WEBVTT 00:00:00.000 --> 00:00:02.640 Okay, let's unpack this. What if I told you that 00:00:02.640 --> 00:00:05.759 right now, the flow of water in the pipes of 00:00:05.759 --> 00:00:09.619 your house is theoretically complex enough to, 00:00:09.619 --> 00:00:11.820 well, to build a functioning computer? Right, 00:00:11.880 --> 00:00:14.300 which sounds completely absurd. Totally absurd. 00:00:14.740 --> 00:00:17.780 Or, you know, that the chaotic, seemingly random 00:00:17.780 --> 00:00:20.039 numbers that govern things like nuclear physics 00:00:20.039 --> 00:00:24.920 or financial markets actually harbor these perfect... 00:00:25.129 --> 00:00:27.910 hidden geometric shapes. Yeah, that's the kind 00:00:27.910 --> 00:00:29.530 of reality -bending stuff we're getting into 00:00:29.530 --> 00:00:32.429 today. Exactly. Welcome to today's Deep Dive. 00:00:32.570 --> 00:00:35.350 We are looking at a comprehensive, biographical, 00:00:35.549 --> 00:00:38.770 and academic source detailing the life, the mind, 00:00:38.990 --> 00:00:42.329 and the real -world impact of Terence Tao. widely 00:00:42.329 --> 00:00:44.429 regarded as one of the greatest living mathematicians. 00:00:44.609 --> 00:00:46.429 Yeah. Right. And this source covers his life 00:00:46.429 --> 00:00:48.850 right up to the present day in 2026. Because 00:00:48.850 --> 00:00:50.670 as a listener, you're probably someone who loves 00:00:50.670 --> 00:00:53.289 those big aha moments, right? You want the deep 00:00:53.289 --> 00:00:55.109 knowledge without wading through hundreds of 00:00:55.109 --> 00:00:57.329 pages of academic jargon. Which is good, because 00:00:57.329 --> 00:00:59.429 Tao's daily thoughts probably look like an alien 00:00:59.429 --> 00:01:02.130 language to most of us. Oh, completely. But the 00:01:02.130 --> 00:01:04.599 breakthroughs he makes. They directly dictate 00:01:04.599 --> 00:01:06.859 the technology you rely on every single day. 00:01:07.379 --> 00:01:09.480 So my question is, what does it take for the 00:01:09.480 --> 00:01:12.140 world's top mathematicians, the absolute smartest 00:01:12.140 --> 00:01:14.980 people on earth, to call someone their Mr. Fix 00:01:14.980 --> 00:01:17.120 -It? What's fascinating here is that Terrence 00:01:17.120 --> 00:01:20.640 Tau isn't just a solitary genius churning out 00:01:20.640 --> 00:01:24.480 numbers in a void. He represents a complete paradigm 00:01:24.480 --> 00:01:27.439 shift in how modern human knowledge is actually 00:01:27.439 --> 00:01:29.739 advanced. Yeah. We're not talking about the stereotype 00:01:29.739 --> 00:01:31.769 of the isolated guy in a basement. Not at all. 00:01:31.909 --> 00:01:34.530 We are going to see how a mind like his operates. 00:01:34.590 --> 00:01:37.569 I mean, from fundamentally challenging our understanding 00:01:37.569 --> 00:01:40.909 of human intellectual development to actively 00:01:40.909 --> 00:01:43.189 shaping federal scientific policy. So let's start 00:01:43.189 --> 00:01:45.109 with that intellectual development, because honestly, 00:01:45.250 --> 00:01:47.409 the timeline of Tao's early life reads like a 00:01:47.409 --> 00:01:49.250 glitch in The Matrix. It really does. He was 00:01:49.250 --> 00:01:52.290 born in 1975 in Adelaide, Australia. His parents 00:01:52.290 --> 00:01:54.189 were first generation immigrants from Hong Kong. 00:01:54.730 --> 00:01:56.390 His dad was a pediatrician, and his mom had a 00:01:56.390 --> 00:01:58.790 first class honors degree in math and physics. 00:01:59.090 --> 00:02:01.969 So an environment that was very primed for academic 00:02:01.969 --> 00:02:05.189 focus. Right. Highly supportive. But what happens 00:02:05.189 --> 00:02:07.689 next just breaks our standard models of human 00:02:07.689 --> 00:02:10.370 cognition. Because by age nine, he is taking 00:02:10.370 --> 00:02:13.729 university -level math courses. He skipped five 00:02:13.729 --> 00:02:17.030 grades. And it wasn't just like rapid acceleration 00:02:17.030 --> 00:02:19.509 through a curriculum. He was performing at a 00:02:19.509 --> 00:02:22.409 level of foundational comprehension that completely 00:02:22.409 --> 00:02:24.689 baffled the researchers who were studying him. 00:02:24.849 --> 00:02:26.990 Yeah. And the detail that really sets the scale 00:02:26.990 --> 00:02:29.469 here, the one that just made my jaw drop, is 00:02:29.469 --> 00:02:32.389 his SAT score. Oh, the Johns Hopkins study. Yes. 00:02:32.810 --> 00:02:36.250 At eight years old, he takes the SAT math section. 