WEBVTT 1 00:00:01.199 --> 00:00:06.200 Welcome to the Sentient Code, where intelligence is engineered, autonomy 2 00:00:06.280 --> 00:00:10.439 is emerging, and a line between human and machine grows thinner. 3 00:00:10.800 --> 00:00:15.359 Each episode, we decode the algorithms, explore the robotics, and 4 00:00:15.439 --> 00:00:19.000 examine the ideas shaping the future of artificial minds. 5 00:00:23.879 --> 00:00:26.320 Welcome in everybody. I'm your host, and I'm so glad 6 00:00:26.359 --> 00:00:27.239 you're joining us today. 7 00:00:27.399 --> 00:00:30.199 Yes, welcome, I'm thrilled to be here as your resident 8 00:00:30.280 --> 00:00:32.320 tech and theoretical science guide. 9 00:00:32.719 --> 00:00:35.840 You know, when you picture the absolute frontier of human knowledge, 10 00:00:36.320 --> 00:00:42.920 specifically in something as incredibly rigid and ancient as theoretical geometry, 11 00:00:43.560 --> 00:00:46.039 you probably picture alone genius right. 12 00:00:45.920 --> 00:00:48.240 Like pacing in front of a chalkboard. 13 00:00:47.960 --> 00:00:51.399 Exactly, pacing around totally covered in chalk dust. There is 14 00:00:51.439 --> 00:00:55.759 this deep seated expectation of human struggle, you know, of 15 00:00:55.880 --> 00:00:59.240 raw human intuition just wrestling with the universe's hidden rules. 16 00:00:59.280 --> 00:01:01.359 It's a very antasized view of science. 17 00:01:01.399 --> 00:01:04.000 Honestly, yeah, it really is. And you definitely do not 18 00:01:04.079 --> 00:01:07.439 picture someone just booting up a consumer application on their laptop, 19 00:01:07.719 --> 00:01:09.879 typing into a chatbox and having an algorithm do the 20 00:01:09.920 --> 00:01:10.439 heavy lifting. 21 00:01:10.519 --> 00:01:11.719 No, you definitely don't. 22 00:01:11.760 --> 00:01:14.680 But today our mission is to explore a monumental shift 23 00:01:14.760 --> 00:01:18.760 in artificial intelligence and human knowledge. We are examining the 24 00:01:18.840 --> 00:01:22.200 exact moment a consumer AI model crossed the line from 25 00:01:22.239 --> 00:01:25.439 simply predicting the next word in the sentence to generating 26 00:01:25.480 --> 00:01:29.480 an entirely novel mathematical proof in theoretical geometry. 27 00:01:29.640 --> 00:01:32.120 And I can't stress enough how huge this is. It 28 00:01:32.200 --> 00:01:36.480 represents a definitive line in the sand for cognitive technology 29 00:01:36.959 --> 00:01:41.200 because historically there has always been this massive, seemingly unbridgable 30 00:01:41.239 --> 00:01:46.000 gap between AI as a conversational assistant, a tool that 31 00:01:46.079 --> 00:01:49.159 can draft a polite email, or summarize your meeting notes 32 00:01:49.319 --> 00:01:52.120 or write a grocery list, exactly the gap between that 33 00:01:52.280 --> 00:01:55.959 and AI as a rigorous logical reasoning engine. What we 34 00:01:56.000 --> 00:01:58.959 are breaking down today isn't just some clever parlor trick 35 00:01:59.000 --> 00:02:02.439 of code, looking at a complete paradigm shift and how 36 00:02:02.480 --> 00:02:04.719 theoretical research is actively conducted. 37 00:02:04.799 --> 00:02:07.159 It's challenging the very boundaries of what a machine is 38 00:02:07.200 --> 00:02:10.280 capable of achieving in the realm of purely abstract thought. 39 00:02:10.479 --> 00:02:11.039 It really is. 40 00:02:11.240 --> 00:02:15.039 And here's where it gets really interesting. Chat GPT five 41 00:02:15.080 --> 00:02:19.599 point two, specifically, its thinking model didn't just regurgitate existing 42 00:02:19.680 --> 00:02:23.439 mass that it memorized from a textbook during its training phase. No, no, all, 43 00:02:23.479 --> 00:02:26.039 It created something entirely new. It stepped into a domain 44 00:02:26.039 --> 00:02:29.719 of original discovery, which frankly fundamentally upends the narrative that 45 00:02:29.800 --> 00:02:31.719 AI is just a sophisticated mimic. 46 00:02:32.080 --> 00:02:35.520 Yeah, the assumption for years was that large language models 47 00:02:35.520 --> 00:02:37.879 were inherently limited by their training. 48 00:02:37.599 --> 00:02:41.039 Data, right, the whole stochastic parrot idea exactly. 49 00:02:41.360 --> 00:02:44.159 The consensus was that they could remix, they could summarize, 50 00:02:44.199 --> 00:02:47.639 and they could translate, but they couldn't genuinely invent because 51 00:02:47.639 --> 00:02:53.120 a mathematical proof requires a flawless, unbroken chain of rigorous logic. 