1 00:00:00,000 --> 00:00:04,400 Okay, so get this word diving into AI that does math. 2 00:00:04,400 --> 00:00:06,240 Not just like adding numbers or anything. 3 00:00:06,240 --> 00:00:07,080 No, no, no, no, no, no. 4 00:00:07,080 --> 00:00:07,920 Talking like. 5 00:00:07,920 --> 00:00:08,760 Way beyond that. 6 00:00:08,760 --> 00:00:11,480 Mind bending, cutting edge math. 7 00:00:11,480 --> 00:00:14,560 That most of us probably wouldn't even recognize as math. 8 00:00:14,560 --> 00:00:18,360 You sent this paper over called Frontier Math, 9 00:00:18,360 --> 00:00:22,160 a benchmark for evaluating advanced mathematical reasoning 10 00:00:22,160 --> 00:00:23,680 in AI. 11 00:00:23,680 --> 00:00:24,640 And wow. 12 00:00:24,640 --> 00:00:25,640 Yeah, it's a. 13 00:00:25,640 --> 00:00:26,480 It's a lot. 14 00:00:26,480 --> 00:00:27,800 It's a fascinating paper. 15 00:00:27,800 --> 00:00:30,840 What they've essentially done is built an obstacle course, 16 00:00:30,840 --> 00:00:33,520 but for AI, it's called Frontier Math. 17 00:00:33,520 --> 00:00:36,240 And it's a collection of some of the toughest math problems 18 00:00:36,240 --> 00:00:39,520 out there, stuff that even expert mathematicians struggle with. 19 00:00:39,520 --> 00:00:39,860 Yeah. 20 00:00:39,860 --> 00:00:42,400 And they didn't just stick to like one area of math either, 21 00:00:42,400 --> 00:00:42,720 right? 22 00:00:42,720 --> 00:00:44,200 They kind of threw everything at it. 23 00:00:44,200 --> 00:00:45,040 So real mix. 24 00:00:45,040 --> 00:00:48,200 Like number theory, algebraic geometry. 25 00:00:48,200 --> 00:00:50,560 There was even something called category theory, 26 00:00:50,560 --> 00:00:51,840 which honestly, I had to Google. 27 00:00:51,840 --> 00:00:52,600 Yeah, you and me both. 28 00:00:52,600 --> 00:00:54,960 That's not exactly dinner table conversation. 29 00:00:54,960 --> 00:00:57,040 So it's really pushing the boundaries of what we think 30 00:00:57,040 --> 00:00:58,760 about when we talk about AI and math. 31 00:00:58,760 --> 00:01:02,960 And the big question is, can AI solve new problems, 32 00:01:02,960 --> 00:01:05,320 not just stuff that's already in textbooks? 33 00:01:05,320 --> 00:01:05,820 All right. 34 00:01:05,820 --> 00:01:08,720 So did any of the AIs become like the next Einstein? 35 00:01:08,720 --> 00:01:09,640 Well, not quite. 36 00:01:09,640 --> 00:01:12,400 It turns out even the most advanced AI models 37 00:01:12,400 --> 00:01:15,960 could only solve a tiny fraction of the problems. 38 00:01:15,960 --> 00:01:16,920 Less than 2%. 39 00:01:16,920 --> 00:01:17,960 Less than 2%. 40 00:01:17,960 --> 00:01:19,120 That's kind of humbling. 41 00:01:19,120 --> 00:01:21,160 So much for robots taking over the world, right? 42 00:01:21,160 --> 00:01:23,080 Well, it's not quite that simple. 43 00:01:23,080 --> 00:01:26,600 What this really shows us is how complex and nuanced 44 00:01:26,600 --> 00:01:29,120 advanced mathematical reasoning really is. 45 00:01:29,120 --> 00:01:30,920 It's not just about crunching numbers. 46 00:01:30,920 --> 00:01:35,680 It's about deep understanding, creative problem solving, 47 00:01:35,680 --> 00:01:39,000 and connecting ideas that sometimes seem totally unrelated. 48 00:01:39,000 --> 00:01:40,720 OK, so like what, give me an example. 49 00:01:40,720 --> 00:01:42,960 What kind of problems were these AI struggling with? 50 00:01:42,960 --> 00:01:43,560 Sure. 51 00:01:43,560 --> 00:01:46,800 So one example is a problem related to Arton's primitive root 52 00:01:46,800 --> 00:01:48,880 conjecture, which is all about figuring out 53 00:01:48,880 --> 00:01:52,120 how often a specific pattern appears in prime numbers. 54 00:01:52,120 --> 00:01:52,680 OK. 55 00:01:52,680 --> 00:01:53,880 Sounds simple enough. 56 00:01:53,880 --> 00:01:56,680 But it's actually a notoriously difficult problem 57 00:01:56,680 --> 00:01:59,320 that mathematicians have been working on for decades. 58 00:01:59,320 --> 00:02:01,880 So you're giving these AIs unsolved problems. 59 00:02:01,880 --> 00:02:02,840 Exactly. 60 00:02:02,840 --> 00:02:04,400 Trial by fire. 61 00:02:04,400 --> 00:02:06,720 Another example is a problem involving finding 62 00:02:06,720 --> 00:02:09,160 a very specific polynomial. 63 00:02:09,160 --> 00:02:12,080 But it requires understanding the link between shapes 64 00:02:12,080 --> 00:02:13,160 and equations. 65 00:02:13,160 --> 00:02:16,920 A level of abstraction that AI still really struggles with. 66 00:02:16,920 --> 00:02:20,120 So why are we even bothering with this frontier math thing? 67 00:02:20,120 --> 00:02:22,880 If the AI is like failing so miserably. 