00:02:36.810 --> 00:02:38.650 An exam designed to challenge 17 and 18 -year 00:02:38.650 --> 00:02:41.849 -olds, right? Yeah. And he scores a 760. At eight. 00:02:42.080 --> 00:02:44.659 at eight. The source notes he's one of only three 00:02:44.659 --> 00:02:47.080 children in the entire history of the Johns Hopkins 00:02:47.080 --> 00:02:49.599 study of exceptional talent program to hit a 00:02:49.599 --> 00:02:51.819 700 or above at that age. It's staggering. Taking 00:02:51.819 --> 00:02:53.879 college math at age nine is like a middle schooler 00:02:53.879 --> 00:02:57.060 getting drafted into the NBA. It just it shouldn't 00:02:57.060 --> 00:02:59.759 be neurologically possible. Well, Julian Stanley, 00:02:59.860 --> 00:03:02.120 who directed the study of mathematically precocious 00:03:02.120 --> 00:03:04.840 youth at Johns Hopkins, actually evaluated Tau. 00:03:05.539 --> 00:03:07.819 And Stanley stated that Tau had the greatest 00:03:07.819 --> 00:03:10.360 mathematical reasoning ability he had ever found 00:03:10.360 --> 00:03:12.759 in all his years of intensive searching. Wow. 00:03:13.219 --> 00:03:14.979 And the pivotal word there is reasoning, right? 00:03:15.020 --> 00:03:17.319 That distinction is everything, yeah. As opposed 00:03:17.319 --> 00:03:20.199 to just calculation speed. The popular stereotype 00:03:20.199 --> 00:03:23.340 of the math prodigy is, um, the human calculator, 00:03:23.639 --> 00:03:25.759 you know, someone who can instantly multiply 00:03:25.759 --> 00:03:28.080 12 -digit numbers in their head. Right, like 00:03:28.080 --> 00:03:30.580 a neat cognitive trick. Exactly. While that's 00:03:30.580 --> 00:03:32.599 impressive, it's often a dead end when it comes 00:03:32.599 --> 00:03:35.060 to higher mathematics. Because higher math isn't 00:03:35.060 --> 00:03:37.340 about arithmetic, it's about structure, it's 00:03:37.340 --> 00:03:39.479 about logic and architecture. So he was building 00:03:39.479 --> 00:03:42.240 something much deeper. Yes. Tau's early development, 00:03:42.539 --> 00:03:44.979 which was nurtured very carefully by his parents 00:03:44.979 --> 00:03:48.259 to prevent burnout, was all about absorbing the 00:03:48.259 --> 00:03:51.159 underlying logic of incredibly diverse mathematical 00:03:51.159 --> 00:03:54.719 fields. He was building this immensely adaptable, 00:03:54.780 --> 00:03:57.939 abstract architecture in his mind. And he just 00:03:57.939 --> 00:03:59.740 kept stress testing that architecture. I mean, 00:03:59.860 --> 00:04:01.620 he becomes the youngest medalist in the history 00:04:01.620 --> 00:04:04.139 of the International Mathematical Olympiad. Bronze 00:04:04.139 --> 00:04:07.530 at 10, silver at 11. gold at 12. Just walking 00:04:07.530 --> 00:04:10.229 up the podium year after year. Yeah. He earns 00:04:10.229 --> 00:04:14.129 his master's at 16, a PhD from Princeton at 21, 00:04:14.629 --> 00:04:17.350 and becomes UCLA's youngest full professor at 00:04:17.350 --> 00:04:20.290 24. It's an absolute rocket ship trajectory. 00:04:20.350 --> 00:04:23.029 It is. But this is the point in the source material 00:04:23.029 --> 00:04:26.069 where his story diverges from the cultural myth 00:04:26.069 --> 00:04:28.829 of the genius. Like we said earlier, you hear 00:04:28.829 --> 00:04:31.509 a trial prodigy and you instantly picture the 00:04:31.509 --> 00:04:34.730 lone wolf unable to relate to peers. The isolated 00:04:34.730 --> 00:04:37.709 academic working in a silo furiously scribbling 00:04:37.709 --> 00:04:40.670 on a chalkboard. Right. But Tao's actual career 00:04:40.670 --> 00:04:43.470 shatters that myth completely. It does. And in 00:04:43.470 --> 00:04:45.970 doing so, it reveals how modern mathematics is 00:04:45.970 --> 00:04:47.970 truly driven at the highest echelons, because 00:04:47.970 --> 00:04:50.569 he is incredibly collaborative. Yeah, the source 00:04:50.569 --> 00:04:52.970 mentions he has an Erdo's number of two. And 00:04:52.970 --> 00:04:56.189 by 2015, he had 68 different co -authors on his 00:04:56.189 --> 00:04:58.430 papers. Which is a huge number in pure math. 00:04:58.629 --> 00:05:00.430 For those unfamiliar with the term, having an 00:05:00.430 --> 00:05:02.990 Erdo's number is sort of like the math world's 