Google Just SOLVED MATH?!

Added: 2026-05-28

[00:00:00]So over the past few years, Google DeepMind has been quietly building towards something much bigger than just chat bots. First, there was Alph Go, where AI defeated one of the world's best goal players in what many considered an impossible milestone at the time. It even used the now infamous move 37 to win one of the matches. A move so novel the commentators thought it was a mistake. Then came Alpha Fold, which basically solved a 50-year-old biology problem by predicting the structure of every protein. Something many researchers say dramatically accelerated biological research. And now, Demis Hassabis keeps talking about this idea that AI could trigger an entirely new golden age of discovery where AI systems can actually help humanity generate brand new knowledge similar to the move 37 in Go. And in fact, at Google IO just a few days ago, Demis literally said, "We may be standing in the foothills of the singularity while showcasing projects like Gemini for science and other AI systems designed specifically to accelerate scientific research. But what really caught my attention this week was this brand new paper they dropped titled Advancing Mathematics Research with AIdriven Formal Proof Search." Because what they essentially created here are AI agents capable of autonomously solving real open mathematical problems.

[00:01:27]And unlike normal AI outputs that can hallucinate or make things up, these proofs are formally verified stepby step by software to make sure the reasoning is actually correct. And as we'll see, they've already solved several decades old math problems. So yeah, while that might sound niche at first or even kind of abstract, the bigger implication here is honestly insane. This is one of the clearest signs yet that AI is actually starting to discover things that humanity didn't already know and that might be the most impactful and meaningful thing AI can do. So first, what exactly did they build here? Well, the framework is called Alpha Proof Nexus. And basically, it's a system that connects frontier language models with lean, which is a formal proof assistant that can mechanically verify mathematical proofs. So instead of just asking an AI model to write out a natural language proof and hoping it's right, Alpha Proof Nexus has the model generate proof code in lean directly and lean then checks the proof step by step almost like a compiler for mathematics.

[00:02:38]So if the proof has even one broken logical step, it doesn't pass. In fact, in lean, that missing proof or step gets marked with something called sorry. And then the agent's job is to replace that sorry with a real proof that lean accepts. Now to actually do that, it uses multiple sub aents that independently search for different proof paths. Each one tries to modify the proof, checks it with lean, reads the error messages when it fails, and then tries again. This is what they call the Ralph loop. Their stronger version also coordinates these sub aents using an evolutionary algorithm and can even call on Alpha Proof, Deep Mind's Olympiad level theorem proving system. So in plain English for the non-mathematical wizards out there, it's basically generate a proof attempt, which is basically like generating a solution, check it with lean, the mechanical proof verifier, learn from the errors, try again, and just keep searching until it finally works. If you think about it, this is actually very similar to Alph Go, where the system continuously searches through enormous numbers of possible moves, learns from the feedback, eliminates bad paths, reinforces better ones, and gradually converges towards stronger solutions over time. Except instead of searching for winning moves in a board game, it's now searching for mathematically correct proofs inside formal mathematics. But here's where things start to get a little crazy. Because according to the paper, their fullfeatured agent autonomously solved nine open herdish problems out of 353 attempted, including two questions that had apparently remained open for over 56 years. It also solved 44 open conjectures from the online encyclopedia of integer sequences, whatever that is, along with helping resolve several other active research problems. So again, these weren't questions you can find the answer to in textbooks or even online.

[00:04:44]These were legitimate open mathematical problems that had never been solved before. And some of them are so difficult and obscure that even the best of the best mathematical minds couldn't solve them. if they tried. Now, another detail that really stood out to me was the cost. According to the researchers, many of these problems were solved at an inference cost of only a few hundred per problem, which is kind of insane when you think about it. I mean, traditionally, solving problems like this can sometimes take human researchers weeks, months, or even years of work. And so even if it takes a single human researcher just one whole week to solve one of these problems, this system is still much cheaper. Now obviously this system is still very limited and specialized unlike the human researcher would be but you can already start to see the direction this is heading in.

[00:05:36]>> I think that the AI is the ultimate tool for science in the in the limit. It's why I started this whole journey was to um try and as a scientist understand better the world around us and I felt that our minds br you know we could use uh an incredible tool to help even the smartest experts uh more quickly navigate all the complexity of the data that we collect and try and find connections and insights and structure in that data and uh what better tool than AI to do that and I think that's coming to fruition now And it's just a very very exciting time to see the pace of science pick up in all sorts of fields, many fields where we've been stuck for 30 40 years um like we were with protein folding. And I think we're going to see a lot of those um uh breakthroughs over the next decade or so.

[00:06:27]>> So yeah, this paper isn't just about solving mathematics. It's really about accelerating scientific discovery with the help of AI. As Demis said, we already saw Alphold help accelerate biological research by solving protein folding. And now we're seeing AI systems capable of generating formally verified mathematical proofs. But this is just the beginning. Mathematics, physics, medicine, chemistry, material science, engineering, basically every major scientific field will be affected by this. This could mean new medicines, new materials, new energy systems, new technologies, all discovered at a pace faster than ever before in human history. I mean, when you accelerate the process of scientific discovery itself, you're literally pressing the fast forward button on human progress. And the long-term implications of that are almost impossible to fully comprehend.

[00:07:27]So, yeah. Thanks for watching. I hope you guys enjoyed this breakdown of Google's new alpha proof nexus framework. And shout out to Google DeepMind for continuing to pump out this incredible research on seemingly a weekly basis. Thank you also to everyone who continues to support this channel by liking and subscribing. And as always, I'll be catching you guys in the next