68 00:02:22,880 --> 00:02:24,880 Well, it's not about making AI look bad. 69 00:02:24,880 --> 00:02:27,280 It's about giving us a reality check 70 00:02:27,280 --> 00:02:30,680 and helping researchers see where AI excels and, more 71 00:02:30,680 --> 00:02:32,160 importantly, where it falls short. 72 00:02:32,160 --> 00:02:34,440 So it's like a roadmap for future research. 73 00:02:34,440 --> 00:02:35,560 Exactly. 74 00:02:35,560 --> 00:02:38,560 By pinpointing the areas where AI struggles, 75 00:02:38,560 --> 00:02:40,520 frontier math can guide researchers 76 00:02:40,520 --> 00:02:42,600 in developing better algorithms and approaches. 77 00:02:42,600 --> 00:02:43,680 It's like a to-do list. 78 00:02:43,680 --> 00:02:44,180 Yeah. 79 00:02:44,180 --> 00:02:47,000 For AI researchers, must improve geometric reasoning skills, 80 00:02:47,000 --> 00:02:49,080 need to understand abstract concepts better, 81 00:02:49,080 --> 00:02:51,520 and figure out those prime number patterns while you're at it. 82 00:02:51,520 --> 00:02:52,480 Exactly. 83 00:02:52,480 --> 00:02:54,520 But it's not just for training AI. 84 00:02:54,520 --> 00:02:56,680 Frontier math also helps us understand 85 00:02:56,680 --> 00:02:59,680 the very principles of mathematical reasoning 86 00:02:59,680 --> 00:03:01,840 and how to translate those principles into something 87 00:03:01,840 --> 00:03:03,080 a computer can use. 88 00:03:03,080 --> 00:03:05,600 So we're trying to teach AI to think like a mathematician. 89 00:03:05,600 --> 00:03:06,320 It's ambitious. 90 00:03:06,320 --> 00:03:07,600 That sounds very ambitious. 91 00:03:07,600 --> 00:03:08,120 Yeah. 92 00:03:08,120 --> 00:03:11,320 To get a better grasp of what that might actually involve, 93 00:03:11,320 --> 00:03:13,120 the researchers behind frontier math 94 00:03:13,120 --> 00:03:15,960 interviewed some big names in mathematics, even 95 00:03:15,960 --> 00:03:18,040 fields metalists. 96 00:03:18,040 --> 00:03:18,760 Wow. 97 00:03:18,760 --> 00:03:20,080 So the math all stars? 98 00:03:20,080 --> 00:03:20,320 Yeah. 99 00:03:20,320 --> 00:03:21,760 What do they have to say? 100 00:03:21,760 --> 00:03:23,320 They're all about AI and math. 101 00:03:23,320 --> 00:03:26,600 Well, they were impressed by how far AI has come, 102 00:03:26,600 --> 00:03:28,360 but they were also realistic. 103 00:03:28,360 --> 00:03:30,480 It's unlikely that AI will be conducting 104 00:03:30,480 --> 00:03:33,040 independent mathematical research anytime soon. 105 00:03:33,040 --> 00:03:33,440 OK. 106 00:03:33,440 --> 00:03:36,080 So no robots taking over universities just yet. 107 00:03:36,080 --> 00:03:37,880 That's probably a relief to some people. 108 00:03:37,880 --> 00:03:38,480 Probably. 109 00:03:38,480 --> 00:03:40,280 But here's where it gets really interesting. 110 00:03:40,280 --> 00:03:44,400 The mathematician said that AI could become a powerful tool 111 00:03:44,400 --> 00:03:47,400 for human mathematicians, almost like a super powered 112 00:03:47,400 --> 00:03:48,480 research assistant. 113 00:03:48,480 --> 00:03:49,040 OK. 114 00:03:49,040 --> 00:03:49,480 I like that. 115 00:03:49,480 --> 00:03:50,400 I can get behind that. 116 00:03:50,400 --> 00:03:51,600 What would that look like, though? 117 00:03:51,600 --> 00:03:53,720 So imagine a computer that could instantly verify 118 00:03:53,720 --> 00:03:56,800 complex calculations, test hypotheses, 119 00:03:56,800 --> 00:03:59,080 and even help generate new ideas that 120 00:03:59,080 --> 00:04:01,920 would free up mathematicians to focus on the more creative parts 121 00:04:01,920 --> 00:04:02,440 of their work. 122 00:04:02,440 --> 00:04:02,680 Yeah. 123 00:04:02,680 --> 00:04:04,960 That sounds like a dream for a lot of mathematicians, I know. 124 00:04:04,960 --> 00:04:05,480 Yeah. 125 00:04:05,480 --> 00:04:06,240 Yeah. 126 00:04:06,240 --> 00:04:07,160 It really does. 127 00:04:07,160 --> 00:04:08,440 And that's a key takeaway here. 128 00:04:08,440 --> 00:04:11,600 It's not about AI replacing mathematicians. 129 00:04:11,600 --> 00:04:15,000 It's about AI augmenting human capabilities 130 00:04:15,000 --> 00:04:17,240 and helping us push the boundaries of mathematical 131 00:04:17,240 --> 00:04:18,560 knowledge even further. 132 00:04:18,560 --> 00:04:21,840 So they actually tested some AI models on frontier math, right? 133 00:04:21,840 --> 00:04:22,440 Absolutely. 134 00:04:22,440 --> 00:04:23,800 It wasn't just all talk. 135 00:04:23,800 --> 00:04:26,000 They wanted to see how the state of the art stacked up. 136 00:04:26,000 --> 00:04:27,200 So who were the contestants? 137 00:04:27,200 --> 00:04:29,280 Well, they put six leading language models 138 00:04:29,280 --> 00:04:31,760 through their paces, including some big names 139 00:04:31,760 --> 00:04:36,480 you might recognize, OpenAI's GPT40 and 01 Preview, 140 00:04:36,480 --> 00:04:39,520 Google DeepMind's Gemini 1.5 Pro, 141 00:04:39,520 --> 00:04:44,960 Anthropics Clawed 3.5 Sonnet, and even XAI's Grock 2 Beta. 142 00:04:44,960 --> 00:04:45,960 Wow. 143 00:04:45,960 --> 00:04:47,360 A real battle of the Titans. 