00:05:02.990 --> 00:05:06.310 version of the six degrees of Kevin Bacon. But 00:05:06.310 --> 00:05:08.550 it's centered around the incredibly prolific 00:05:08.560 --> 00:05:12.180 Hungarian mathematician Paul Erdős. Right, so 00:05:12.180 --> 00:05:14.439 if you co -authored a paper with Erdős, your 00:05:14.439 --> 00:05:16.500 number is one. If you co -authored with someone 00:05:16.500 --> 00:05:19.379 who co -authored with him, you're a two. It's 00:05:19.379 --> 00:05:22.360 a playful metric, sure, but it perfectly illustrates 00:05:22.360 --> 00:05:24.240 his integration into the global mathematical 00:05:24.240 --> 00:05:27.079 community. That level of intense collaboration 00:05:27.079 --> 00:05:29.579 is a defining characteristic of his methodology. 00:05:30.360 --> 00:05:32.879 Charles Fefferman, a math professor at Princeton, 00:05:33.360 --> 00:05:35.759 pointed out that frustrated researchers actively 00:05:35.759 --> 00:05:38.540 compete to interest Tao in their problems. They 00:05:38.540 --> 00:05:40.779 compete for his attention. Literally. He operates 00:05:40.779 --> 00:05:43.079 as a sort of Mr. Fix -It for the world's most 00:05:43.079 --> 00:05:45.680 brilliant minds. When top -tier researchers hit 00:05:45.680 --> 00:05:47.920 a wall they just cannot scale, they bring the 00:05:47.920 --> 00:05:50.180 problem to him. And he doesn't just fix problems 00:05:50.180 --> 00:05:53.860 in his own backyard either. Timothy Gowers, another 00:05:53.860 --> 00:05:56.600 legendary mathematician, compared Tao to David 00:05:56.600 --> 00:06:00.180 Hilbert. That's massive praise. Hilbert is historically 00:06:00.180 --> 00:06:04.160 viewed as the last person to know all of mathematics, 00:06:04.839 --> 00:06:06.980 back before the field splittered into thousands 00:06:06.980 --> 00:06:09.180 of hyper -specialized sub -disciplines. Right. 00:06:09.720 --> 00:06:12.300 And Gowers pointed out that Tao has this uncanny, 00:06:12.500 --> 00:06:15.740 almost bizarre ability to write authoritatively 00:06:15.740 --> 00:06:18.399 on fields he doesn't officially work in, from 00:06:18.399 --> 00:06:22.399 quantum mechanics to image processing to ergodic 00:06:22.399 --> 00:06:24.569 theory. He steps into a foreign discipline and 00:06:24.569 --> 00:06:27.089 just immediately grasps it at the intuitive level 00:06:27.089 --> 00:06:29.930 of a lifelong expert. Which leads us to the primes. 00:06:30.560 --> 00:06:33.259 Because that structural intuition is the driving 00:06:33.259 --> 00:06:36.000 force behind his most famous accessible breakthrough. 00:06:36.060 --> 00:06:40.240 Uh. The Green Tao Theorem. Uh, yes. In 2004, 00:06:40.579 --> 00:06:42.579 Tao collaborated with British mathematician Ben 00:06:42.579 --> 00:06:45.620 Green to tackle a massive problem involving prime 00:06:45.620 --> 00:06:48.259 numbers. Now we know prime numbers thin out and 00:06:48.259 --> 00:06:50.079 become highly unpredictable the higher you count. 00:06:50.220 --> 00:06:52.360 Right, they seem to pop up at random across the 00:06:52.360 --> 00:06:53.920 number line. Wait, let me push back on this for 00:06:53.920 --> 00:06:55.879 a second. Prime numbers are supposed to be the 00:06:55.879 --> 00:06:58.500 ultimate, indivisible, unpredictable loners of 00:06:58.500 --> 00:07:01.230 the math world. They are. there be an organized, 00:07:01.509 --> 00:07:03.829 equally spaced progression of them? Are we saying 00:07:03.829 --> 00:07:08.009 there's a hidden, rigid architecture to seemingly 00:07:08.009 --> 00:07:10.970 random primes? That is exactly what they proved. 00:07:11.209 --> 00:07:13.430 The Green Tao Theorem proves that somewhere in 00:07:13.430 --> 00:07:15.889 the infinity of integers, you can always find 00:07:15.889 --> 00:07:18.990 a progression of prime numbers, of equal spacing, 00:07:19.209 --> 00:07:21.129 and of any length. Okay, give me an example. 