11:48.549 had absolutely no idea how to calculate these 00:11:48.549 --> 00:11:51.750 partitions for large numbers without just counting 00:11:51.750 --> 00:11:53.950 them one by one. Which is impossible. Totally 00:11:53.950 --> 00:11:56.759 impossible. So Ramanujan and Hardy set out to 00:11:56.759 --> 00:11:59.539 create a formula that could predict the exact 00:11:59.539 --> 00:12:02.500 number of partitions for any integer to infinity. 00:12:02.700 --> 00:12:04.559 And to solve it, they created this thing called 00:12:04.559 --> 00:12:07.559 the circle method. Yes, the circle method. I 00:12:07.559 --> 00:12:09.440 read through this part of the source material 00:12:09.440 --> 00:12:11.480 a few times, and I'll admit the mechanics of 00:12:11.480 --> 00:12:13.840 it are really hard to visualize. Like, how does 00:12:13.840 --> 00:12:16.840 a circle help you count whole numbers? It's tricky, 00:12:17.279 --> 00:12:20.980 but imagine you have a massive complex landscape 00:12:20.980 --> 00:12:24.960 of data. but you only care about specific isolated 00:12:24.960 --> 00:12:27.460 peaks within that landscape. Okay, peaks in a 00:12:27.460 --> 00:12:29.759 landscape. The circle method uses the boundary 00:12:29.759 --> 00:12:33.019 of a circle. in the complex plane, which is a 00:12:33.019 --> 00:12:36.279 continuous, smooth curve, to enclose and analyze 00:12:36.279 --> 00:12:39.000 the behavior of functions near the edges of that 00:12:39.000 --> 00:12:40.919 circle. So you're drawing a boundary. Right. 00:12:41.100 --> 00:12:43.580 By using calculus to integrate around this path, 00:12:43.799 --> 00:12:46.059 they could essentially sift out the exact discrete 00:12:46.059 --> 00:12:48.080 whole numbers they were looking for. Oh, wow. 00:12:48.139 --> 00:12:50.759 They used continuous flowing mathematics to perfectly 00:12:50.759 --> 00:12:54.039 cache discrete, jagged numbers. That is so cool. 00:12:54.080 --> 00:12:56.720 So they basically built a mathematical net to 00:12:56.720 --> 00:12:59.000 catch the trillion different ways to add up to 00:12:59.000 --> 00:13:02.210 200. exactly what they did. And Rimojin's intuition 00:13:02.210 --> 00:13:05.309 saw where the net needed to be cast, while Hardy's 00:13:05.309 --> 00:13:08.029 rigorous calculus built the actual mesh of the 00:13:08.029 --> 00:13:11.049 net so it wouldn't break. Without Hardy, Rimojin's 00:13:11.049 --> 00:13:13.610 insights would have just remained incomprehensible 00:13:13.610 --> 00:13:16.950 visions on a slate. Right. But without Rimojin, 00:13:17.450 --> 00:13:20.110 Hardy would never have had the raw, otherworldly 00:13:20.110 --> 00:13:22.549 material to build those mathematical roads in 00:13:22.549 --> 00:13:24.590 the first place. It's the ultimate partnership. 00:13:24.799 --> 00:13:28.080 But this incredible output came at a massive 00:13:28.080 --> 00:13:30.980 physical cost. It really did. The sources paint 00:13:30.980 --> 00:13:33.700 a pretty grim picture of Ramanujan's time in 00:13:33.700 --> 00:13:35.879 England. I mean, it's World War I. Rationing 00:13:35.879 --> 00:13:38.240 is in full effect. Food was scarce for everyone. 00:13:38.480 --> 00:13:41.039 And Ramanujan is struggling immensely to maintain 00:13:41.039 --> 00:13:43.340 his strict vegetarian diet in a country that 00:13:43.340 --> 00:13:45.980 barely has enough food to begin with. Plus, he's 00:13:45.980 --> 00:13:48.259 working obsessively. He would sometimes forget 00:13:48.259 --> 00:13:50.860 to eat entirely. And his health just deteriorates 00:13:50.860 --> 00:13:53.240 rapidly. He ends up confined to a sanatorium. 