144 00:04:47,360 --> 00:04:47,920 It was. 145 00:04:47,920 --> 00:04:48,760 So how did they do it? 146 00:04:48,760 --> 00:04:49,800 Did anyone crack the code? 147 00:04:49,800 --> 00:04:52,920 Well, remember how we said that even the most advanced AI 148 00:04:52,920 --> 00:04:56,120 models could only solve less than 2% of the problems? 149 00:04:56,120 --> 00:04:56,440 Yeah. 150 00:04:56,440 --> 00:04:57,640 That applies here, too. 151 00:04:57,640 --> 00:05:00,200 None of the models were able to get a 2% success 152 00:05:00,200 --> 00:05:01,520 rate on the full benchmarks. 153 00:05:01,520 --> 00:05:02,000 Wow. 154 00:05:02,000 --> 00:05:04,400 So AI still has a long way to go when 155 00:05:04,400 --> 00:05:06,080 it comes to this kind of advanced math. 156 00:05:06,080 --> 00:05:07,200 It really does. 157 00:05:07,200 --> 00:05:09,160 But that's not necessarily a bad thing, right? 158 00:05:09,160 --> 00:05:09,920 No, it's not. 159 00:05:09,920 --> 00:05:13,480 It just shows we're still in the early stages of developing 160 00:05:13,480 --> 00:05:16,920 AI that can truly reason like a mathematician. 161 00:05:16,920 --> 00:05:20,960 It's like comparing a toddler learning their ABCs 162 00:05:20,960 --> 00:05:22,560 to a professor writing a novel. 163 00:05:22,560 --> 00:05:24,040 Yeah, that's a good analogy. 164 00:05:24,040 --> 00:05:27,480 But even though the overall success rate was low, 165 00:05:27,480 --> 00:05:29,840 there were some interesting variations 166 00:05:29,840 --> 00:05:34,360 in how the different models approached the problems. 167 00:05:34,360 --> 00:05:35,080 Interesting. 168 00:05:35,080 --> 00:05:36,080 Yeah. 169 00:05:36,080 --> 00:05:39,520 So some models like OpenAI's 01 Preview 170 00:05:39,520 --> 00:05:41,880 were more inclined to jump straight to a solution, 171 00:05:41,880 --> 00:05:44,400 even if they hadn't fully explored all the options. 172 00:05:44,400 --> 00:05:48,080 More like confident guessers than careful problem solvers. 173 00:05:48,080 --> 00:05:48,640 Kind of. 174 00:05:48,640 --> 00:05:51,280 Other models like Grock 2 Beta were more 175 00:05:51,280 --> 00:05:53,960 willing to experiment and try different strategies 176 00:05:53,960 --> 00:05:55,880 before settling on a final answer. 177 00:05:55,880 --> 00:05:57,160 They were much more methodical. 178 00:05:57,160 --> 00:05:58,640 So more like detectives. 179 00:05:58,640 --> 00:05:59,140 Yeah. 180 00:05:59,140 --> 00:06:00,560 Carefully piecing together the clues. 181 00:06:00,560 --> 00:06:01,200 Exactly. 182 00:06:01,200 --> 00:06:02,000 I like that. 183 00:06:02,000 --> 00:06:03,600 And I bet all that experimenting used up 184 00:06:03,600 --> 00:06:04,640 a lot of computing power. 185 00:06:04,640 --> 00:06:05,440 It did. 186 00:06:05,440 --> 00:06:07,800 And that's another interesting thing about Frontier Math. 187 00:06:07,800 --> 00:06:10,280 It's not just about finding the right answer. 188 00:06:10,280 --> 00:06:12,920 It's also about understanding the process 189 00:06:12,920 --> 00:06:15,680 of mathematical reasoning and figuring out 190 00:06:15,680 --> 00:06:18,680 how AI can learn to emulate that process. 191 00:06:18,680 --> 00:06:20,240 So it's more than just a test. 192 00:06:20,240 --> 00:06:20,740 It is. 193 00:06:20,740 --> 00:06:24,120 It's a roadmap for the future of AI and math. 194 00:06:24,120 --> 00:06:24,840 Exactly. 195 00:06:24,840 --> 00:06:27,720 It's a framework for developing AI that can not only 196 00:06:27,720 --> 00:06:31,320 solve complex math problems, but also understand 197 00:06:31,320 --> 00:06:34,000 the underlying logic and creativity that 198 00:06:34,000 --> 00:06:36,320 drives mathematical discovery. 199 00:06:36,320 --> 00:06:36,920 This is cool. 200 00:06:36,920 --> 00:06:41,280 It's not just about measuring AI's capabilities today. 201 00:06:41,280 --> 00:06:43,520 It's about setting a vision for the future. 202 00:06:43,520 --> 00:06:44,080 Yeah. 203 00:06:44,080 --> 00:06:44,600 Wow. 204 00:06:44,600 --> 00:06:45,120 It is. 205 00:06:45,120 --> 00:06:47,200 This has been an incredible deep dive so far. 206 00:06:47,200 --> 00:06:49,760 We've talked about the goals of Frontier Math, 207 00:06:49,760 --> 00:06:51,520 the process of creating these problems, 208 00:06:51,520 --> 00:06:55,040 and then the results of testing these different AIs. 209 00:06:55,040 --> 00:06:57,120 And it's clear that there is a lot more to explore here. 210 00:06:57,120 --> 00:06:57,640 There is. 211 00:06:57,640 --> 00:06:58,880 So I'm glad we have more time to dig in. 212 00:06:58,880 --> 00:06:59,640 I am too. 213 00:06:59,640 --> 00:07:01,720 OK, so we've talked about what Frontier Math is trying to do, 214 00:07:01,720 --> 00:07:03,160 but let's get into the nitty gritty. 