GPT-5.4 Just Solved a 60-Year-Old Math Problem

GPC 5.4 just solved a 60-year-old maths problem that some of the smartest mathematicians on the planet couldn't crack. And I want to be really clear here about what that means because this isn't a party trick, this isn't AI completing someone else's homework. A Stanford professor named Jared Duker Lichman spent four years working on a related version of this problem. He proved one part of it in 2022, but the other part, the one from 1966, was still open.

Posed by Paul Erdos, Andras Sikorsky, and Andrei Smeridi, three of the greatest mathematicians of the 20th century, and GPC 5.4 Pro just solved it. Let me give you some context on why this is different from anything we've ever seen before. This wasn't a problem sitting in a textbook waiting for someone to look it up. This was a research level conjecture about prime numbers and something called primitive sets.

A primitive set is basically a set of numbers where none of the numbers divides another, right? The primes are the most famous example. The conjecture is about how to compare these sets in a very specific mathematical way. It had been open since 1966, 60 years, right?

And when GPT 5.4 solved it, it didn't just find the answer. It actually found a completely different path to get there. One that had the entire field completely missing, right? Nobody else had seen this answer before.

And here's what makes it so wild. Lichman explained it himself on X. He said, every mathematician who worked on this problem since Erdos' original 1935 paper used the same general approach. They would take the problem, convert it into probability, and work from there.

It was just the natural way to think about it, right? So natural, in fact, that nobody seriously questioned it. GPT 5.4 rejected that path entirely. So instead, it kept the analysis in a different mathematical language the whole time using something called the van Mangold function.

Most math students see this function and think it looks weird and arbitrary. It's piecewise, meaning it's defined differently depending on the output, sorry, the input. It looks unmotivated. GPT 5.4 used it anyway.

And it turns out that function encodes a fundamental identity about prime factorization that cracks the exact part of the problem everyone had been stuck on. Lichman compared it to chess, right? He said, it's like the main openings in chess had been studied deeply for decades. And of course they have been, right?

And then AI comes along and finds new opening line that had been overlooked. And not because it was hidden, but because human aesthetic bias made everyone assume that it was not worth exploring. The approach wasn't worse, it was actually cleaner. And Terry Tao, widely considered the best living mathematician on earth, had already suspected that the probabilistic approach people kept using was unnecessarily complicated.

GPT 5.4 essentially confirmed that suspicion and then went around it. So what's actually happening here and why now? GPT 5.4 isn't just better at retrieving facts, it's reasoning through problems in ways that don't follow the conventional paths. That's different.

For decades, AI was great at pattern matching. You know, find what looks similar and reproduce it. But what happened here was the opposite. GPT 5.4 ignored the most familiar pattern and found something less obvious.

Something humans have been conditioned to try, right? Lichtman said the, sorry, too conditioned to try. Lichtman said the bad reason to use the path GPT 5.4 found is that it's hard to build intuition for it unless you've already gone down the natural path first. So human mathematicians were almost trapped by their own understanding and biases.

The more you know, the more certain routes feel wrong. GPT 5.4 didn't have that problem. And this points to something bigger that I want you to sit with. Every field has conventional wisdom and assumptions, the right way to approach a problem, for example.

And that moves everyone makes, the moves everyone makes, right? Medicine, law, marketing, engineering. Every discipline has assumptions baked in about what's worth trying and what isn't. These assumptions come from experience.

They're usually right, but sometimes they're wrong. And humans are really bad at noticing when they're wrong because the assumptions feel like common sense. AI doesn't inherit those assumptions the same way. That's what you're watching here.

Not just a faster calculator, but something that explores differently. If you want to learn how to actually use AI like this in your business, by the way, how to use it to solve problems that you've been approaching the same way for years, come join us in the AI Profit Board. And we've got 2,800 business owners in the right now actively using AI automation, right? We run four weekly live coaching calls where we go deep on how to apply these tools to get more leads, more customers, and more output with less time.

There's a 30-day roadmap built specifically around using AI in your business. Daily shows with step by step walkthroughs and a prompt library covering everything that you need. There's also a member map so you can connect with people near you who are doing the same sort of things. Link in the comments description or go to the AIprofitboard.com.

Now, let me bring this back down to earth for a second because I know what some of you are thinking. You're thinking, okay, interesting, but what does maths research have to do with me? Here's the connection. The reason this matters isn't the maths bit, right?

It's the method. GPT 5.4 demonstrated that it can take a domain where humans have been operating for the same way for decades and then find a fundamentally different path. One that's not just creative, it's correct. Verifiably, rigorously correct in the field where there's no room for like, kind of right.

And that's a bar and it just cleared it, right? Think about your own work. How many processes in your business were designed five years ago or a few years ago with assumptions and never questioned since? How many things you do a certain way just because you learned that's the right way to do it?

The same cognitive trap that held mathematicians back from solving Erdos' 1196 is holding most businesses back from growing faster. You're attached to the conventional approach. AI can find the other path, the one that works better, that nobody tried because it just didn't seem right. Now, I want to be careful here because I don't want to oversell this, right?

GPT 5.4 didn't do this alone. Lichtman said on X that he's planning to make some announcements about this result soon, right? The implication is that the proof still required human collaboration, human verification, human context. It was part GPT 5.4 and part human.