00:13:53.500 --> 00:13:55.860 And it's during this really dark period that 00:13:55.860 --> 00:13:58.220 we get one of the most famous anecdotes in all 00:13:58.220 --> 00:14:01.940 of mathematics. Oh, the 1729 story. Yes. It perfectly 00:14:01.940 --> 00:14:04.000 encapsulates how Roman Nugent viewed the world. 00:14:04.779 --> 00:14:06.860 So Hardy goes to visit Roman Nugent when he is 00:14:06.860 --> 00:14:09.600 sick in the hospital. Okay. Hardy walks in feeling 00:14:09.600 --> 00:14:12.600 kind of awkward, you know, and he bluntly complains 00:14:12.600 --> 00:14:16.039 that the taxicab he rode in had the number 1729. 00:14:16.299 --> 00:14:18.840 Classic Hardy. Just awkward small talk. Right. 00:14:19.200 --> 00:14:21.139 And Hardy remarks that it seemed like rather 00:14:21.139 --> 00:14:24.080 a dull one, and he hoped it wasn't a bad omen. 00:14:24.259 --> 00:14:26.159 And Ramanujan is lying there, right, severely 00:14:26.159 --> 00:14:29.419 ill. And he instantly replies, no, it is a very 00:14:29.419 --> 00:14:32.059 interesting number. Yes. It is the smallest number 00:14:32.059 --> 00:14:35.159 expressible as the sum of two cubes in two different 00:14:35.159 --> 00:14:37.440 ways. Just think about how fast his brain had 00:14:37.440 --> 00:14:40.019 to process that to do it in a split second. It's 00:14:40.019 --> 00:14:42.980 insane. He instantly knew that 10 cubed is 1 00:14:42.980 --> 00:14:47.149 ,000, and 9 cubed is 729. Add them together, 00:14:47.269 --> 00:14:50.590 you get 1729. He also instantly knew that 12 00:14:50.590 --> 00:14:53.909 cubed is 1728 and one cubed is one. Add them 00:14:53.909 --> 00:14:57.029 together, you also get 1729. And no other number 00:14:57.029 --> 00:15:00.429 smaller than 1729 has that property. Exactly. 00:15:00.590 --> 00:15:02.549 Most people would need a calculator and like 00:15:02.549 --> 00:15:04.789 an hour to figure that out. And his brain just 00:15:04.789 --> 00:15:07.370 produced it as a reflex. J .E. Littlewood, who 00:15:07.370 --> 00:15:09.289 was another brilliant mathematician who worked 00:15:09.289 --> 00:15:13.159 with him, he later said, Every positive integer 00:15:13.159 --> 00:15:15.879 was one of Ramanujan's personal friends. That's 00:15:15.879 --> 00:15:17.779 a beautiful way to phrase it. He didn't view 00:15:17.779 --> 00:15:21.559 numbers as abstract quantities, you know. He 00:15:21.559 --> 00:15:24.240 recognized them as distinct entities with unique 00:15:24.240 --> 00:15:27.240 characteristics and relationships. But sadly, 00:15:27.659 --> 00:15:30.340 that genius couldn't save his body. No, he couldn't. 00:15:30.429 --> 00:15:32.929 The mental and physical toll combined, and it 00:15:32.929 --> 00:15:34.929 led to a suicide attempt where he actually threw 00:15:34.929 --> 00:15:37.490 himself in front of a train on the London Underground. 00:15:37.929 --> 00:15:40.429 Just incredibly tragic. He survived and Hardy 00:15:40.429 --> 00:15:42.669 actually intervened with Scotland Yard to keep 00:15:42.669 --> 00:15:45.870 him out of prison. But finally, in 1919, his 00:15:45.870 --> 00:15:48.269 health is so completely shattered that he returns 00:15:48.269 --> 00:15:50.870 to India. And he dies there the following year. 00:15:51.149 --> 00:15:54.990 at just 32 years old. 32! It's just devastating. 00:15:55.230 --> 00:15:57.289 And the tragedy of his early death is really 00:15:57.289 --> 00:15:59.409 compounded by a medical analysis that was done 00:15:59.409 --> 00:16:02.389 decades later in 1994. Right, because at the 00:16:02.389 --> 00:16:04.690 time of his death he was diagnosed with tuberculosis. 00:16:04.970 --> 00:16:08.509 Exactly. But the 1994 analysis of his medical 00:16:08.509 --> 00:16:11.409 records, looking at his specific symptoms, it 00:16:11.409 --> 00:16:14.529 strongly suggests he actually had hepatic amoebiasis. 