215 00:07:03,160 --> 00:07:05,040 How was it actually created? 216 00:07:05,040 --> 00:07:07,080 Yeah, this whole thing sounds super complex. 217 00:07:07,080 --> 00:07:08,920 I mean, it must have taken a massive effort 218 00:07:08,920 --> 00:07:10,000 to put it all together. 219 00:07:10,000 --> 00:07:11,200 You're telling me. 220 00:07:11,200 --> 00:07:13,880 It was a huge collaborative project 221 00:07:13,880 --> 00:07:18,480 involving over 60 mathematicians from top universities 222 00:07:18,480 --> 00:07:19,720 all over the world. 223 00:07:19,720 --> 00:07:22,360 Wow, like a mathematical dream team? 224 00:07:22,360 --> 00:07:23,600 Yeah, basically. 225 00:07:23,600 --> 00:07:25,360 And these weren't just any mathematicians. 226 00:07:25,360 --> 00:07:28,440 We're talking former Olympiad champions, professors, 227 00:07:28,440 --> 00:07:29,360 researchers. 228 00:07:29,360 --> 00:07:31,680 They even had a Fields Medalist on the team. 229 00:07:31,680 --> 00:07:32,680 A Fields Medalist? 230 00:07:32,680 --> 00:07:33,080 Wow. 231 00:07:33,080 --> 00:07:34,240 OK, now I'm impressed. 232 00:07:34,240 --> 00:07:34,680 Right. 233 00:07:34,680 --> 00:07:35,560 So what were they doing? 234 00:07:35,560 --> 00:07:38,520 Well, they were the masterminds behind the problems 235 00:07:38,520 --> 00:07:39,560 in Frontier Math. 236 00:07:39,560 --> 00:07:42,440 They were tasked with crafting these original, really 237 00:07:42,440 --> 00:07:45,840 challenging problems that would push AI to its limits. 238 00:07:45,840 --> 00:07:48,560 Like the architects of this AI obstacle course. 239 00:07:48,560 --> 00:07:49,040 Yeah. 240 00:07:49,040 --> 00:07:50,960 But I bet that came with some pretty strict rules, right? 241 00:07:50,960 --> 00:07:53,560 You can't just throw any old math problem at these AI models. 242 00:07:53,560 --> 00:07:54,920 Oh, absolutely. 243 00:07:54,920 --> 00:07:56,560 There were very specific guidelines 244 00:07:56,560 --> 00:07:57,680 for creating these problems. 245 00:07:57,680 --> 00:07:59,760 First, they had to be completely original, 246 00:07:59,760 --> 00:08:03,360 no textbook problems, no rehashed online challenges, 247 00:08:03,360 --> 00:08:04,120 nothing like that. 248 00:08:04,120 --> 00:08:06,800 Right, you don't want the AI models cheating 249 00:08:06,800 --> 00:08:08,840 by like memorizing solutions they've seen before. 250 00:08:08,840 --> 00:08:09,440 Exactly. 251 00:08:09,440 --> 00:08:11,480 Second, the problems had to have solutions. 252 00:08:11,480 --> 00:08:13,280 That could be verified automatically, 253 00:08:13,280 --> 00:08:16,520 usually in the form of numbers or symbolic expressions. 254 00:08:16,520 --> 00:08:17,240 Oh, OK. 255 00:08:17,240 --> 00:08:18,880 So a computer could grade the answers. 256 00:08:18,880 --> 00:08:19,440 Exactly. 257 00:08:19,440 --> 00:08:20,600 No human bias. 258 00:08:20,600 --> 00:08:21,200 Right. 259 00:08:21,200 --> 00:08:25,280 And third, the problems had to be guest proof, no flukes, 260 00:08:25,280 --> 00:08:26,920 no lucky guesses. 261 00:08:26,920 --> 00:08:30,040 The AI model had to demonstrate real mathematical 262 00:08:30,040 --> 00:08:31,040 understanding. 263 00:08:31,040 --> 00:08:33,960 So basically, they had to create a test that 264 00:08:33,960 --> 00:08:37,000 was tough enough to challenge the AI, 265 00:08:37,000 --> 00:08:39,120 fair in its evaluation. 266 00:08:39,120 --> 00:08:40,520 And impossible to cheat on. 267 00:08:40,520 --> 00:08:41,200 Pretty much. 268 00:08:41,200 --> 00:08:42,240 That's a tall order. 269 00:08:42,240 --> 00:08:43,200 It was. 270 00:08:43,200 --> 00:08:45,600 And to make sure they met those standards, 271 00:08:45,600 --> 00:08:48,800 each problem went through a rigorous peer review process, 272 00:08:48,800 --> 00:08:50,120 just like in academic research. 273 00:08:50,120 --> 00:08:50,720 Wow. 274 00:08:50,720 --> 00:08:52,640 Each problem was reviewed by at least one 275 00:08:52,640 --> 00:08:56,040 other mathematician, who was an expert in that specific area 276 00:08:56,040 --> 00:08:56,640 of math. 277 00:08:56,640 --> 00:08:57,840 So it was like a scientific journal. 278 00:08:57,840 --> 00:08:58,320 Right. 279 00:08:58,320 --> 00:08:59,280 But for math problems. 280 00:08:59,280 --> 00:08:59,840 Yeah, exactly. 281 00:08:59,840 --> 00:09:01,200 They really went above and beyond. 282 00:09:01,200 --> 00:09:01,720 They did. 283 00:09:01,720 --> 00:09:04,280 And that's a big part of what sets frontier math apart 284 00:09:04,280 --> 00:09:06,160 from other AI benchmarks. 