Okay, so get this word diving into AI that does math.
Not just like adding numbers or anything.
No, no, no, no, no, no.
Talking like.
Way beyond that.
Mind bending, cutting edge math.
That most of us probably wouldn't even recognize as math.
You sent this paper over called Frontier Math,
a benchmark for evaluating advanced mathematical reasoning
in AI.
And wow.
Yeah, it's a.
It's a lot.
It's a fascinating paper.
What they've essentially done is built an obstacle course,
but for AI, it's called Frontier Math.
And it's a collection of some of the toughest math problems
out there, stuff that even expert mathematicians struggle with.
Yeah.
And they didn't just stick to like one area of math either,
right?
They kind of threw everything at it.
So real mix.
Like number theory, algebraic geometry.
There was even something called category theory,
which honestly, I had to Google.
Yeah, you and me both.
That's not exactly dinner table conversation.
So it's really pushing the boundaries of what we think
about when we talk about AI and math.
And the big question is, can AI solve new problems,
not just stuff that's already in textbooks?
All right.
So did any of the AIs become like the next Einstein?
Well, not quite.
It turns out even the most advanced AI models
could only solve a tiny fraction of the problems.
Less than 2%.
That's kind of humbling.
So much for robots taking over the world, right?
Well, it's not quite that simple.
What this really shows us is how complex and nuanced
advanced mathematical reasoning really is.
It's not just about crunching numbers.
It's about deep understanding, creative problem solving,
and connecting ideas that sometimes seem totally unrelated.
OK, so like what, give me an example.
What kind of problems were these AI struggling with?
Sure.
So one example is a problem related to Arton's primitive root
conjecture, which is all about figuring out
how often a specific pattern appears in prime numbers.
OK.
Sounds simple enough.
But it's actually a notoriously difficult problem
that mathematicians have been working on for decades.
So you're giving these AIs unsolved problems.
Exactly.
Trial by fire.
Another example is a problem involving finding
a very specific polynomial.
But it requires understanding the link between shapes
and equations.
A level of abstraction that AI still really struggles with.
So why are we even bothering with this frontier math thing?
If the AI is like failing so miserably.
Well, it's not about making AI look bad.
It's about giving us a reality check
and helping researchers see where AI excels and, more
importantly, where it falls short.
So it's like a roadmap for future research.
Exactly.
By pinpointing the areas where AI struggles,
frontier math can guide researchers
in developing better algorithms and approaches.
It's like a to-do list.
Yeah.
For AI researchers, must improve geometric reasoning skills,
need to understand abstract concepts better,
and figure out those prime number patterns while you're at it.
Exactly.
But it's not just for training AI.
Frontier math also helps us understand
the very principles of mathematical reasoning
and how to translate those principles into something
a computer can use.
So we're trying to teach AI to think like a mathematician.
It's ambitious.
That sounds very ambitious.
Yeah.
To get a better grasp of what that might actually involve,
the researchers behind frontier math
interviewed some big names in mathematics, even
fields metalists.
Wow.
So the math all stars?
Yeah.
What do they have to say?
They're all about AI and math.
Well, they were impressed by how far AI has come,
but they were also realistic.
It's unlikely that AI will be conducting
independent mathematical research anytime soon.
OK.
So no robots taking over universities just yet.
That's probably a relief to some people.
Probably.
But here's where it gets really interesting.
The mathematician said that AI could become a powerful tool
for human mathematicians, almost like a super powered
research assistant.
OK.
I like that.
I can get behind that.
What would that look like, though?
So imagine a computer that could instantly verify
complex calculations, test hypotheses,
and even help generate new ideas that
would free up mathematicians to focus on the more creative parts
of their work.
Yeah.
That sounds like a dream for a lot of mathematicians, I know.
Yeah.
It really does.
And that's a key takeaway here.
It's not about AI replacing mathematicians.
It's about AI augmenting human capabilities
and helping us push the boundaries of mathematical
knowledge even further.
So they actually tested some AI models on frontier math, right?
Absolutely.
It wasn't just all talk.
They wanted to see how the state of the art stacked up.
So who were the contestants?