00:16:14.769 --> 00:16:16.990 Which was what exactly? It was a complication 00:16:16.990 --> 00:16:19.110 from episodes of dysentery that he had suffered 00:16:19.110 --> 00:16:22.120 years earlier back in India. And the truly heartbreaking 00:16:22.120 --> 00:16:24.500 part of that finding is that if he had been properly 00:16:24.500 --> 00:16:27.460 diagnosed, hepatogamy biases was a completely 00:16:27.460 --> 00:16:29.860 treatable and curable condition at that time. 00:16:30.360 --> 00:16:33.220 A simple misdiagnosis robbed the world of decades 00:16:33.220 --> 00:16:36.279 of his mind. Which brings us to a major question 00:16:36.279 --> 00:16:39.879 for today. When he died at 32, did mathematics 00:16:39.879 --> 00:16:42.409 stall? Or are we still playing catch -up to the 00:16:42.409 --> 00:16:44.470 equations he left behind? Oh, we are absolutely 00:16:44.470 --> 00:16:46.750 still playing catch -up. The sheer density of 00:16:46.750 --> 00:16:49.470 what he produced in such a short time is staggering. 00:16:49.649 --> 00:16:54.110 Really? Even today? Yes. In 1976, a mathematician 00:16:54.110 --> 00:16:56.629 named George Andrews found what is now known 00:16:56.629 --> 00:16:59.789 as Ramanujan's lost notebook in the library at 00:16:59.789 --> 00:17:02.490 Trinity College. The lost note? Yeah. It contained 00:17:02.490 --> 00:17:07.410 87 pages of unorganized, incredibly complex material 00:17:07.410 --> 00:17:11.180 from the last year of his life in India. Mathematicians 00:17:11.180 --> 00:17:13.960 have spent the last 50 years just deciphering 00:17:13.960 --> 00:17:16.220 those final scribbles. Give us an example of 00:17:16.220 --> 00:17:18.200 how those abstract scribbles actually impact 00:17:18.200 --> 00:17:20.000 the world today. We aren't just talking about 00:17:20.000 --> 00:17:22.799 academic parlor tricks, right? Far from it. Consider 00:17:22.799 --> 00:17:25.119 his work on the tau function. Okay, the tau function. 00:17:25.259 --> 00:17:27.480 Without getting too lost in the weeds, the tau 00:17:27.480 --> 00:17:30.039 function deals with deep symmetries in something 00:17:30.039 --> 00:17:33.200 called modular forms. All right. Ramanujan proposed 00:17:33.200 --> 00:17:35.740 a conjecture about these symmetries based purely 00:17:35.740 --> 00:17:39.059 on his intuition. And decades later, Proving 00:17:39.059 --> 00:17:41.819 the Ramanujan conjecture laid the groundwork 00:17:41.819 --> 00:17:44.700 for a massive theory involving Gullo representations. 00:17:45.380 --> 00:17:47.880 Which do what? They essentially map the hidden 00:17:47.880 --> 00:17:50.660 symmetries of algebraic equations. Wait, symmetries 00:17:50.660 --> 00:17:53.180 of algebraic equations? Isn't that the exact 00:17:53.180 --> 00:17:56.700 framework Andrew Wiles used in the 1990s to finally 00:17:56.700 --> 00:18:00.220 prove Fermat's last theorem? Exactly. A problem 00:18:00.220 --> 00:18:02.319 that had stumped the brightest minds on Earth 00:18:02.319 --> 00:18:06.859 for 350 years was finally solved, in part because 00:18:06.859 --> 00:18:09.839 the mathematical architecture Ramanujan envisioned 00:18:09.839 --> 00:18:13.759 decades earlier. That is mind blowing. His ideas 00:18:13.759 --> 00:18:16.750 permeate modern physics, the theory of black 00:18:16.750 --> 00:18:19.769 holes, and even the highly complex algorithms 00:18:19.769 --> 00:18:22.730 used by computer scientists to calculate pi at 00:18:22.730 --> 00:18:25.450 unprecedented speeds today. It really puts into 00:18:25.450 --> 00:18:27.930 perspective how uniquely powerful his intuition 00:18:27.930 --> 00:18:30.670 was, especially compared to the established academic 00:18:30.670 --> 00:18:33.670 elite at the time. It does. The mathematician 00:18:33.670 --> 00:18:37.390 Paul Erdos once passed on a personal rating system 00:18:37.390 --> 00:18:39.869 that Hardy used to rank mathematical talent. 