52 00:02:53.240 --> 00:02:54.960 There's no faking it none. 53 00:02:55.000 --> 00:02:57.639 There is absolutely no room for the kind of fluid, 54 00:02:57.879 --> 00:03:01.680 probabilistic approximation that languae, which models usually rely on to 55 00:03:01.800 --> 00:03:05.800 generate human sounding text. So to see a commercial off 56 00:03:05.840 --> 00:03:10.319 the shelf system bridge that gap into deterministic logic is well, 57 00:03:10.360 --> 00:03:11.599 it's frankly staggering. 58 00:03:11.800 --> 00:03:15.120 It is. So to really understand the magnitude of this shift, 59 00:03:15.120 --> 00:03:17.000 we need to look at the actual mathematics. We need 60 00:03:17.000 --> 00:03:20.240 to understand what problem the AI actually solved, Because this 61 00:03:20.360 --> 00:03:23.520 isn't a basic high school algebra, No, far from it. 62 00:03:23.639 --> 00:03:26.080 We are talking about the twenty twenty four conjecture proposed 63 00:03:26.120 --> 00:03:28.319 by the mathematicians ran In Tang, And just to set 64 00:03:28.319 --> 00:03:30.960 the stage for you listening, let's clarify what a conjecture 65 00:03:31.000 --> 00:03:31.800 actually is in. 66 00:03:31.759 --> 00:03:33.120 This context, good idea. 67 00:03:33.319 --> 00:03:38.080 A conjecture is essentially an educated, highly informed guess based 68 00:03:38.080 --> 00:03:43.080 on undeniable patterns. Imagine you observe one hundred apples falling 69 00:03:43.120 --> 00:03:45.719 from a tree, and you conjecture that there is an 70 00:03:45.800 --> 00:03:47.439 invisible force pulling them down. 71 00:03:47.520 --> 00:03:50.080 You see the pattern, but you don't have the math right. 72 00:03:50.159 --> 00:03:52.240 You can see the pattern, but you haven't written the 73 00:03:52.319 --> 00:03:57.039 universal equation of gravitation yet. The theorem is that final, 74 00:03:57.479 --> 00:04:01.800 undeniable mathematical proof that blames the why and the how 75 00:04:02.080 --> 00:04:04.879 so perfectly that it simply cannot be disputed. 76 00:04:05.039 --> 00:04:06.840 I love that analogy, and I would actually take it 77 00:04:06.919 --> 00:04:09.240 even further into the realm of structural engineering. 78 00:04:09.319 --> 00:04:10.280 Oh okay, let's hear it. 79 00:04:10.360 --> 00:04:13.240 So a conjecture is like designing a radically new type 80 00:04:13.240 --> 00:04:16.360 of suspension bridge. You run wind tunnel tests, you build 81 00:04:16.439 --> 00:04:19.600 scale models, and all the empirical evidence suggests the bridge 82 00:04:19.600 --> 00:04:21.279 will hold the weight of a thousand cars. 83 00:04:21.800 --> 00:04:23.279 So you're pretty confident. 84 00:04:22.959 --> 00:04:26.160 Right, you know it should work. But the theorem is 85 00:04:26.240 --> 00:04:32.279 the absolute foundational physics calculation that guarantees mathematically the bridge 86 00:04:32.319 --> 00:04:36.279 will never collapse under any circumstances, the air type proof exactly. 87 00:04:36.920 --> 00:04:39.920 In mathematics, moving from the wind tunnel to the foundational 88 00:04:39.959 --> 00:04:44.680 physics can take decades or even centuries of agonizing trial 89 00:04:44.720 --> 00:04:48.040 and error. The twenty twenty four Ran and Tang conjecture 90 00:04:48.160 --> 00:04:50.560 was one of those problems. It was a brick wall 91 00:04:50.680 --> 00:04:52.199 that human mathematicians had hit. 92 00:04:52.399 --> 00:04:55.439 So let's talk about that brick wall. The specific problem 93 00:04:55.480 --> 00:04:59.360 falls under something called spectral region characterization. 94 00:04:58.920 --> 00:05:01.319 Which sounds in incredibly intimidating. 95 00:05:01.519 --> 00:05:03.319 It does. Now for those of you who might not 96 00:05:03.360 --> 00:05:07.120 spend your weekends reading high level geometry papers, imagine you 97 00:05:07.199 --> 00:05:10.519 are blindfolded in an oddly shaped room and you clap 98 00:05:10.560 --> 00:05:13.839 your hands. By listening to the echoes the spectrum of 99 00:05:13.879 --> 00:05:17.079 sound frequencies bouncing off the walls, you try to draw 100 00:05:17.120 --> 00:05:19.639 the exact geometric shape of the room perfectly. 101 00:05:19.879 --> 00:05:21.680 That's a great special way to think about. 