I was recently watching a video by Mo Gada.
It was a keynote he was giving.
He's a former Google X executive.
And he was saying that AI is no longer just writing code.
It's actually correcting human math.
He gives this really incredible example where he says basically for the last 56 years he's been using the same matrix multiplication method for code.
And this is something that he said is like very standard.
People agree on this for a very long time.
And he said that recently he was, you know, talking to AI and telling it basically to improve itself.
And he said when he told AI to improve itself, the AI realized that their matrix multiplication method was flawed.
And so, instead of trying to go and optimize the software that he had created, that they had for AI, which is what he assumed it would do,
Instead, it invented a completely new way of doing math.
And he said to essentially optimize itself.
And he said that that new invention resulted in a 26 in performance boost and the removal of hundreds of millions of dollars in cost and energy use for Google.
So like this massive upgrade uptick in basically optimization.
This is a fascinating concept.
When I first saw that, I was really fascinated by the fact that AI is definitely getting better at math.
But beyond just getting better at solving math or solving math the way that we might solve it, it's creating new ways to solve math and coming up with completely new methods when it thinks that our methods are flawed.
So today on the podcast, I want to get into AI and math where it is today, because there's also a whole bunch of really interesting news about math problems that have been solved recently.
And I think it's easy to talk about AI hallucinations and how AI can't do X Y, Z.
I honestly think like, beyond the hype, what I'm actually seeing in my day-to-day use of AI is that it is getting like startlingly good and it's improving very quickly and And I think a lot of that isn't necessarily that maybe the model's getting better, but the tooling we're adding.
Anyways, we're going to get into all of it on the podcast.
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All right, let's get into the state of AI and math today.
I wanted to start this off by saying that AI models right now are starting to crack a whole bunch of high level math problems.
I was recently on X and I saw a tweet from Bartosz Nasrecki where he said GPT-5 Pro solved in just 15 minutes, without any internet searches, the presentation problem known as Yu Tsumurutsu's 554th problem.
He said this is the first model to solve this task completely.
DD recently posted on X and said 120 out of 120 and just shared all of the solutions huge milestone in AI.
I saw another really interesting story where over the weekend, Neil Somani, who is a software engineer he's a former quant and now he has a startup but he was testing how well OpenAI's newest AI model could handle really difficult math problems And he said he had a.
He saw something that was really surprised him.
Essentially, he pasted in a really long unsolved math problem.
So there's these lists online, by the way, that like there's one Hungarian mathematician.
He's got like a thousand problems he's posted online that have never been solved.
And basically people take them and they put them into AI models to see if the AI model can solve them.
And it's like, oh, my gosh, like AGI is here.
The AI model could solve it.
Recently, we had one last year that Google's AI model solved.
And so anyways, it's kind of always an exciting thing when they get solved.
So he posted an unsolved math problem into ChatGPT.
He let it run for 15 minutes.
He came back and it had a solution for him.
But you never know, right?
Like maybe this is just hallucinated.
So he goes and checks the solution, and it turns out that it was actually right.
There's kind of these online verification tools.
One of them in particular is called Harmonic, and it's basically just designed to make sure that the logical arguments of solving a math problem are sound.
And apparently, once he pasted in ChatGBT's response, everything checked out.
It said it was accurate.
This is a quote from him.
He said I want to get a sense of where AI systems can actually solve open math problems and when they still get stuck.
So I think he was really surprised by the fact that just how it had actually solved this problem.
So problems that were previously out of reach, he says he thinks are now solvable.
But I want to talk to you about how it solves this problem, its line of reasoning, because what's cool with ChatGPT and with reasoning is you can go and look through its chain of thought and.
And so he's.
Obviously he was formerly a quant.
He's a huge math nerd.
So he can go and understand his chain of thought.
And it was fascinating.
So this is how ChatGPT got to solving this.
You know, very complex, previously unsolved math problem.
Basically what it did is it pulled out a bunch of well-known ideas from mathematicians.
So first it does research, it gets all of these, it tries to connect them in a logical way.
In this particular case, it went and found some information about Legend's Formula, Bertrand's Prostulate and the Star of David Theorem.
And then, what absolutely blew my mind, it went and it found an old math overflow post from 2013, where there was a Harvard mathematician named Noam Elixes who had a really interesting solution to a related problem.
Right,
So not the same problem at all, but it was kind of a related problem.
It goes and finds that.
And then, instead of copying, just like the solution of how you know that former Harvard mathematician solved that problem, it took a completely different approach and ended up producing a much more complete answer to the question that was connected to some works of Paul Erdos, which is one of the most influential mathematicians of the 20th century.
I think for anyone that is skeptical about machine intelligence, this is amazing, because this isn't just one isolated example.
I think a lot of people are seeing like AI tools are already being used by a lot of different researchers.
They're helping in a lot of different things searching through academic papers and checking complex arguments.
But I think since ChatGPT 5.2 came out, which is what Somani was using.
He says that he has seen a huge shift in its reasoning, basically, than earlier versions.