00:07:21.370 --> 00:07:24.269 The source uses a very simple one, 3, 7, and 00:07:24.269 --> 00:07:27.410 11. They are all primes, and the spacing between 00:07:27.410 --> 00:07:30.430 each is exactly 4. Okay, so that's an arithmetic 00:07:30.430 --> 00:07:32.750 progression of length 3. Right. What Green and 00:07:32.750 --> 00:07:34.870 Tao proved is that you can find equally spaced 00:07:34.870 --> 00:07:37.269 progressions of any length you choose. No matter 00:07:37.269 --> 00:07:39.629 how impossibly long, it's hiding somewhere out 00:07:39.629 --> 00:07:41.629 there in the primes. But how do you prove something 00:07:41.629 --> 00:07:43.990 like that for infinity? I mean, without just 00:07:43.990 --> 00:07:46.209 checking numbers forever? Well, they didn't do 00:07:46.209 --> 00:07:48.410 it by brute -forcing calculations. They used 00:07:48.410 --> 00:07:51.269 a brilliant conceptual leap using something called 00:07:51.269 --> 00:07:53.490 a transference principle. Okay, what is that? 00:07:53.610 --> 00:07:56.350 Essentially, there was an older, very powerful 00:07:56.350 --> 00:07:59.350 theorem called Szemeredi's theorem. It already 00:07:59.350 --> 00:08:01.829 proved that these kinds of equally spaced progressions 00:08:01.829 --> 00:08:05.949 exist. But, and here's the catch, Szemeredi's 00:08:05.949 --> 00:08:08.589 theorem only works on dense sets of integers. 00:08:08.870 --> 00:08:11.569 And primes aren't dense. Exactly. Because prime 00:08:11.569 --> 00:08:14.009 numbers thin out as they get larger, they are 00:08:14.009 --> 00:08:16.649 mathematically considered a sparse set. So Szemeredi's 00:08:16.649 --> 00:08:19.069 theorem couldn't see them. The theoretical tool 00:08:19.069 --> 00:08:21.149 fundamentally didn't fit the material they were 00:08:21.149 --> 00:08:23.879 working with. So Tallo essentially repurposed 00:08:23.879 --> 00:08:26.839 a theoretical sledgehammer to turn it into a 00:08:26.839 --> 00:08:28.959 scalpel. That's a great way to visualize it. 00:08:29.139 --> 00:08:31.560 Tallo and Green figured out how to mathematically 00:08:31.560 --> 00:08:34.659 embed the sparse prime numbers inside a larger 00:08:34.659 --> 00:08:37.879 pseudorandom set of numbers. Oh, wow. Yeah. By 00:08:37.879 --> 00:08:40.139 doing this, they effectively created a mathematical 00:08:40.139 --> 00:08:42.559 lens. When you look at the primes through this 00:08:42.559 --> 00:08:46.080 specific lens, they suddenly appear dense relative 00:08:46.080 --> 00:08:48.299 to their new surroundings. And once they look 00:08:48.299 --> 00:08:50.700 dense, Szemeredi's theorem could be applied. 00:08:51.410 --> 00:08:54.230 Precisely. Tau's genius lies in translation. 00:08:54.730 --> 00:08:57.529 He takes a specialized tool built for one highly 00:08:57.529 --> 00:09:00.769 abstract area of math, radically re -engineers 00:09:00.769 --> 00:09:03.169 the environment, and forces the tool to work 00:09:03.169 --> 00:09:05.929 in a completely alien landscape. Here's where 00:09:05.929 --> 00:09:08.889 it gets really interesting. Because that defining 00:09:08.889 --> 00:09:11.230 cognitive trait, finding hidden architecture 00:09:11.230 --> 00:09:14.840 in seemingly random in complete data sets isn't 00:09:14.840 --> 00:09:17.279 just a party trick for abstract prime numbers. 00:09:17.340 --> 00:09:20.220 Not at all. That exact same cognitive leap crosses 00:09:20.220 --> 00:09:22.399 over into technologies that you, the listener, 00:09:22.799 --> 00:09:25.419 interact with all the time. Pure mathematics 00:09:25.419 --> 00:09:27.899 is the invisible bedrock of applied technology, 00:09:28.519 --> 00:09:31.039 and Tao's work in compressed sensing proves this 00:09:31.039 --> 00:09:33.539 perfectly. Yes. His work with Emmanuel Candice? 00:09:33.789 --> 00:09:35.789 They prove that you can accurately reconstruct 00:09:35.789 --> 00:09:38.789 a signal or a highly detailed image from vastly 00:09:38.789 --> 00:09:41.429 incomplete, seemingly random measurements. The 00:09:41.429 --> 00:09:43.690 source mentions they utilize tools of convex 00:09:43.690 --> 00:09:46.409 optimization, specifically the Danzig selector 00:09:46.409 --> 00:09:48.850 and restricted linear isometry. Which are incredibly 00:09:48.850 --> 00:09:51.429 intimidating terms. Very intimidating. But let's 00:09:51.429 --> 00:09:54.490 break down the mechanism. The source uses a jigsaw 00:09:54.490 --> 00:09:56.909 puzzle analogy, where normally you need every 00:09:56.909 --> 00:09:59.309 single piece to see the picture. But let's tweak 00:09:59.309 --> 00:10:02.370 that. It's like being handed a 1000 piece jigsaw 00:10:02.370 --> 00:10:05.679 puzzle with 800 pieces missing. And a mathematical 00:10:05.679 --> 00:10:08.519 formula perfectly hallucinates the exact missing 00:10:08.519 --> 00:10:10.980 image based on the 200 pieces you do have. That's 00:10:10.980 --> 00:10:13.320 