102 00:05:21.480 --> 00:05:21.800 It, right. 103 00:05:21.839 --> 00:05:26.000 That's essentially spectral region characterization. The Ran and Tang conjecture 104 00:05:26.040 --> 00:05:30.240 suggested that for certain highly complex multidimensional shapes, you could 105 00:05:30.240 --> 00:05:35.160 perfectly characterize their geometric boundaries using only a specific mathematical 106 00:05:35.240 --> 00:05:37.120 subset of these echoes. 107 00:05:36.839 --> 00:05:39.360 And everyone in the field felt the pattern was true. 108 00:05:39.519 --> 00:05:42.199 Yeah, they felt it in their bones, but actually proving 109 00:05:42.240 --> 00:05:45.319 it mathematically was considered wildly complex. 110 00:05:45.040 --> 00:05:48.240 Because the complexity comes from the sheer number of variables 111 00:05:48.560 --> 00:05:53.839 and the topological constraints of multidimensional space. Human mathematicians struggle 112 00:05:53.879 --> 00:05:57.079 to hold all those simultaneous constraints in their working memory. 113 00:05:57.160 --> 00:05:59.079 There's just too much to juggle, exactly. 114 00:05:59.439 --> 00:06:03.000 But searchers at the Free University of Brussels, specifically the 115 00:06:03.120 --> 00:06:08.879 VUB Data Analytics Lab, they decided to approach this bottleneck differently. 116 00:06:09.279 --> 00:06:12.279 They didn't assign a team of PhD students to grind 117 00:06:12.319 --> 00:06:13.319 through the equations. 118 00:06:13.399 --> 00:06:16.240 They handed the problem over to chat GPT five point two, 119 00:06:16.279 --> 00:06:18.839 thinking they did, okay, let's unpack this, or well, let's 120 00:06:18.879 --> 00:06:20.920 unpack this right now, because I want to push back 121 00:06:20.920 --> 00:06:23.879 a little bit on this idea of complete AI autonomy, 122 00:06:24.079 --> 00:06:26.160 and I think this is where the nuance is really critical. 123 00:06:26.240 --> 00:06:27.399 Fair Enough, the. 124 00:06:27.480 --> 00:06:30.560 VUB researchers noted that the final proof didn't just spit 125 00:06:30.600 --> 00:06:34.319 out perfectly on the first try. It emerged from seven 126 00:06:34.439 --> 00:06:38.759 distinct CHAT sessions with chat GPT, and there were four 127 00:06:38.879 --> 00:06:41.240 evolving versions of the mathematical argument. 128 00:06:41.360 --> 00:06:42.279 Yes, that's accurate. 129 00:06:42.680 --> 00:06:46.519 So my question for you is does taking seven sessions 130 00:06:46.680 --> 00:06:49.800 and four distinct versions mean the AI was essentially just 131 00:06:49.920 --> 00:06:54.519 flailing around hallucinating math until the humans finally stepped in, 132 00:06:54.839 --> 00:06:56.720 corrected all the errors and fixed it. 133 00:06:56.800 --> 00:06:59.120 That is a vital question because it forces us to 134 00:06:59.120 --> 00:07:02.199 look at the actual mechanism of how these thinking models operate. 135 00:07:02.560 --> 00:07:04.879 If you look at the progression of those seven sessions, 136 00:07:04.959 --> 00:07:06.319 it absolutely. 137 00:07:05.800 --> 00:07:07.800 Was not flailing, So what was doing. 138 00:07:08.399 --> 00:07:12.600 Chat GPT five point two uses a process called test 139 00:07:12.600 --> 00:07:17.199 time compute or chain of thought reasoning. Instead of instantly 140 00:07:17.240 --> 00:07:21.199 predicting the next word, it generates vast hidden reasoning trees. 141 00:07:21.639 --> 00:07:25.319 It explores thousands of mathematical pathways in its multi dimensional 142 00:07:25.480 --> 00:07:28.759 latent space. In the first session, the AI proposed a 143 00:07:28.839 --> 00:07:32.680 massive overretching structural approach to the proof, but in doing 144 00:07:32.720 --> 00:07:35.519 so it made a subtle error. It assumed a specific 145 00:07:35.560 --> 00:07:38.560 boundary condition would hold up symmetrically, which doesn't work in 146 00:07:38.600 --> 00:07:41.800 the specific non Euclidean space required for this problem. 147 00:07:41.480 --> 00:07:44.279 So basically hallucinated geometric rule that didn't apply. 148 00:07:44.680 --> 00:07:48.360 It made an invalid assumption based on probabilistic mapping. Yes, 149 00:07:49.160 --> 00:07:52.639 but here is the critical part. The human researchers didn't 150 00:07:52.680 --> 00:07:56.120 rewrite the proof. They didn't No, they didn't solve the 151 00:07:56.160 --> 00:07:59.199 math for the AI. They simply acted as a constraint 152 00:07:59.519 --> 00:08:04.240 the system, effectively saying, hey, your assumption about this specific 153 00:08:04.279 --> 00:08:07.120 boundary fails under these topological conditions. 