285 00:09:06,160 --> 00:09:08,480 It's not just about throwing a bunch of random problems 286 00:09:08,480 --> 00:09:08,920 together. 287 00:09:08,920 --> 00:09:11,800 It's about carefully selecting and crafting problems. 288 00:09:11,800 --> 00:09:14,240 That represent the true complexity and diversity 289 00:09:14,240 --> 00:09:16,000 of advanced mathematics. 290 00:09:16,000 --> 00:09:18,720 OK, so we talked about the rigor, the originality. 291 00:09:18,720 --> 00:09:20,200 What about the content itself? 292 00:09:20,200 --> 00:09:21,640 Like what kind of mathematical areas 293 00:09:21,640 --> 00:09:22,680 are we talking about here? 294 00:09:22,680 --> 00:09:25,280 Well, they didn't want to limit the AI models to just one 295 00:09:25,280 --> 00:09:27,200 narrow area of math. 296 00:09:27,200 --> 00:09:30,200 So they included problems from a wide range of fields. 297 00:09:30,200 --> 00:09:33,920 We've got number theory, algebraic geometry, category 298 00:09:33,920 --> 00:09:36,680 theory, even some areas that I had to brush up on. 299 00:09:36,680 --> 00:09:39,080 It's like a smorgasbord of mathematical delights. 300 00:09:39,080 --> 00:09:39,760 It is. 301 00:09:39,760 --> 00:09:41,520 And I imagine that variety is important, right? 302 00:09:41,520 --> 00:09:43,040 And it wouldn't be a very good test 303 00:09:43,040 --> 00:09:46,840 if it only focused on one tiny slice of the mathematical world. 304 00:09:46,840 --> 00:09:48,280 Exactly. 305 00:09:48,280 --> 00:09:51,040 By covering such a broad spectrum of mathematics, 306 00:09:51,040 --> 00:09:54,880 frontier math tests the AI's ability to think flexibly 307 00:09:54,880 --> 00:09:57,240 and apply their knowledge across different domains, 308 00:09:57,240 --> 00:09:58,720 which is something human mathematicians 309 00:09:58,720 --> 00:09:59,840 have to do all the time. 310 00:09:59,840 --> 00:10:00,720 That's a good point. 311 00:10:00,720 --> 00:10:03,440 It's not just about memorizing formulas 312 00:10:03,440 --> 00:10:06,200 or solving specific types of equations. 313 00:10:06,200 --> 00:10:08,360 It's about understanding the underlying principles 314 00:10:08,360 --> 00:10:11,880 of mathematics and being able to apply those principles 315 00:10:11,880 --> 00:10:13,600 in creative and unexpected ways. 316 00:10:13,600 --> 00:10:14,640 Yeah, you got it. 317 00:10:14,640 --> 00:10:16,800 And the way they structured the problems is also interesting. 318 00:10:16,800 --> 00:10:19,680 They designed them to mimic how human mathematicians actually 319 00:10:19,680 --> 00:10:20,800 solve problems. 320 00:10:20,800 --> 00:10:21,960 Ooh, how so? 321 00:10:21,960 --> 00:10:24,120 So the AI models aren't just given a problem 322 00:10:24,120 --> 00:10:25,720 and told to find the answer. 323 00:10:25,720 --> 00:10:28,520 They're also given the ability to write and execute 324 00:10:28,520 --> 00:10:31,360 Python code, to test their ideas, 325 00:10:31,360 --> 00:10:32,800 and explore different approaches. 326 00:10:32,800 --> 00:10:35,840 So it's like giving them a virtual whiteboard. 327 00:10:35,840 --> 00:10:39,000 And a set of mathematical tools to play with. 328 00:10:39,000 --> 00:10:39,640 Exactly. 329 00:10:39,640 --> 00:10:41,880 They're not just passively receiving information. 330 00:10:41,880 --> 00:10:44,680 They're actively engaging with the problem. 331 00:10:44,680 --> 00:10:45,600 Exactly. 332 00:10:45,600 --> 00:10:48,320 It's all about giving the AI models the freedom 333 00:10:48,320 --> 00:10:53,160 to experiment, make mistakes, and learn from those mistakes, 334 00:10:53,160 --> 00:10:54,800 just like human mathematicians do. 335 00:10:54,800 --> 00:10:55,520 That's so cool. 336 00:10:55,520 --> 00:10:58,320 So frontier math is not just about finding the right answer. 337 00:10:58,320 --> 00:11:01,000 It's about the entire process of mathematical reasoning. 338 00:11:01,000 --> 00:11:01,600 Exactly. 339 00:11:01,600 --> 00:11:04,440 It's about teaching AI to think like a mathematician, 340 00:11:04,440 --> 00:11:05,800 not just mimic one. 341 00:11:05,800 --> 00:11:06,440 Precisely. 342 00:11:06,440 --> 00:11:07,720 That's much more challenging. 343 00:11:07,720 --> 00:11:08,440 It is. 344 00:11:08,440 --> 00:11:10,200 And it requires a completely different approach 345 00:11:10,200 --> 00:11:11,360 to AI development. 346 00:11:11,360 --> 00:11:12,040 It does. 347 00:11:12,040 --> 00:11:14,680 I'm really starting to grasp the depth and ambition 348 00:11:14,680 --> 00:11:15,560 of this whole project. 349 00:11:15,560 --> 00:11:18,840 It's not just about measuring AI's current capabilities. 350 00:11:18,840 --> 00:11:22,640 It's about setting a vision for the future of AI in mathematics. 