exactly it, because most real -world signals, 00:10:13.559 --> 00:10:16.519 like a photograph or an audio wave, have an underlying 00:10:16.519 --> 00:10:19.419 simplicity or sparsity. Right. If you take a 00:10:19.419 --> 00:10:21.879 few random but mathematically optimal measurements, 00:10:22.480 --> 00:10:25.379 a formula can perfectly reconstruct the entire 00:10:25.379 --> 00:10:27.899 missing data set. And if we connect this to the 00:10:27.899 --> 00:10:29.899 bigger picture, we see why this matters to you 00:10:29.899 --> 00:10:33.539 directly. Medical imaging. Medical imaging. Historically, 00:10:33.740 --> 00:10:36.860 an MRI machine had to collect a massive, exhaustive 00:10:36.860 --> 00:10:39.299 amount of data to build a picture of your internal 00:10:39.299 --> 00:10:42.519 organs. It was gathering every single piece of 00:10:42.519 --> 00:10:44.720 that jigsaw puzzle. Which meant a patient had 00:10:44.720 --> 00:10:47.740 to lie perfectly still inside a loud, claustrophobic 00:10:47.740 --> 00:10:50.720 magnetic tube for a very long time. Which is 00:10:50.720 --> 00:10:53.279 terrifying. Especially for pediatric patients. 00:10:53.600 --> 00:10:56.679 Absolutely. But applying the mathematics of compressed 00:10:56.679 --> 00:10:59.720 sensing that Tau helped pioneer means the MRI 00:10:59.720 --> 00:11:02.220 machine no longer needs every piece of data. 00:11:02.379 --> 00:11:04.320 It can just hallucinate the rest. Basically. 00:11:04.559 --> 00:11:06.639 It can take a fraction of the measurements much 00:11:06.639 --> 00:11:10.179 faster and let the mathematical algorithms flawlessly 00:11:10.179 --> 00:11:13.759 reconstruct the clear image. It revolutionized 00:11:13.759 --> 00:11:16.440 medical imaging, drastically cutting down scan 00:11:16.440 --> 00:11:19.179 times and reducing patient trauma. And it doesn't 00:11:19.179 --> 00:11:22.000 stop at medical imaging either. The source outlines 00:11:22.000 --> 00:11:24.740 his work with mathematician Van Vu on random 00:11:24.740 --> 00:11:27.399 matrices. Right, moving from medical tech to 00:11:27.399 --> 00:11:31.159 sheer chaos. Yeah. Now, a random matrix is basically 00:11:31.159 --> 00:11:35.200 a giant grid of numbers used to model highly 00:11:35.200 --> 00:11:38.549 complex chaotic systems. Imagine a massive spreadsheet 00:11:38.549 --> 00:11:40.889 where every single cell is filled with a roll 00:11:40.889 --> 00:11:43.269 of the dice. Physicists and data scientists use 00:11:43.269 --> 00:11:45.269 these grids to model things that are too chaotic 00:11:45.269 --> 00:11:47.830 to track individually, like the energy levels 00:11:47.830 --> 00:11:50.190 of heavy atoms or the behavior of global financial 00:11:50.190 --> 00:11:53.649 markets. It models pure chaos. Bakow and Vanvoo 00:11:53.649 --> 00:11:56.490 proved universality principles within these massive 00:11:56.490 --> 00:11:59.370 data sets, specifically showing how things called 00:11:59.370 --> 00:12:02.470 eigenvalues scatter uniformly. Can we break down 00:12:02.470 --> 00:12:04.350 an eigenvalue? Because I know that's a term that 00:12:04.350 --> 00:12:06.919 trips a lot of people up. Sure. Think of a matrix 00:12:06.919 --> 00:12:09.580 as a machine that stretches or rotates space. 00:12:10.159 --> 00:12:12.659 An eigenvalue is simply the scale factor of that 00:12:12.659 --> 00:12:14.840 stretch. It's like a fundamental frequency hiding 00:12:14.840 --> 00:12:16.799 inside that grid of numbers. Okay, that makes 00:12:16.799 --> 00:12:19.159 sense. If you take a massive random matrix, our 00:12:19.159 --> 00:12:21.340 spreadsheet of dice rolls, and you map out all 00:12:21.340 --> 00:12:23.860 of its eigenvalues on a graph, you would expect 00:12:23.860 --> 00:12:26.019 them to be scattered in a completely chaotic, 00:12:26.299 --> 00:12:28.940 unpredictable mess. Because the inputs were random. 