154 00:08:07.279 --> 00:08:08.160 Oh wow, right. 155 00:08:08.560 --> 00:08:13.079 The AI then took that new constraint, recalculated as reasoning tree, 156 00:08:13.439 --> 00:08:16.879 pruned the logical branches that led to the contradiction, and 157 00:08:17.000 --> 00:08:20.920 generated a completely novel mathematical pathway to bridge the gap. 158 00:08:21.600 --> 00:08:24.600 The AI acted as the primary engine of discovery. 159 00:08:24.920 --> 00:08:27.360 So the AI is the one doing the creative heavy lifting. 160 00:08:27.680 --> 00:08:31.639 It's drawing the complex architectural blueprints, and the humans are 161 00:08:31.639 --> 00:08:33.440 just checking the math to make sure the load bearing 162 00:08:33.519 --> 00:08:35.519 walls are mathematically sound and Wi'll collapse. 163 00:08:35.720 --> 00:08:38.000 I would elevate that even slightly. The human isn't just 164 00:08:38.120 --> 00:08:40.840 checking the walls. They are verifying the integrity of the 165 00:08:40.879 --> 00:08:43.759 novel materials the AI just invented to build those walls. 166 00:08:43.799 --> 00:08:44.360 It's wild. 167 00:08:44.639 --> 00:08:48.159 The vub researchers explicitly stated that they are among the 168 00:08:48.240 --> 00:08:53.159 first to demonstrate a commercially available large language model, independently 169 00:08:53.200 --> 00:08:57.360 developing original mathematical proofs. It didn't just crunch numbers like 170 00:08:57.399 --> 00:09:01.840 a calculator. It provided the structural geometric insight that humans 171 00:09:01.840 --> 00:09:02.440 had been missing. 172 00:09:02.960 --> 00:09:05.440 And because the AI took the lead in exploring the 173 00:09:05.440 --> 00:09:08.600 structure and the architecture of the proof, the researchers have 174 00:09:08.679 --> 00:09:12.200 coined a brand new and honestly slightly unconventional term for 175 00:09:12.240 --> 00:09:14.879 this methodology. They're calling it vibe proving. 176 00:09:15.279 --> 00:09:19.559 Vibe proving. It is a remarkably colloquial term to introduce 177 00:09:19.600 --> 00:09:23.039 into the lexicon of high level theoretical geometry. 178 00:09:23.120 --> 00:09:25.960 It really is, and it connects directly to a massive 179 00:09:26.000 --> 00:09:28.879 trend we've seen in software development called vibe coding. 180 00:09:28.960 --> 00:09:30.480 Right, which has been everywhere lately. 181 00:09:30.639 --> 00:09:33.879 Yeah, for context, Vibe coding was this recent phenomenon where 182 00:09:34.000 --> 00:09:37.360 AI progressed from being a simple autocomplete tool for programmers 183 00:09:37.759 --> 00:09:42.159 to near autonomously generating entire software architectures. You don't write 184 00:09:42.159 --> 00:09:44.879 the code, You just give the AI the vibe or 185 00:09:44.919 --> 00:09:47.159 the high level conceptual goal of the app you want, 186 00:09:47.480 --> 00:09:49.679 and the AI handles the front end, the back end, 187 00:09:49.960 --> 00:09:50.960 the database routing. 188 00:09:51.039 --> 00:09:52.279 It does the whole thing. 189 00:09:52.360 --> 00:09:55.120 Exactly and now we are seeing that exact same cognitive 190 00:09:55.200 --> 00:09:58.440 leap in theoretical mathematics. But I have to ask you, 191 00:09:59.080 --> 00:10:02.279 does the word vibe sound just a little too unscientific 192 00:10:02.440 --> 00:10:06.519 for something is incredibly rigorous and unyielding as theoretical math. 193 00:10:06.679 --> 00:10:09.240 It sounds incredibly casual on the surface. I'll give you that. 194 00:10:09.639 --> 00:10:13.080 But what's fascinating here is how accurately that term maps 195 00:10:13.200 --> 00:10:17.519 to the actual cognitive process happening within the machine's neural network. 196 00:10:17.759 --> 00:10:19.480 Really, how so well. 197 00:10:19.399 --> 00:10:22.960 Language models organize concepts in a high dimensional latent space 198 00:10:23.080 --> 00:10:28.240 based on proximity and relationship, not rigid syntax. Vibe proving 199 00:10:28.399 --> 00:10:31.399 describes the phase where the human and the AI fluidly 200 00:10:31.480 --> 00:10:34.480 explore the conceptual space of a problem, so they're kind 201 00:10:34.480 --> 00:10:37.440 of feeling it out exactly. They're navigating the vibe of 202 00:10:37.480 --> 00:10:40.879 the solution, the intuitive structural direction of the math, before 203 00:10:40.919 --> 00:10:45.360 hardening it into the unforgiving formal syntax of a mathematical proof. Honestly, 204 00:10:45.720 --> 00:10:48.320 it perfectly mirrors how human mathematicians work. 205 00:10:48.519 --> 00:10:49.080 That makes sense. 