A lot of this is because of tooling.
When you give tools to these models, different formulas and algorithms and calculators, they're better.
But its reasoning was so good.
It was going and doing research, finding old posts, finding solutions to similar problems, adapting them to this problem and writing more complete versions of it, which was incredible.
So i think we're going to start seeing way more breakthroughs uh, with where ai is being used to do this.
Now, it's kind of interesting because, like ai isn't out just there in a vacuum, it's not just running around solving all the math problems of the world.
Like you have to point it in a direction.
It needs a person to point in a direction for now anyways, and so it's amazing, as we just pick what directions to point it in, how it's able to solve so many things.
Um, something that was interesting to me is that uh, samani was looking specifically at iridos's problems.
It's just this famous list of a thousand unanswered math questions, like i was telling you about, which it's been online for years, but what's interesting is like, the range of the problem.
So there's like some simple puzzles, there's some extremely difficult challenges.
Uh anyways, this basically makes it a really popular benchmark for testing human and machine problem solving and um, I think since Christmas, 15 problems on the EarDose list have moved from open to solved.
So open means, you know, like, here's a problem, no one has solved it, to being officially solved.
11 of the cases, the published solution explicitly mentioned AI tools as part of the process.
So whether you know that was like an AI model 100 solving the problem or a human was most likely in a lot of these cases a human was using AI tools to help them.
And 11 out of 15 of those ear dose problems that got solved since Christmas were using AI tools.
So in my mind, this is just no doubt that this is really pushing the field forward and in really novel, interesting new ways.
I think not everyone is claiming that AI can now replace mathematicians.
Terence Tao, he's one of the world's most respected mathematicians.
He's basically tracked the progress carefully and he says that in a whole bunch of different cases, AI systems produce meaningfully new ideas on their own, but in other areas they helped by finding relevant past research that humans could build on right.
Like in the case we were talking about earlier.
You know it was going and it was finding some work that a Harvard mathematician had done and it was kind of adapting it to its problem.
But, like to be honest, that's still amazing because it did come up with something new and it did adapt it in a new way.
So it's like, obviously it's drawing on something.
Anyways, I think...
I think a lot of, like, mathematicians say this, like, look, like, it's still using human research.
Well, of course it's using human research.
Like, where do you think its training data came from?
Where do you think it was, like, what was it fed?
How can it do this?
It's using human knowledge to be able to do this, but it is coming up with new novel things, which is interesting because you know, at that rate, eventually it could just come up with stuff without human knowledge, theoretically right.
That's kind of the interesting thing.
Fully independent AI mathematicians are still a long way off, according to Tao, but he does say that those tools are already making a huge difference.
So there was a recent post that he also made that he suggested that AI might be especially good at tackling less famous, overlooked problems.
A lot of those questions are not unsolvable, but they just simply never get enough attention from human experts.
Because AI systems can work really like methodically.
They can search through thousands of possibilities.
And I guess like if I'm being 100% honest, it's also because they don't get bored.
And because of this, Tao basically argued that a lot of those systems might be able to solve problems using AI that humans have not solved alone on their own.
Not because humans are incapable, but because you know, we're humans and solving really long, complex math problems maybe is boring for some people.
Okay, so another reason that I think progress is accelerating a lot is a growing focus on making math arguments easier to check.
So traditionally, proofs are written in natural language, which can hide a lot of the small mistakes or some of the unclear steps.
So there's a bunch of new software tools that are allowing researchers to translate those arguments into a really precise format that can be automatically verified.
This process is slow and it's tedious by hand, but if you're using an AI system which, of course, these things are getting increasingly better at helping with it makes it way easier to confirm results and then also to build on them, right.
Because the faster you can actually check that the AI model or even a person solved a problem correctly, the faster you can say okay, here's how we solve this type of problem.
Now we'll use this kind of as a building block for future problems in this direction, and there's more problems that you can solve.
There's an interesting comment made by the founder of Harmonic.
It's this tool that checks the math problems.
And his name's Tudor Arkhamik.
And something that he said that's really interesting is that the most important signal is not how many problems actually get solved, but who's willing to use the tools.
Here's a quote from him.
He said, What matters is that serious math and computer science professors are actually using them.
These are people whose careers depend on being careful and credible.
So when they say they rely on AI tools, that says a lot.
And honestly, I think it really does.
I think basically the real world implications is going to go a lot further than just math, right?
Because the same abilities that help an AI reason through on you know, for example, like an abstract problem it could still.
It can actually be used and applied into fields like engineering economics medicine science, right.
Like, progress in a lot of those fields is often slow because problems are really complex.
They're hard to verify.
So as the ai systems get better at actually exploring ideas and checking work and connecting past knowledge, they are going to dramatically speed up research and innovation.
So for me, the advancements being made in AI and math isn't just exciting for math, but for so many other areas that are going to benefit.
And the reasoning capability of these models improving means that so many different areas are going to improve, including software engineering which personally, is getting me really excited this week.
All right, guys, thank you so much for tuning into the podcast.
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