351 00:11:22,640 --> 00:11:23,640 You nailed it. 352 00:11:23,640 --> 00:11:26,160 Frontier math is laying the groundwork. 353 00:11:26,160 --> 00:11:30,120 For AI to become a true partner in mathematical exploration 354 00:11:30,120 --> 00:11:31,840 and discovery. 355 00:11:31,840 --> 00:11:32,760 This is awesome. 356 00:11:32,760 --> 00:11:33,360 It is. 357 00:11:33,360 --> 00:11:33,800 OK. 358 00:11:33,800 --> 00:11:37,040 So we've talked a lot about the why and the how of frontier 359 00:11:37,040 --> 00:11:37,600 math. 360 00:11:37,600 --> 00:11:39,360 But let's get down to brass tacks. 361 00:11:39,360 --> 00:11:42,000 We know the overall success rate was pretty low. 362 00:11:42,000 --> 00:11:44,280 But what about the individual AI models? 363 00:11:44,280 --> 00:11:47,160 Were there any major differences in how they performed? 364 00:11:47,160 --> 00:11:47,680 Oh, yeah. 365 00:11:47,680 --> 00:11:48,880 Definitely. 366 00:11:48,880 --> 00:11:51,080 There were some interesting variations. 367 00:11:51,080 --> 00:11:54,400 As we mentioned earlier, some models like Open AI's O1 368 00:11:54,400 --> 00:11:58,840 preview were more prone to jumping straight to a solution 369 00:11:58,840 --> 00:12:00,760 without much exploration. 370 00:12:00,760 --> 00:12:01,260 Right. 371 00:12:01,260 --> 00:12:02,680 Like the quick draw gunslingers. 372 00:12:02,680 --> 00:12:03,160 Yeah. 373 00:12:03,160 --> 00:12:05,400 Firing off answers without taking careful aim. 374 00:12:05,400 --> 00:12:05,960 Exactly. 375 00:12:05,960 --> 00:12:08,440 But others like Grock 2 beta were much more 376 00:12:08,440 --> 00:12:09,920 methodical and experimental. 377 00:12:09,920 --> 00:12:11,080 Like Pace It Snipers. 378 00:12:11,080 --> 00:12:11,680 Yeah. 379 00:12:11,680 --> 00:12:14,080 Carefully surveying the landscape before taking a shot. 380 00:12:14,080 --> 00:12:14,880 Exactly. 381 00:12:14,880 --> 00:12:16,960 And these different approaches actually played out 382 00:12:16,960 --> 00:12:20,640 in the results for the four problems that at least one model 383 00:12:20,640 --> 00:12:21,600 was able to solve. 384 00:12:21,600 --> 00:12:22,360 Oh, interesting. 385 00:12:22,360 --> 00:12:22,600 Yeah. 386 00:12:22,600 --> 00:12:23,640 Tell me more about those. 387 00:12:23,640 --> 00:12:27,880 So one problem involved probability theory and approximations. 388 00:12:27,880 --> 00:12:31,400 And Grock 2 beta, with its methodical approach, 389 00:12:31,400 --> 00:12:33,800 had the highest success rate at 60%. 390 00:12:33,800 --> 00:12:36,120 So Grock was the king of chance and uncertainty. 391 00:12:36,120 --> 00:12:37,160 It seems so. 392 00:12:37,160 --> 00:12:38,200 What about the other problems? 393 00:12:38,200 --> 00:12:41,000 Another problem involved algebraic topology. 394 00:12:41,000 --> 00:12:45,160 This one was aced by O1 preview, achieving a perfect score 395 00:12:45,160 --> 00:12:46,520 of 100%. 396 00:12:46,520 --> 00:12:47,520 Wow. 397 00:12:47,520 --> 00:12:48,320 A perfect score. 398 00:12:48,320 --> 00:12:49,120 I know. 399 00:12:49,120 --> 00:12:53,520 So O1 preview had a knack for those abstract spaces and shapes. 400 00:12:53,520 --> 00:12:54,200 Apparently. 401 00:12:54,200 --> 00:12:55,160 What about the rest? 402 00:12:55,160 --> 00:12:58,320 The third problem focused on group theory and field theory. 403 00:12:58,320 --> 00:13:02,800 And both O1 preview and Gemini 1.5 Pro had decent success rates, 404 00:13:02,800 --> 00:13:05,360 at 80% and 60%, respectively. 405 00:13:05,360 --> 00:13:05,760 OK. 406 00:13:05,760 --> 00:13:07,760 So they were the masters of manipulating 407 00:13:07,760 --> 00:13:09,080 those algebraic structures. 408 00:13:09,080 --> 00:13:10,000 That's pretty impressive. 409 00:13:10,000 --> 00:13:10,680 It is. 410 00:13:10,680 --> 00:13:12,440 The final problem was a tricky combination 411 00:13:12,440 --> 00:13:14,520 of algebraic geometry and combinatorics. 412 00:13:14,520 --> 00:13:18,800 Only two models managed to solve it, O1 mini and Claude 3.5 413 00:13:18,800 --> 00:13:21,040 Sonnet, both with a 20% success rate. 414 00:13:21,040 --> 00:13:23,080 So they were the champions of finding patterns 415 00:13:23,080 --> 00:13:26,560 and relationships in those complex geometric and combinatorial 416 00:13:26,560 --> 00:13:27,200 structures. 417 00:13:27,200 --> 00:13:27,800 It seems. 418 00:13:27,800 --> 00:13:30,680 Even a 20% success rate is pretty good. 419 00:13:30,680 --> 00:13:32,840 When you consider how difficult these problems were. 420 00:13:32,840 --> 00:13:34,040 You're absolutely right. 421 00:13:34,040 --> 00:13:36,200 And it's worth noting that these results highlight 422 00:13:36,200 --> 00:13:40,280 the unique strengths and weaknesses of each AI model 423 00:13:40,280 --> 00:13:42,320 across different areas of mathematics. 