206 00:10:49.200 --> 00:10:51.679 You operate on intuition and a feeling for the shape 207 00:10:51.720 --> 00:10:53.720 of the problem long before you write down the first 208 00:10:53.759 --> 00:10:55.200 formal equation that. 209 00:10:55.120 --> 00:10:58.399 Makes total sense when you frame it as the formalization 210 00:10:58.480 --> 00:11:02.679 of intuition. It's like collaborative brainstorming, but executing at a 211 00:11:02.679 --> 00:11:05.440 mathematical level that most humans simply cannot process. 212 00:11:05.759 --> 00:11:08.799 And this raises an important question about our underlying assumptions 213 00:11:08.840 --> 00:11:13.799 regarding machine intelligence. VUB Professor Vincent Jennis, who was deeply 214 00:11:13.799 --> 00:11:17.679 involved in this research, pointed out a massive public misconception. 215 00:11:18.799 --> 00:11:22.240 He noted that people constantly assume the creativity of AI 216 00:11:22.360 --> 00:11:27.720 systems is fundamentally constrained to merely reformulating their training data. 217 00:11:27.879 --> 00:11:30.600 Right the idea that the AI is just a highly 218 00:11:30.639 --> 00:11:34.559 sophisticated fancy parrot reciting textbooks. It's already read the. 219 00:11:34.519 --> 00:11:38.720 Fancy parrot critique. It is everywhere. But Professor Jennis argues 220 00:11:38.759 --> 00:11:43.080 that this specific geometry proof aggressively dismantles that myth. The 221 00:11:43.120 --> 00:11:45.559 AI wasn't remixing an old proof because there was no 222 00:11:45.639 --> 00:11:46.159 old proof. 223 00:11:46.200 --> 00:11:47.519 It didn't exist yet exactly. 224 00:11:47.600 --> 00:11:52.080 It was interpilating between incredibly complex high dimensional concepts to 225 00:11:52.159 --> 00:11:54.919 find a mathematical coordinate that had never been mapped before. 226 00:11:55.120 --> 00:11:57.879 It was engaging in genuine original discovery. 227 00:11:58.120 --> 00:11:59.840 For those of you who really want to dig into 228 00:11:59.840 --> 00:12:03.000 the granular details, of this. The formal paper detailing this 229 00:12:03.080 --> 00:12:06.840 methodology was published in February twenty twenty six on Archsive. 230 00:12:07.600 --> 00:12:10.039 It is titled and get Ready for this early evidence 231 00:12:10.080 --> 00:12:13.840 of vibe proving with consumer LMS A case study on 232 00:12:13.919 --> 00:12:17.799 Spectral region characterization with chat GBT five point two. 233 00:12:18.039 --> 00:12:22.240 Thinking that title alone is just this wild cultural artifact. 234 00:12:22.360 --> 00:12:25.240 It's amazing you have vibe proving, which sounds like Internet 235 00:12:25.279 --> 00:12:29.559 slying sitting side by side with spectral region characterization, which 236 00:12:29.600 --> 00:12:33.440 is an intensely dense mathematical concept. It is the perfect 237 00:12:33.559 --> 00:12:37.799 encapsulation of consumer technology colliding head on with elite academia. 238 00:12:38.360 --> 00:12:41.679 Now, if a commercial AI is capable of genuine original 239 00:12:41.720 --> 00:12:44.919 creativity in a field as complex as mathematics, it raises 240 00:12:44.960 --> 00:12:48.480 a massive existential question. What exactly is the role of 241 00:12:48.519 --> 00:12:50.120 the human in this new dynamic? 242 00:12:50.200 --> 00:12:51.320 That is the big question. 243 00:12:51.519 --> 00:12:53.200 Because I can tell you this shift has not been 244 00:12:53.279 --> 00:12:56.360 quietly accepted by the public or the scientific community. There 245 00:12:56.440 --> 00:12:58.720 is a fiery debate happening right now about who or 246 00:12:58.759 --> 00:13:00.840 what actually deserves the credit for this discovery. 