00:12:29.100 --> 00:12:32.440 Exactly. But they aren't. Tao and Van Vu proved 00:12:32.440 --> 00:12:35.720 the circular law in a four -moment theorem. They 00:12:35.720 --> 00:12:38.200 showed that as these random matrices get larger, 00:12:38.659 --> 00:12:41.019 their eigenvalues reliably arrange themselves 00:12:41.019 --> 00:12:44.879 into a perfect, uniform geometric disk. So even 00:12:44.879 --> 00:12:47.539 in systems built entirely on random chance, there 00:12:47.539 --> 00:12:50.159 are underlying, universal rules of geometric 00:12:50.159 --> 00:12:53.120 behavior. order rising out of pure mathematical 00:12:53.120 --> 00:12:56.139 chaos. It reveals that chaos at a micro level 00:12:56.139 --> 00:12:59.080 often adheres to strict, beautiful laws at the 00:12:59.080 --> 00:13:01.220 macro level. And his ability to find those laws 00:13:01.220 --> 00:13:03.779 extends into physics, too. Specifically, his 00:13:03.779 --> 00:13:06.919 2016 work on the Navier -Stokes equations. Oh, 00:13:06.919 --> 00:13:09.659 the Navier -Stokes equations. These are the fundamental 00:13:09.659 --> 00:13:12.299 models for fluid dynamics, right? Yeah, they 00:13:12.299 --> 00:13:15.240 describe the physical rules of how water flows 00:13:15.240 --> 00:13:18.120 through a pipe or how air moves over an airplane 00:13:18.120 --> 00:13:20.500 wing. It is one of the most notoriously difficult 00:13:20.840 --> 00:13:23.759 problems in all of physics. I think there's actually 00:13:23.759 --> 00:13:25.940 a million dollar prize for anyone who can fully 00:13:25.940 --> 00:13:29.220 solve it. There is, and the central mystery of 00:13:29.220 --> 00:13:32.200 Navier -Stokes is whether the equations can blow 00:13:32.200 --> 00:13:35.440 up. Blow up, like physically explode. Mathematically 00:13:35.440 --> 00:13:38.289 blow up. In fluid dynamics, a blow -up means 00:13:38.289 --> 00:13:40.870 the mathematics predict that the velocity or 00:13:40.870 --> 00:13:43.710 energy of the fluid becomes infinite in a finite 00:13:43.710 --> 00:13:46.049 amount of time, at which point the physical model 00:13:46.049 --> 00:13:48.350 essentially breaks down. It just stops making 00:13:48.350 --> 00:13:50.509 physical sense. And Tell constructed a variant 00:13:50.509 --> 00:13:52.830 of these equations that does exactly that. It 00:13:52.830 --> 00:13:55.340 self -destructs. He did. But the fascinating 00:13:55.340 --> 00:13:58.320 part is how he theorized this blowup happening. 00:13:58.860 --> 00:14:01.539 He engineered a theoretical fluid equation that 00:14:01.539 --> 00:14:03.639 acts like a test -gating machine. OK, picture 00:14:03.639 --> 00:14:07.159 this. Imagine a whirlpool of water. Now imagine 00:14:07.159 --> 00:14:09.779 that whirlpool uses its rotational energy to 00:14:09.779 --> 00:14:12.600 spawn a smaller, faster whirlpool inside itself. 00:14:12.659 --> 00:14:15.679 Right. And that one spawns an even smaller, even 00:14:15.679 --> 00:14:19.200 faster one. It cascades downward, getting infinitely 00:14:19.200 --> 00:14:21.600 smaller and infinitely faster until it shatters 00:14:21.600 --> 00:14:24.200 the bounds of physics. But he didn't stop there. 00:14:24.440 --> 00:14:27.200 He theorized these cascading fluid equations 00:14:27.200 --> 00:14:30.000 might be able to simulate a Turing complete system. 00:14:30.200 --> 00:14:32.600 Which is wild. A Turing complete system is, at 00:14:32.600 --> 00:14:35.679 its foundational level, a computer, right? Yes, 00:14:36.080 --> 00:14:38.820 any system that is Turing complete has the logical 00:14:38.820 --> 00:14:41.620 architecture to compute anything that any other 00:14:41.620 --> 00:14:44.179 computer can compute provided it has enough time 00:14:44.179 --> 00:14:46.720 and memory. So he is looking at the mathematics 00:14:46.720 --> 00:14:50.639 of how liquids move and realizing you could theoretically 00:14:50.639 --> 00:14:53.700 arrange that flow of water to act as logic gates. 00:14:54.039 --> 00:14:56.059 You could build a functioning computer program 00:14:56.059 --> 00:14:58.440 out of fluid dynamics. It perfectly illustrates 00:14:58.440 --> 00:15:01.120 how his mind bridges physical reality and computational 00:15:01.120 --> 00:15:03.159 theory. He looks at the raw structure of the 00:15:03.159 --> 00:15:05.379 physical universe, the flow of water, and sees 00:15:05.379 --> 00:15:07.700 the architecture of information processing. But 00:15:07.700 --> 00:15:09.639 doing this kind of work, sitting around proving 00:15:09.639 --> 00:15:11.919 that fluid equations can act like logic gates, 00:15:12.539 --> 00:15:14.820 or mapping the uniform scattering of eigenvalues 00:15:14.820 --> 00:15:18.000 that requires immense time, deep focus, and vast 00:15:18.000 --> 00:15:21.190 resources. It does, and pure mathematics often 00:15:21.190 --> 00:15:23.669 doesn't have an immediate, obvious product you 00:15:23.669 --> 00:15:25.669 can package and sell to a tech company tomorrow. 