424 00:13:42,320 --> 00:13:46,000 It's like each model has its own mathematical personality, 425 00:13:46,000 --> 00:13:48,800 excelling in some areas while struggling in others. 426 00:13:48,800 --> 00:13:49,800 That's a great way to put it. 427 00:13:49,800 --> 00:13:51,480 And actually, this diversity of strengths 428 00:13:51,480 --> 00:13:56,040 is a really positive sign for the future of AI in mathematics. 429 00:13:56,040 --> 00:13:56,800 How so? 430 00:13:56,800 --> 00:14:00,480 Well, it means we're not limited to just one single approach 431 00:14:00,480 --> 00:14:03,600 to developing AI that can reason mathematically. 432 00:14:03,600 --> 00:14:06,240 There's no one size fits all solution. 433 00:14:06,240 --> 00:14:10,120 Instead, we can have a whole ecosystem of AI models 434 00:14:10,120 --> 00:14:11,800 with complementary strengths. 435 00:14:11,800 --> 00:14:15,560 So instead of trying to create one super AI that can do it all, 436 00:14:15,560 --> 00:14:18,200 we can have specialized AI models that excel 437 00:14:18,200 --> 00:14:19,560 in different areas of mathematics. 438 00:14:19,560 --> 00:14:20,160 Exactly. 439 00:14:20,160 --> 00:14:22,880 And by combining the insights from all these different models, 440 00:14:22,880 --> 00:14:26,360 we can create even more powerful and versatile AI systems 441 00:14:26,360 --> 00:14:29,280 that can tackle a wider range of mathematical challenges. 442 00:14:29,280 --> 00:14:30,160 That's the idea. 443 00:14:30,160 --> 00:14:31,920 That's a really optimistic perspective. 444 00:14:31,920 --> 00:14:32,240 It is. 445 00:14:32,240 --> 00:14:36,040 It's like assembling a team of mathematical superheroes, 446 00:14:36,040 --> 00:14:37,880 each with their own unique superpowers. 447 00:14:37,880 --> 00:14:39,600 I love that analogy. 448 00:14:39,600 --> 00:14:42,800 And frontier math is providing the training ground 449 00:14:42,800 --> 00:14:45,200 for these future mathematical superheroes 450 00:14:45,200 --> 00:14:46,240 to hone their skills. 451 00:14:46,240 --> 00:14:48,680 This is seriously blowing my mind. 452 00:14:48,680 --> 00:14:52,720 Frontier math is so much more than just a test or a benchmark. 453 00:14:52,720 --> 00:14:55,760 It's a catalyst for innovation and discovery in both AI 454 00:14:55,760 --> 00:14:56,720 and mathematics. 455 00:14:56,720 --> 00:14:57,400 It is. 456 00:14:57,400 --> 00:15:00,640 It's helping us understand not only what AI can do today, 457 00:15:00,640 --> 00:15:02,960 but also what it might be capable of in the future. 458 00:15:02,960 --> 00:15:03,400 Right. 459 00:15:03,400 --> 00:15:05,320 And that's what makes this whole project so exciting. 460 00:15:05,320 --> 00:15:06,440 It is exciting. 461 00:15:06,440 --> 00:15:08,920 This has been an incredible deep dive so far. 462 00:15:08,920 --> 00:15:11,560 We've talked about the motivation behind frontier math, 463 00:15:11,560 --> 00:15:14,320 the meticulous process of creating the problems, 464 00:15:14,320 --> 00:15:17,040 and the impressive, albeit varied, 465 00:15:17,040 --> 00:15:18,880 performance of different AI models. 466 00:15:18,880 --> 00:15:20,560 It's been a fascinating journey, 467 00:15:20,560 --> 00:15:21,800 and we're just getting started. 468 00:15:21,800 --> 00:15:23,680 We've focused a lot on the AI side of things. 469 00:15:23,680 --> 00:15:24,200 Yeah. 470 00:15:24,200 --> 00:15:26,640 But what about the human element in all of this? 471 00:15:26,640 --> 00:15:29,720 What are the implications of frontier math for those of us 472 00:15:29,720 --> 00:15:32,240 who aren't AI researchers or field's medalists? 473 00:15:32,240 --> 00:15:33,680 That's a great question. 474 00:15:33,680 --> 00:15:36,080 And it's something we'll dive into right after this. 475 00:15:36,080 --> 00:15:38,800 So we've talked a lot about the technical side of things, 476 00:15:38,800 --> 00:15:40,200 but let's zoom out a bit. 477 00:15:40,200 --> 00:15:43,520 What does this all mean for the average person? 478 00:15:43,520 --> 00:15:44,560 Yeah, that's a good point. 479 00:15:44,560 --> 00:15:48,760 I mean, I'm all for robot solving complex math problems. 480 00:15:48,760 --> 00:15:51,120 But how does this actually affect our lives? 481 00:15:51,120 --> 00:15:53,400 Well, for one thing. 482 00:15:53,400 --> 00:15:56,840 Frontier math is helping to kind of demystify 483 00:15:56,840 --> 00:15:58,080 advanced mathematics. 484 00:15:58,080 --> 00:15:58,400 OK. 485 00:15:58,400 --> 00:16:01,400 By showing that AI can grapple with these really challenging 486 00:16:01,400 --> 00:16:04,120 problems, it makes the whole field seem a little less 487 00:16:04,120 --> 00:16:04,800 intimidating. 