00:18:39.910 --> 00:18:42.269 Oh, I love this part. It was on a scale from 00:18:42.269 --> 00:18:45.700 0 to 100. And Hardy... who was considered a titan 00:18:45.700 --> 00:18:48.319 in the field, gave himself a 25. A 25 out of 00:18:48.319 --> 00:18:50.980 100. Right. He gave his brilliant colleague Littlewood 00:18:50.980 --> 00:18:53.500 a 30. He gave the great German mathematician 00:18:53.500 --> 00:18:56.519 David Hilbert an 80. And Ramanujan. Ramanujan 00:18:56.519 --> 00:18:59.940 received a 100. Wow. Hardy recognized that Ramanujan 00:18:59.940 --> 00:19:02.480 wasn't just better at mathematics. He was fundamentally 00:19:02.480 --> 00:19:04.740 playing a different game. Which brings us all 00:19:04.740 --> 00:19:07.849 back to you listening right now. Ramanujan's 00:19:07.849 --> 00:19:10.509 story is the ultimate reminder that you don't 00:19:10.509 --> 00:19:13.150 always need the traditional pedigree, you know. 00:19:13.329 --> 00:19:15.789 Absolutely not. You don't need the pristine resume 00:19:15.789 --> 00:19:19.089 or the proper educational background to uncover 00:19:19.089 --> 00:19:22.109 profound truths. Yes, structure and rigor are 00:19:22.109 --> 00:19:24.170 important to translate those truths to the rest 00:19:24.170 --> 00:19:26.690 of the world. We saw that with Hardy providing 00:19:26.690 --> 00:19:28.970 the mathematical scaffolding. Right. But viewing 00:19:28.970 --> 00:19:31.950 a problem from a completely isolated unorthodox 00:19:31.950 --> 00:19:34.960 angle isn't inherently a weakness. Sometimes 00:19:34.960 --> 00:19:37.839 it is your greatest superpower. Ramanujan didn't 00:19:37.839 --> 00:19:40.140 know the rules, which meant he didn't know the 00:19:40.140 --> 00:19:42.460 boundaries of what was supposedly impossible. 00:19:43.059 --> 00:19:44.900 There is a really compelling thought from the 00:19:44.900 --> 00:19:47.960 theoretical physicist Freeman Dyson that captures 00:19:47.960 --> 00:19:50.539 the enduring lesson of Ramanujan's life perfectly. 00:19:50.680 --> 00:19:52.819 What did he say? Dyson once noted that whenever 00:19:52.819 --> 00:19:55.440 he receives letters written in an illegible scroll 00:19:55.440 --> 00:19:58.460 from obscure places, you know, from people entirely 00:19:58.460 --> 00:20:01.269 outside the scientific establishment, he always 00:20:01.269 --> 00:20:03.430 makes a point to read them. Just in case. Exactly. 00:20:03.809 --> 00:20:06.789 He reads them because he hoax against all odds 00:20:06.789 --> 00:20:08.910 that he might be opening a letter from another 00:20:08.910 --> 00:20:12.130 Ramanujan. And in today's hyper -credentialed 00:20:12.130 --> 00:20:15.089 world, a world of absolute information overload 00:20:15.089 --> 00:20:17.390 where algorithms and gatekeepers instantly filter 00:20:17.390 --> 00:20:19.789 out anything that doesn't look professional or 00:20:19.789 --> 00:20:21.470 formatted correctly, it leaves you wondering. 00:20:21.490 --> 00:20:23.630 It really does. How many ramanujans are alive 00:20:23.630 --> 00:20:25.910 right now? How many brilliant, world -changing 00:20:25.910 --> 00:20:28.829 insights are we actively ignoring simply because 00:20:28.829 --> 00:20:30.950 they don't arrive with the proper pedigree? That's 00:20:30.950 --> 00:20:33.289 a profound question. Keep your eyes open for 00:20:33.289 --> 00:20:33.789 the scroll!