00:15:26.409 --> 00:15:28.350 Which brings us to a critical tension in the 00:15:28.350 --> 00:15:31.169 scientific ecosystem. Right. You simply cannot 00:15:31.169 --> 00:15:33.409 have the downstream miracles like the faster 00:15:33.409 --> 00:15:36.950 MRI machines without the upstream, highly abstract 00:15:36.950 --> 00:15:40.009 exploration of pure theory. And that reality 00:15:40.009 --> 00:15:42.470 forced Tau to step out of the academic bubble 00:15:42.470 --> 00:15:45.690 and directly address federal policy. Right. Let's 00:15:45.690 --> 00:15:49.590 get into that. In August 2025, Terrence Tau wrote 00:15:49.590 --> 00:15:51.690 a public article expressing strong disapproval 00:15:51.690 --> 00:15:53.929 of policies enacted by President Donald Trump 00:15:53.929 --> 00:15:56.519 that cut federal research funding. Yeah, it became 00:15:56.519 --> 00:15:58.620 a major issue. Now before we go further, I want 00:15:58.620 --> 00:16:00.840 to be very clear with you, our listeners. As 00:16:00.840 --> 00:16:03.259 guides to this material, we are not taking a 00:16:03.259 --> 00:16:05.759 political side here. We are impartially reporting 00:16:05.759 --> 00:16:08.179 the contents of the source text to understand 00:16:08.179 --> 00:16:10.399 Tao's position. Exactly. We're just looking at 00:16:10.399 --> 00:16:12.700 the ecosystem impacts he highlighted. According 00:16:12.700 --> 00:16:15.460 to the source material, these cuts directly halted 00:16:15.460 --> 00:16:18.940 real -world research. two of Tao's National Science 00:16:18.940 --> 00:16:22.659 Foundation, or NSF, grants were suspended. Yeah, 00:16:22.799 --> 00:16:25.580 one grant supported his direct day -to -day research 00:16:25.580 --> 00:16:29.519 at UCLA. And the other supported UCLA's Institute 00:16:29.519 --> 00:16:32.139 for Pure and Applied Mathematics, known as IPM, 00:16:32.679 --> 00:16:35.460 an institute where Tao actively oversees broad 00:16:35.460 --> 00:16:38.419 research initiatives. He argued that these specific 00:16:38.419 --> 00:16:41.279 funding cuts do catastrophic damage to the scientific 00:16:41.279 --> 00:16:44.879 ecosystem. It is not merely about a celebrated 00:16:44.879 --> 00:16:48.120 fields medal winning mathematician being inconvenienced. 00:16:48.120 --> 00:16:51.580 It is about the entire pipeline of academic talent, 00:16:52.059 --> 00:16:55.259 recruitment and technological innovation. So 00:16:55.259 --> 00:16:57.580 what does this all mean? Can you break down that 00:16:57.580 --> 00:17:00.039 pipeline argument based on his statements? Because 00:17:00.039 --> 00:17:03.039 it is very easy for a taxpayer to look at a budget 00:17:03.039 --> 00:17:06.339 cut to quote -unquote pure mathematics and think, 00:17:06.500 --> 00:17:08.940 well, we have more pressing practical problems 00:17:08.940 --> 00:17:11.059 to solve right now. If we connect this to the 00:17:11.059 --> 00:17:13.380 bigger picture, Tau's counter argument is that 00:17:13.380 --> 00:17:15.680 you cannot separate the abstract from the practical. 00:17:16.140 --> 00:17:18.900 They are an interconnected ecosystem. Think of 00:17:18.900 --> 00:17:21.539 scientific research as a tree. Pure mathematics, 00:17:21.960 --> 00:17:24.319 the highly abstract work involving primes and 00:17:24.319 --> 00:17:26.299 infinite fluids that seems to have no immediate 00:17:26.299 --> 00:17:29.099 use is the root system. Roots, right. Applied 00:17:29.099 --> 00:17:31.299 mathematics forms the trunk and the branches, 00:17:31.779 --> 00:17:33.539 and the practical technologies that build the 00:17:33.539 --> 00:17:36.059 modern world are the fruit, the cryptography 00:17:36.059 --> 00:17:38.839 that secures global banking, the cybersecurity 00:17:38.839 --> 00:17:41.640 infrastructure protecting national grids, the 00:17:41.640 --> 00:17:44.180 signal processing that makes cell networks and 00:17:44.180 --> 00:17:47.759 fast MRI machines possible. All of that is applied 00:17:47.759 --> 00:17:50.119 math. So you can't just harvest the fruit and 00:17:50.119 --> 00:17:52.519 ignore the roots. Precisely the point he was 00:17:52.519 --> 00:17:56.019 making in 2025. You cannot reap the lucrative, 00:17:56.220 --> 00:17:59.250 practical benefits of applied math. without continuously 00:17:59.250 --> 00:18:02.250 