247 00:13:00.960 --> 00:13:04.679 Well, friction is the default human response when you challenge 248 00:13:04.720 --> 00:13:07.919 the definition of creativity, when you threaten the concept of 249 00:13:08.000 --> 00:13:11.759 human exceptionalism and discovery. People are naturally going to push back. 250 00:13:11.879 --> 00:13:14.759 Absolutely. Let's walk through some of the actual public debate, 251 00:13:15.080 --> 00:13:18.639 because observing how people react to this perfectly illustrates the 252 00:13:18.720 --> 00:13:22.919 societal tension. You look at the online commentary surrounding this announcement, 253 00:13:23.159 --> 00:13:25.600 and the perspectives are sharply divided. 254 00:13:25.279 --> 00:13:26.759 Oh completely polarized. 255 00:13:26.879 --> 00:13:29.919 For example, one commenter, who goes by the handle blue Raja, 256 00:13:30.600 --> 00:13:33.960 literally laughed off the idea that the AI solved the 257 00:13:34.000 --> 00:13:38.360 conjecture on its own. Their argument was specifically tied to 258 00:13:38.480 --> 00:13:42.120 those seven chat sessions and four iterations we discussed earlier. 259 00:13:42.240 --> 00:13:43.159 Right the iterations. 260 00:13:43.240 --> 00:13:46.080 They essentially asked, how can you possibly call it independent 261 00:13:46.120 --> 00:13:48.519 problem solving if a human had to prompt it and 262 00:13:48.559 --> 00:13:50.159 correct it seven times? 263 00:13:50.519 --> 00:13:53.240 It is a very defensive reaction, but a predictable one. 264 00:13:53.279 --> 00:13:55.639 People want to look at the human involvement as proof 265 00:13:55.679 --> 00:13:57.120 that the machine is still subordinate. 266 00:13:57.360 --> 00:14:01.519 Yeah, and you see a similar philosophy from another comment enter, Dicabirage, 267 00:14:01.799 --> 00:14:04.960 who took a very structural stance. They argue that while 268 00:14:05.000 --> 00:14:08.480 the technological landscape is changing rapidly, we have to remember 269 00:14:08.480 --> 00:14:11.519 that to this day, no machine is designed to work 270 00:14:11.559 --> 00:14:12.679 completely independently. 271 00:14:12.759 --> 00:14:15.039 Basically treating it like a tool exactly. 272 00:14:15.519 --> 00:14:19.320 They view the AI strictly as playing a major assisting 273 00:14:19.440 --> 00:14:23.600 role like a super powerful calculator, rather than being an 274 00:14:23.639 --> 00:14:25.159 independent mathematical actor. 275 00:14:25.399 --> 00:14:29.679 People constantly try to frame AI using legacy metaphors. They 276 00:14:29.679 --> 00:14:32.679 compare it to a telescope for an astronomer. But a 277 00:14:32.720 --> 00:14:35.679 telescope doesn't tell the astronomer which galaxy to look at, 278 00:14:35.879 --> 00:14:38.960 and it certainly doesn't hypothesize about the chemical composition of 279 00:14:39.000 --> 00:14:40.000 the stars it sees. 280 00:14:40.080 --> 00:14:40.840 That's a great point. 281 00:14:40.919 --> 00:14:43.200 A much more accurate way to look at this dynamic 282 00:14:43.320 --> 00:14:46.759 is like a human deploying an autonomous deep sea subversible 283 00:14:46.960 --> 00:14:50.200 into the mariana trench of mathematics. Okay, like that, You 284 00:14:50.279 --> 00:14:52.159 drop it into the dark. You don't know what the 285 00:14:52.240 --> 00:14:55.879 terrain looks like. The machine navigates the crushing pressure, maps 286 00:14:55.919 --> 00:14:59.799 the unseen topology and surfaces with high definition video of 287 00:14:59.840 --> 00:15:01.120 a species no one. 288 00:15:01.000 --> 00:15:02.960 Has ever seen, and you just get to watch the video. 289 00:15:03.200 --> 00:15:07.120 Yes, the human deployed the submersible and reviewed the footage, 290 00:15:07.440 --> 00:15:12.000 but the machine did the exploring. It is a generative collaborator, 291 00:15:12.320 --> 00:15:13.519 not a passive lens. 292 00:15:13.840 --> 00:15:17.000 I love that submersible analogy because it highlights the element 293 00:15:17.039 --> 00:15:20.360 of the unknown. But then on the complete opposite end 294 00:15:20.360 --> 00:15:23.919 of the spectrum, you have commenters like Captain Obvious, who 295 00:15:23.960 --> 00:15:27.200 pointed out what they see as the harsh, undeniable truth 296 00:15:27.240 --> 00:15:30.759 of the situation, which is they stated point blank that 297 00:15:30.840 --> 00:15:34.480 without chat GPT five point two, this proof simply would 298 00:15:34.559 --> 00:15:37.799 not have happened. They called it troubling that people can't 299 00:15:37.840 --> 00:15:40.639 accept the reality of machine intelligence when it is actively 300 00:15:40.679 --> 00:15:42.840 proving unsolved geometry right in front of them. 301 00:15:42.919 --> 00:15:44.279 Yeah, that's the reality check. 