GPT 5.4 produced the insight, but Lichtman recognized what it was. He understood why the Van Malgraaff path actually worked. He had the domain knowledge to evaluate the solution and check if it's correct. That's the actual model for how AI is going to work in most fields for the foreseeable future.

AI finds a path and humans verify and apply it, which means the question isn't whether AI is coming for your job or your field. The question is whether you're building the skills to be the person who can evaluate what AI produces, to know when it's right, to know when it's wrong, to take the output and actually do something real and practical with it. Lichtman spent four years on a related problem before GPT 5.4 came along. Those four years meant he had the knowledge to recognize what GPT 5.4 produced was valid.

Someone without that background, so for example, for me, I wouldn't know if the solution is correct or not, right? Someone without that background just wouldn't have been able to do anything with the output. It would have been meaningless text. So depth and domain expertise still matters.

Understanding still matters. Your job isn't competing with AI at generating ideas. Your job is to understand your domain well enough to use what AI actually generates. Now here's where this gets even more interesting and this is the part people are not paying attention to just yet.

The problem GPT 5.4 solved wasn't just hard. It was a kind of hard where the field had essentially given up trying new approaches. When even Terry Tao is noticing that the standard method is probably wrong but nobody's found a better one, that's not a problem people are actively working on every day. It faded into the background, right?

A known unsolved thing that researchers occasionally kind of poked at and then moved on from. GPT 5.4 just put it back on the table with a solution. How many problems in your industry are sitting in that exact category? Known pain points.

Things people have tried to fix but failed. Approaches that didn't work well enough. Problems where the field kind of sort of accepted, ah that's just how things are. Those are the exact problems AI is positioned to revisit with fresh eyes.

An SEO agency for example could use AI to find link building angles that everyone in the industry has kind of ignored or given up on because they seem too obvious or too weird, right? A content team could use it to find content structures that consistently perform better but that nobody systematically tests it. A service business could use it to map out client workflows that have inefficiency so baked in that the team doesn't even notice them anymore. The math result is the proof of concept.

The application goes everywhere. It applies to everyone and everywhere watching this, right? And there's a detail in this story I want to go back to because I think it gets lost. Jared Lichman is an assistant professor at Stanford.

He's a number theorist. He's been working on problems in this family for years. He said his mentors actually recommended against working on the original conjecture. Too hard, too risky for a young researcher to spend years on.

Something that might not work out. He worked on it anyway. Then GPT 5.4 walks in and solves the next one. He posted about this with what reads like genuine excitement, right?

It's not anxiety. It's not defensiveness. It's excitement because the result moves his field forward. The conjecture that was open since 1966 is now closed.

The road is clearer. He called it surreal. That's a useful frame. When AI solves a problem in your field or, you know, in your industry, the right question isn't what does this mean for me?

It's what does this open up that wasn't open before? What's now possible that wasn't last week? For Lichman, this might mean that the broader theory around primitive tests gets cleaner. Terry Tao suspected the probabilistic approach was a detour.

If GPT 5.4's method generalizes, it might simplify a whole area of number theory that's been tangled up for decades. For you, it means the problems you thought were too complicated to automate might not be, right? The analysis that used to take your team like three days might be doable in an afternoon. The research process that required a specialist might be accessible with the right prompts and the right model.

The trajectory here is clear. GPT 5.4 Pro is better at open-ended reasoning than anything that came before. It's not just faster. It found an approach that humans missed for six years in a field where some of the humans were, you know, some of the best people in the world and the smartest people ever were working on this.

And that's a meaningful data point about what this generation of models can do. And the next version will be better. This is worse it's going to be. So here's what I'd actually take away from this.

First, if you're sleeping on GPT 5.4, stop. This isn't a marginal upgrade. The jump in reasoning capability is real. It's showing up in pieces and places that matter.

Second, start identifying the conventional wisdom in your own work. What are the things you do a certain way? Because that's always been the right way to do it. Those are your ERDOS 1196 moments, right?

The places where AI might find a different path that you've been too close to see. And third, build your domain knowledge, not just your AI skills. Lichtman could evaluate the proof because he spent years on the problem, right? You need the same depth in your area.

AI gives you the paths, but you need to know which ones to take. And fourth, watch what happens with this result over the next few months. Lichtman said announcements are coming, right? More information is coming.

If GPT 5.4's method generalizes into the broader theory, the way Tao suspected it might, this becomes one of the more significant AI-assisted breakthroughs in academic mathematics. And that matters because maths is where rigorous proof lives. If AI can operate at that level, the ceiling on what it can do elsewhere just got way higher. And the models are reasoning now, not retrieving, right?

Not just completing patterns. Actually reasoning through problems that require original thought. What that means, for example, for every business, every professional, every person who uses these tools, well, we're only just starting to figure that out. If you want to stay ahead of this and actually learn how to use AI like GPT 5.4 in your business, to get more leads, more clients, and save time, come join us in the AI Profit Boardroom.

We've got 2,800 business owners already using these tools. We run four live coaching calls every week where we dig into exactly how to use models like GPT 5.4 to automate all the processes in your business and get more customers. And we'll be going deep on how to apply the reasoning capabilities of these newer models to your specific business. There's a daily 30-day roadmap, daily step-by-step tutorials, a prompt library, and a member map so you can find and connect with people near you who are in the same space.

If you're serious about not falling behind on this, the link's in the comments description or go to the AIProfitBoardroom.com.