OpenAI’s New AI Is Doing Things We Barely Understand

Something is changing in the world of mathematics and science. And it is changing fast. OpenAI just released hundreds of AI-generated mathematical results, including claims that would have sounded completely impossible just a few months ago. I've been scrolling so much here, sorry, and hope your eyes are okay. And we are still at letter C. A total of 722 papers. The headlines keep talking about the controversy. I'd like to avoid that, because very few people are talking about the works themselves, so I would like to talk a bit about the mathematics. And I feel a bit conflicted. I'll tell you why at the end, because I need to show you the results for it to make sense. Now, hold on to your papers, Fellow Scholars, and let's talk about 2 of my favorite results. One, fire a laser into a triangular mirror room and let it bounce forever. Haha! I am a light transport researcher by trade, so of course, I am going to frame a billiard ball problem like this. Much, much cooler. If the triangle has at least one angle that is irrational relative to pi, then almost every ray ends up visiting every spot, go in every direction, spending an equal amount of time everywhere. Whoa! This is the problem of irrational triangular billiards. Super challenging to prove, because irrational angles don't settle into a repeating pattern. So, our usual tricks are completely useless here. It is like a ball you want to lift, but you can't get a proper handle on. Really tough. OpenAI claims they proved this for every triangle of this kind. By the way, these explanations come with the risk of simplifying things. And I am also not an expert, just a student, but I am trying my best here. 2. Draw an ugly planar region full of weirdly shaped holes. Apply a stretch that keeps angles intact, we call it a conformal transformation. And— You can watch the holes morph into perfect circles or points while angles are preserved. It is incredibly challenging to prove because the holes can become infinitely tiny, and worse, even tangled, making the final shape very hard to control. Before, we only knew that it would happen in easier cases, but now, OpenAI claims that this always works. Wow. Now, I will note that I don't have any relationship with OpenAI, they ignore all my mails, and they don't share any models with early access with me. Which they do for a lot of people. Not me. Okay, so, some mathematicians are very happy, some, not so much. Why? Well, if you look at the papers and the solutions, hmm, how do I put it? These are not elegant proofs. Some of them are a big ball of barf. And this raises an important question. What is the goal of mathematics? If we have a mathematical question, some people just want the result. What is the answer to the question? Yes or no? n or n squared? Example. We can write fluid and smoke simulations ourselves, we know the theory. But we can also train a neural network that can often do what we can already do, but do it faster. So, what did it do? Well, we don't know. The answer is not an elegant algorithm, but activations inside a neural network. The answer is a big bunch of numbers. These proofs are kinda like that. You mostly need another AI to make sense out of them. And some people say, that's a tool, and I want that tool. They say, I don't care what's inside. But for others, the goal of mathematics is to learn something new. The Pythagorean theorem has many proofs, we only need one. 100 proofs is not any better than one in terms of proving. However, every single one of those 100 proofs are illuminating our minds Differently. Each of them teaches us a new lesson. And people in this camp are not happy with this approach of putting a firehose of data out there and asking people to do the work. And look, I am just a student. I am here to learn. And I get it, both of these viewpoints make sense to me. In any case, these are incredible achievements. But I still feel a bit conflicted. Why? Dear Fellow Scholars, this is Two Minute Papers with Dr. Károly Zsolnai-Fehér. Well, if we look back to just about 6 years ago, GPT-3, people said, well, it can't even add numbers together reliably. But 2 years ago, people said, well, it can't even solve high school competition problems reliably. 1 year ago, people said, it can't even win the Mathematical Olympiad gold medal reliably. And just a month ago, it very likely solved a millennium problem that no human had ever solved before. This was the Navier-Stokes equation with the fluids. Now, people are saying that it did not come up with anything novel. Just combining already existing puzzle pieces, they say. I would like to note that to me, this sounds like an ever-receding argument. If we look at what we had 6 years ago, a technique that couldn't even add numbers, and now, on some tasks, it may be, or will soon be better than all of us combined. Then, I think it is easy to see how powerful these AI techniques are becoming. Now, they have hundreds of results, each of which took them about 3 hours to compute. On average. That is insane. You are seeing a miracle unfold before your eyes. But not so fast. This is currently only possible with a model that is not available for us. Not for the little man. It is only available for maybe a handful of people in frontier labs. It's a big club, and we ain't in it. And I am not so sure if I feel too good about that. If this technology can advance mathematics and science at this level, I think access to it needs to be shared with everyone. And there is a way to do that. The answer is open weights models that we can run and own ourselves. We have to come together and contribute to these projects. Because we need more of those. Writing code is contributing. Doing experiments is contributing. Just telling others about it is contributing too. And then, all of us would get the opportunity to push humanity forward. We have to make it happen! I'd love that. That is the way of the scholar. What a time to be alive! Oh wait. I wanted to wait a bit with the video to have the dust settle a bit. To let it breathe a little. And what do I see? 3 papers had been withdrawn due to feedback from the community. To my knowledge, likely also using an LLM to find out about it. Now that is exactly what I meant by democratizing this technology. We need to make sure that this is not an expensive hobby, but something that all of us can take part in. Subscribe and hit the bell to see more. I use LaMDA to reproduce AI research papers, often in minutes. It's also great to train your own models or fine-tune an existing one. Run inference, or text to image or video? Easy peasy. Running a DeepSeek chatbot or agent? Super fast, super reliable. Lambda gives you powerful NVIDIA GPUs to run your own experiments. I test ideas from the papers I cover, and moments later, results. Love it! Seriously, try it out now at lambda.ai/papers.