302 00:15:44.360 --> 00:15:46.600 So you have this massive spectrum from it's just a 303 00:15:46.639 --> 00:15:50.399 fancy calculator to the machine is the one driving human progress. 304 00:15:50.840 --> 00:15:53.799 And this tension isn't just happening in comments sections, you know, 305 00:15:54.360 --> 00:15:57.159 it is exactly what the researchers themselves are grappling with 306 00:15:57.240 --> 00:15:59.639 in the lab. The line between a tool and a 307 00:15:59.679 --> 00:16:02.360 co op is blurring at a staggering pace. 308 00:16:02.600 --> 00:16:03.240 It really is. 309 00:16:03.600 --> 00:16:06.320 We can look at the perspective of Breckt Verbiggen, a 310 00:16:06.360 --> 00:16:11.159 postdoctoral researcher in the VUB Data Analytics Lab. He openly 311 00:16:11.200 --> 00:16:14.480 admitted that he had long suspected a model like CHATGPT 312 00:16:15.000 --> 00:16:20.480 could eventually help improve unsolved mathematical problems. The theoretical possibility 313 00:16:20.559 --> 00:16:21.519 was already. 314 00:16:21.080 --> 00:16:23.600 In his mind, so he went into this experiment expecting 315 00:16:23.639 --> 00:16:24.559 a level of success. 316 00:16:24.799 --> 00:16:28.360 He did, but even with that baseline expectation, he stated 317 00:16:28.360 --> 00:16:31.559 that he was still thoroughly surprised by how incredibly efficient 318 00:16:31.600 --> 00:16:32.799 the process actually was. 319 00:16:32.919 --> 00:16:33.320 Wow. 320 00:16:33.600 --> 00:16:36.360 When an expert researcher who expects the technology to be 321 00:16:36.440 --> 00:16:39.600 groundbreaking is still taken aback by its real world capability. 322 00:16:39.960 --> 00:16:41.799 While it tells you that the system is operating at 323 00:16:41.840 --> 00:16:45.759 a cognitive level that defies our current frameworks for understanding intelligence. 324 00:16:46.080 --> 00:16:48.720 So what does this all mean for you listening? If 325 00:16:48.759 --> 00:16:51.639 you are a mathematician, a physicist, or really any kind 326 00:16:51.639 --> 00:16:55.120 of theoretical researcher relying on logic, how does this fundamentally 327 00:16:55.200 --> 00:16:56.440 alter your day to day life? 328 00:16:56.519 --> 00:16:57.440 It changes everything. 329 00:16:57.919 --> 00:17:00.799 If the AI is doing the structural heavy lifting, generating 330 00:17:00.840 --> 00:17:04.839 the blueprints and exploring the Mariana trench of data, what 331 00:17:04.880 --> 00:17:06.759 are the humans actually doing with their time? 332 00:17:07.039 --> 00:17:11.119 It completely inverts the traditional scientific workflow. We can look 333 00:17:11.119 --> 00:17:15.839 at the conclusion drawn by VUB professor Andre Sealgaba. According 334 00:17:15.880 --> 00:17:18.920 to him, the new reality of research is that formulating 335 00:17:18.960 --> 00:17:22.680 candidate proofs the ideation phase is essentially instantaneous. 336 00:17:22.720 --> 00:17:24.640 Now instantaneous, Yes. 337 00:17:24.559 --> 00:17:28.799 The AI can generate potential logical pathways and complex geometric 338 00:17:28.839 --> 00:17:31.759 structures at a speed and volume that no human mind 339 00:17:31.799 --> 00:17:32.720 could ever match. 340 00:17:32.880 --> 00:17:35.640 So the creative bottleneck, you know, the years of steering 341 00:17:35.640 --> 00:17:37.400 at a chalkboard waiting for inspiration. 342 00:17:37.599 --> 00:17:41.079 Yeah, that's just gone, completely gone. The new bottleneck is us. 343 00:17:41.319 --> 00:17:44.599 The human researchers are the friction in the system. Human 344 00:17:44.680 --> 00:17:46.880 verification takes immense time. 345 00:17:46.799 --> 00:17:48.039 Oh, because they have to check it all. 346 00:17:48.200 --> 00:17:51.559 Think about what verifying a proof actually entails. A human 347 00:17:51.599 --> 00:17:55.039 mathematician has to sit down with a complex, potentially forty 348 00:17:55.079 --> 00:17:58.359 page mathematical document generated by an AI and go line 349 00:17:58.400 --> 00:17:59.960 by line, equation by equation. 350 00:18:00.319 --> 00:18:01.599 Sounds exhausting, it is. 351 00:18:01.799 --> 00:18:05.799 They have to ensure that every logical operator, every topological mapping, 352 00:18:05.799 --> 00:18:09.440 and every algebraic bridge is ironclad. It takes weeks for 353 00:18:09.480 --> 00:18:12.240 a human to verify what the AI conceptualized in a 354 00:18:12.240 --> 00:18:13.000 matter of seconds. 