Well, they put six leading language models
through their paces, including some big names
you might recognize, OpenAI's GPT40 and 01 Preview,
Google DeepMind's Gemini 1.5 Pro,
Anthropics Clawed 3.5 Sonnet, and even XAI's Grock 2 Beta.
Wow.
A real battle of the Titans.
It was.
So how did they do it?
Did anyone crack the code?
Well, remember how we said that even the most advanced AI
models could only solve less than 2% of the problems?
Yeah.
That applies here, too.
None of the models were able to get a 2% success
rate on the full benchmarks.
Wow.
So AI still has a long way to go when
it comes to this kind of advanced math.
It really does.
But that's not necessarily a bad thing, right?
No, it's not.
It just shows we're still in the early stages of developing
AI that can truly reason like a mathematician.
It's like comparing a toddler learning their ABCs
to a professor writing a novel.
Yeah, that's a good analogy.
But even though the overall success rate was low,
there were some interesting variations
in how the different models approached the problems.
Interesting.
Yeah.
So some models like OpenAI's 01 Preview
were more inclined to jump straight to a solution,
even if they hadn't fully explored all the options.
More like confident guessers than careful problem solvers.
Kind of.
Other models like Grock 2 Beta were more
willing to experiment and try different strategies
before settling on a final answer.
They were much more methodical.
So more like detectives.
Yeah.
Carefully piecing together the clues.
Exactly.
I like that.
And I bet all that experimenting used up
a lot of computing power.
It did.
And that's another interesting thing about Frontier Math.
It's not just about finding the right answer.
It's also about understanding the process
of mathematical reasoning and figuring out
how AI can learn to emulate that process.
So it's more than just a test.
It is.
It's a roadmap for the future of AI and math.
Exactly.
It's a framework for developing AI that can not only
solve complex math problems, but also understand
the underlying logic and creativity that
drives mathematical discovery.
This is cool.
It's not just about measuring AI's capabilities today.
It's about setting a vision for the future.
Yeah.
Wow.
It is.
This has been an incredible deep dive so far.
We've talked about the goals of Frontier Math,
the process of creating these problems,
and then the results of testing these different AIs.
And it's clear that there is a lot more to explore here.
There is.
So I'm glad we have more time to dig in.
I am too.
OK, so we've talked about what Frontier Math is trying to do,
but let's get into the nitty gritty.
How was it actually created?
Yeah, this whole thing sounds super complex.
I mean, it must have taken a massive effort
to put it all together.
You're telling me.
It was a huge collaborative project
involving over 60 mathematicians from top universities
all over the world.
Wow, like a mathematical dream team?
Yeah, basically.
And these weren't just any mathematicians.
We're talking former Olympiad champions, professors,
researchers.
They even had a Fields Medalist on the team.
A Fields Medalist?
Wow.
OK, now I'm impressed.
Right.
So what were they doing?
Well, they were the masterminds behind the problems
in Frontier Math.
They were tasked with crafting these original, really
challenging problems that would push AI to its limits.
Like the architects of this AI obstacle course.
Yeah.
But I bet that came with some pretty strict rules, right?
You can't just throw any old math problem at these AI models.
Oh, absolutely.
There were very specific guidelines
for creating these problems.
First, they had to be completely original,
no textbook problems, no rehashed online challenges,
nothing like that.
Right, you don't want the AI models cheating
by like memorizing solutions they've seen before.
Exactly.
Second, the problems had to have solutions.
That could be verified automatically,
usually in the form of numbers or symbolic expressions.
Oh, OK.
So a computer could grade the answers.
Exactly.
No human bias.
Right.
And third, the problems had to be guest proof, no flukes,
no lucky guesses.
The AI model had to demonstrate real mathematical
understanding.
So basically, they had to create a test that
was tough enough to challenge the AI,
fair in its evaluation.
And impossible to cheat on.
Pretty much.
That's a tall order.
It was.
And to make sure they met those standards,
each problem went through a rigorous peer review process,
just like in academic research.
Wow.
Each problem was reviewed by at least one
other mathematician, who was an expert in that specific area
of math.
So it was like a scientific journal.
Right.
But for math problems.
Yeah, exactly.
They really went above and beyond.
They did.
And that's a big part of what sets frontier math apart
from other AI benchmarks.
It's not just about throwing a bunch of random problems
together.