funding the foundational abstract pure math. 00:18:02.430 --> 00:18:05.170 It's a pipeline. Exactly. When federal policies 00:18:05.170 --> 00:18:07.730 cut funding at the root by suspending NSF grants 00:18:07.730 --> 00:18:09.849 for pure research and crippling institutes like 00:18:09.849 --> 00:18:12.450 IPAM, you stall advancements across the entire 00:18:12.450 --> 00:18:15.069 spectrum. You fail to recruit the next generation 00:18:15.069 --> 00:18:18.410 of brilliant minds, and the entire tree of innovation 00:18:18.410 --> 00:18:22.220 eventually withers. Wow. We have covered an incredible 00:18:22.220 --> 00:18:24.539 landscape of human thought today. We really have. 00:18:24.720 --> 00:18:26.599 We started in Adelaide with an eight -year -old 00:18:26.599 --> 00:18:30.480 whose 760 SAT score and unparalleled reasoning 00:18:30.480 --> 00:18:32.900 abilities completely shattered our understanding 00:18:32.900 --> 00:18:35.480 of cognitive development. And then we explored 00:18:35.480 --> 00:18:37.779 how he destroyed the myth of the lone genius 00:18:37.779 --> 00:18:40.339 to become the ultimate collaborative Mr. Fix 00:18:40.339 --> 00:18:43.240 -It. We saw him build mathematical lenses to 00:18:43.240 --> 00:18:45.740 reveal the hidden infinite architecture of prime 00:18:45.740 --> 00:18:48.789 numbers in the Green Tao Theorem. We unpacked 00:18:48.789 --> 00:18:51.829 how his insights into underlying sparsity directly 00:18:51.829 --> 00:18:54.529 translate to the compressed sensing that powers 00:18:54.529 --> 00:18:57.329 modern medical imaging. Saving actual lives in 00:18:57.329 --> 00:19:00.390 MRI machines. Exactly. And finally, we looked 00:19:00.390 --> 00:19:03.690 at his 2025 advocacy, fiercely defending the 00:19:03.690 --> 00:19:05.650 fragile funding pipeline that makes all of his 00:19:05.650 --> 00:19:08.029 invisible architecture possible. It is a testament 00:19:08.029 --> 00:19:11.390 to a mind uniquely capable of zooming in to manipulate 00:19:11.390 --> 00:19:14.309 the most microscopic, chaotic details of random 00:19:14.309 --> 00:19:17.250 matrices and zooming out to see the overarching 00:19:17.250 --> 00:19:20.250 structure of both fluid physics and human scientific 00:19:20.250 --> 00:19:22.750 progress. And while you, listening right now, 00:19:22.849 --> 00:19:24.970 might not be calculating prime progressions or 00:19:24.970 --> 00:19:27.769 modeling fluid logic gates on your commute, it 00:19:27.769 --> 00:19:29.910 is undeniable that the mathematical architecture 00:19:29.910 --> 00:19:33.109 Terence Tao generates forms the invisible scaffolding 00:19:33.109 --> 00:19:35.609 of your digital and physical life. It's everywhere. 00:19:35.849 --> 00:19:39.150 But before we wrap up, I know there is one final 00:19:39.150 --> 00:19:41.809 staggering thought from the source material that 00:19:41.809 --> 00:19:44.650 really pushes the boundaries of how we view reality. 00:19:45.309 --> 00:19:47.769 Yeah, I want to leave you with this to mull over. 00:19:48.190 --> 00:19:50.930 It goes back to Tau's speculation about the Navier 00:19:50.930 --> 00:19:53.990 -Stokes equations. The concept that fluid dynamics, 00:19:54.549 --> 00:19:57.170 the actual physical movement of water, could 00:19:57.170 --> 00:20:00.150 theoretically simulate a Turing complete computer. 00:20:00.289 --> 00:20:03.640 Right. If the flow of water in a pipe is mathematically 00:20:03.640 --> 00:20:06.339 complex enough to run a computer program, wait, 00:20:06.400 --> 00:20:08.799 let me phrase this better, if water can compute, 00:20:09.259 --> 00:20:10.900 what does that say about the universe we live 00:20:10.900 --> 00:20:13.480 in? Oh, wow. Are the physical laws of nature 00:20:13.480 --> 00:20:16.599 just an ongoing, infinitely complex calculation 00:20:16.599 --> 00:20:19.539 waiting for a mind like Terence Towse to finally 00:20:19.539 --> 00:20:22.000 decode the output? The universe itself as an 00:20:22.000 --> 00:20:24.380 active computation, with the physical elements 00:20:24.380 --> 00:20:27.410 acting as the code. That is incredible. Thank 00:20:27.410 --> 00:20:29.450 you for joining us on this deep dive. Keep looking 00:20:29.450 --> 00:20:31.549 closely at your world, keep asking why the pieces 00:20:31.549 --> 00:20:33.650 fit together, and keep questioning the hidden 00:20:33.650 --> 00:20:34.490 patterns around you.