355 00:18:13.039 --> 00:18:14.240 That's a crazy imbalance. 356 00:18:14.440 --> 00:18:18.079 The researcher stress that human involvement remains absolutely essential for 357 00:18:18.160 --> 00:18:22.960 this final verification and for resolving any subtle hallucinations. But 358 00:18:23.160 --> 00:18:25.440 it is grueling work because. 359 00:18:25.160 --> 00:18:28.519 The AI might have the vibe right and the overarching 360 00:18:28.599 --> 00:18:32.359 architectural structure right, but you still need a human building 361 00:18:32.400 --> 00:18:36.400 inspector to comb through every single millimeter of the foundation 362 00:18:36.839 --> 00:18:39.160 to ensure reality hasn't been warped, and. 363 00:18:39.079 --> 00:18:42.079 That highlights the current dual nature of these systems. We 364 00:18:42.160 --> 00:18:45.880 see exactly where large language models are most revolutionary in 365 00:18:46.039 --> 00:18:50.599 rapidly exploring complex, high dimensional theoretical ideas, and where the 366 00:18:50.720 --> 00:18:54.759 challenges in deterministic validations still exist. Right the bottleneck of 367 00:18:54.799 --> 00:18:59.880 scientific discovery has officially shifted from human creativity to human verification. 368 00:19:00.400 --> 00:19:02.880 It really is a fascinating journey when you synthesize all 369 00:19:02.920 --> 00:19:05.359 of this together. We have moved from an era where 370 00:19:05.440 --> 00:19:09.039 artificial intelligence was celebrated simply for mimicking human speech and 371 00:19:09.079 --> 00:19:12.039 passing basic Turing tests to an era where it serves 372 00:19:12.079 --> 00:19:16.799 as an active, generative research partner capable of original mathematical discovery. 373 00:19:16.920 --> 00:19:18.200 It's a completely new world. 374 00:19:18.400 --> 00:19:21.079 It is forever changing the pace and the trajectory of 375 00:19:21.160 --> 00:19:25.200 theoretical science. We are no longer waiting years or decades 376 00:19:25.519 --> 00:19:28.119 for a brilliant human mind to suddenly see a hidden 377 00:19:28.160 --> 00:19:31.000 pattern in the universe. We are now waiting on human 378 00:19:31.039 --> 00:19:35.480 minds to slowly, painstakingly verify the brilliant patterns that the 379 00:19:35.519 --> 00:19:37.079 AI has already found. 380 00:19:36.920 --> 00:19:38.920 And if we connect this to the bigger picture, this 381 00:19:39.039 --> 00:19:43.680 current dynamic where humans are the slow manual verifiers might 382 00:19:43.759 --> 00:19:47.960 just be a temporary transitional phase. Really yeah, Professor Algaba 383 00:19:48.000 --> 00:19:52.319 made a very telling and slightly intimidating final prediction. He 384 00:19:52.440 --> 00:19:56.079 noted that while human verification is currently the primary bottleneck 385 00:19:56.119 --> 00:19:59.240 slowing down research, language models will soon evolve to help 386 00:19:59.319 --> 00:20:00.640 us verify the those proofs too. 387 00:20:00.799 --> 00:20:03.680 Wow, let's really think about the implications that you're saying. 388 00:20:03.680 --> 00:20:06.640 The AI generates the novel mathematical proof, and then another 389 00:20:06.680 --> 00:20:09.440 AI model, or perhaps a different reasoning instance of the 390 00:20:09.480 --> 00:20:12.799 exact same AI, acts as the rigorous verifier to check 391 00:20:12.839 --> 00:20:13.680 the logic. 392 00:20:13.680 --> 00:20:16.599 That is, the undeniable trajectory we are on. As these 393 00:20:16.599 --> 00:20:20.480 systems become more deterministic and develop rigorous self correction mechanisms, 394 00:20:20.720 --> 00:20:23.200 the human role might shift even further away from the 395 00:20:23.240 --> 00:20:24.759 actual mathematical mechanics. 396 00:20:25.119 --> 00:20:26.200 So what's left for us? 397 00:20:26.480 --> 00:20:31.079 Humans might transition purely into the realm of philosophical directors, 398 00:20:31.160 --> 00:20:35.160 basically simply selecting which unsolved mysteries of the universe are 399 00:20:35.200 --> 00:20:37.799 worth pointing the AI at in the first place. 400 00:20:38.039 --> 00:20:40.759 Which brings up a final lingering thought. I want to 401 00:20:40.839 --> 00:20:43.880