488 00:16:04,800 --> 00:16:06,280 So it makes it feel more accessible. 489 00:16:06,280 --> 00:16:06,920 Exactly. 490 00:16:06,920 --> 00:16:08,400 Especially for students or anyone 491 00:16:08,400 --> 00:16:10,800 who might feel intimidated by higher level math. 492 00:16:10,800 --> 00:16:11,240 Right. 493 00:16:11,240 --> 00:16:13,560 Like if a computer can understand it, maybe I can too. 494 00:16:13,560 --> 00:16:14,440 Exactly. 495 00:16:14,440 --> 00:16:16,840 And beyond that, frontier math is also 496 00:16:16,840 --> 00:16:20,240 helping to accelerate the pace of mathematical discovery. 497 00:16:20,240 --> 00:16:20,960 How so? 498 00:16:20,960 --> 00:16:23,560 As AI gets better at solving math problems, 499 00:16:23,560 --> 00:16:25,240 it can become a really powerful tool 500 00:16:25,240 --> 00:16:27,760 for human mathematicians, automating 501 00:16:27,760 --> 00:16:31,160 tedious calculations, checking for errors, 502 00:16:31,160 --> 00:16:33,400 even helping to generate new ideas. 503 00:16:33,400 --> 00:16:34,920 Like a super powered research assistant. 504 00:16:34,920 --> 00:16:35,920 Yeah, exactly. 505 00:16:35,920 --> 00:16:36,640 That's pretty cool. 506 00:16:36,640 --> 00:16:40,640 And this kind of collaboration between humans and AI 507 00:16:40,640 --> 00:16:43,040 could lead to breakthroughs in all sorts of fields, 508 00:16:43,040 --> 00:16:48,200 cryptography, material science, even fundamental physics. 509 00:16:48,200 --> 00:16:49,320 Wow. 510 00:16:49,320 --> 00:16:52,120 So frontier math is having ripple effects, 511 00:16:52,120 --> 00:16:54,760 far beyond the world of pure mathematics. 512 00:16:54,760 --> 00:16:55,480 It is. 513 00:16:55,480 --> 00:16:57,000 And maybe even more importantly, 514 00:16:57,000 --> 00:16:59,600 frontier math is forcing us to rethink what 515 00:16:59,600 --> 00:17:01,080 it means to do math. 516 00:17:01,080 --> 00:17:01,760 OK. 517 00:17:01,760 --> 00:17:02,560 How so? 518 00:17:02,560 --> 00:17:04,920 Well, traditionally, we viewed math 519 00:17:04,920 --> 00:17:07,040 as a purely human endeavor, something 520 00:17:07,040 --> 00:17:10,160 that requires special kind of intuition and creativity 521 00:17:10,160 --> 00:17:12,120 that machines could never replicate. 522 00:17:12,120 --> 00:17:14,320 But frontier math is kind of challenging that assumption. 523 00:17:14,320 --> 00:17:14,640 Yeah. 524 00:17:14,640 --> 00:17:16,880 It's blurring the lines between human and machine 525 00:17:16,880 --> 00:17:17,520 intelligence. 526 00:17:17,520 --> 00:17:18,200 Right. 527 00:17:18,200 --> 00:17:20,600 And that raises all sorts of interesting questions 528 00:17:20,600 --> 00:17:22,960 about the nature of mathematical thinking 529 00:17:22,960 --> 00:17:25,400 and the potential for AI to become a true partner 530 00:17:25,400 --> 00:17:26,880 in mathematical exploration. 531 00:17:26,880 --> 00:17:29,600 So we're on the verge of a new era in mathematics. 532 00:17:29,600 --> 00:17:30,000 Maybe. 533 00:17:30,000 --> 00:17:32,520 Where humans and AI work together. 534 00:17:32,520 --> 00:17:33,760 That's pretty exciting. 535 00:17:33,760 --> 00:17:34,120 It is. 536 00:17:34,120 --> 00:17:35,680 This has been an incredible deep dive. 537 00:17:35,680 --> 00:17:36,120 It has. 538 00:17:36,120 --> 00:17:39,440 We've gone from the nitty gritty details of AI algorithms 539 00:17:39,440 --> 00:17:42,560 to the philosophical implications of machines doing math. 540 00:17:42,560 --> 00:17:43,880 It's been a great discussion. 541 00:17:43,880 --> 00:17:47,320 And for our listeners, if you're feeling adventurous, 542 00:17:47,320 --> 00:17:49,800 we'll include links to some of the frontier math problems 543 00:17:49,800 --> 00:17:51,080 in the show notes. 544 00:17:51,080 --> 00:17:53,080 Let us know if you managed to crack the code. 545 00:17:53,080 --> 00:17:54,200 Good luck. 546 00:17:54,200 --> 00:17:56,360 And remember, even if you don't solve them, 547 00:17:56,360 --> 00:17:58,360 just trying to understand these problems 548 00:17:58,360 --> 00:18:01,040 is a great way to stretch your mathematical muscles. 549 00:18:01,040 --> 00:18:02,160 That's a good point. 550 00:18:02,160 --> 00:18:04,480 The journey is just as important as the destination. 551 00:18:04,480 --> 00:18:05,080 Absolutely. 552 00:18:05,080 --> 00:18:07,240 Especially in the world of mathematics. 553 00:18:07,240 --> 00:18:08,720 So keep exploring. 554 00:18:08,720 --> 00:18:09,760 Keep questioning. 555 00:18:09,760 --> 00:18:10,080 Yeah. 556 00:18:10,080 --> 00:18:12,320 And keep pushing the boundaries of what's possible. 557 00:18:12,320 --> 00:18:13,080 Well said. 558 00:18:13,080 --> 00:18:17,640 And we'll see you next time.