It's about carefully selecting and crafting problems.
That represent the true complexity and diversity
of advanced mathematics.
OK, so we talked about the rigor, the originality.
What about the content itself?
Like what kind of mathematical areas
are we talking about here?
Well, they didn't want to limit the AI models to just one
narrow area of math.
So they included problems from a wide range of fields.
We've got number theory, algebraic geometry, category
theory, even some areas that I had to brush up on.
It's like a smorgasbord of mathematical delights.
It is.
And I imagine that variety is important, right?
And it wouldn't be a very good test
if it only focused on one tiny slice of the mathematical world.
Exactly.
By covering such a broad spectrum of mathematics,
frontier math tests the AI's ability to think flexibly
and apply their knowledge across different domains,
which is something human mathematicians
have to do all the time.
That's a good point.
It's not just about memorizing formulas
or solving specific types of equations.
It's about understanding the underlying principles
of mathematics and being able to apply those principles
in creative and unexpected ways.
Yeah, you got it.
And the way they structured the problems is also interesting.
They designed them to mimic how human mathematicians actually
solve problems.
Ooh, how so?
So the AI models aren't just given a problem
and told to find the answer.
They're also given the ability to write and execute
Python code, to test their ideas,
and explore different approaches.
So it's like giving them a virtual whiteboard.
And a set of mathematical tools to play with.
Exactly.
They're not just passively receiving information.
They're actively engaging with the problem.
Exactly.
It's all about giving the AI models the freedom
to experiment, make mistakes, and learn from those mistakes,
just like human mathematicians do.
That's so cool.
So frontier math is not just about finding the right answer.
It's about the entire process of mathematical reasoning.
Exactly.
It's about teaching AI to think like a mathematician,
not just mimic one.
Precisely.
That's much more challenging.
It is.
And it requires a completely different approach
to AI development.
It does.
I'm really starting to grasp the depth and ambition
of this whole project.
It's not just about measuring AI's current capabilities.
It's about setting a vision for the future of AI in mathematics.
You nailed it.
Frontier math is laying the groundwork.
For AI to become a true partner in mathematical exploration
and discovery.
This is awesome.
It is.
OK.
So we've talked a lot about the why and the how of frontier
math.
But let's get down to brass tacks.
We know the overall success rate was pretty low.
But what about the individual AI models?
Were there any major differences in how they performed?
Oh, yeah.
Definitely.
There were some interesting variations.
As we mentioned earlier, some models like Open AI's O1
preview were more prone to jumping straight to a solution
without much exploration.
Right.
Like the quick draw gunslingers.
Yeah.
Firing off answers without taking careful aim.
Exactly.
But others like Grock 2 beta were much more
methodical and experimental.
Like Pace It Snipers.
Yeah.
Carefully surveying the landscape before taking a shot.
Exactly.
And these different approaches actually played out
in the results for the four problems that at least one model
was able to solve.
Oh, interesting.
Yeah.
Tell me more about those.
So one problem involved probability theory and approximations.
And Grock 2 beta, with its methodical approach,
had the highest success rate at 60%.
So Grock was the king of chance and uncertainty.
It seems so.
What about the other problems?
Another problem involved algebraic topology.
This one was aced by O1 preview, achieving a perfect score
of 100%.
Wow.
A perfect score.
I know.
So O1 preview had a knack for those abstract spaces and shapes.
Apparently.
What about the rest?
The third problem focused on group theory and field theory.
And both O1 preview and Gemini 1.5 Pro had decent success rates,
at 80% and 60%, respectively.
OK.
So they were the masters of manipulating
those algebraic structures.
That's pretty impressive.
It is.
The final problem was a tricky combination
of algebraic geometry and combinatorics.
Only two models managed to solve it, O1 mini and Claude 3.5
Sonnet, both with a 20% success rate.
So they were the champions of finding patterns
and relationships in those complex geometric and combinatorial
structures.
It seems.
Even a 20% success rate is pretty good.
When you consider how difficult these problems were.
You're absolutely right.
And it's worth noting that these results highlight
the unique strengths and weaknesses of each AI model
across different areas of mathematics.
It's like each model has its own mathematical personality,
excelling in some areas while struggling in others.
That's a great way to put it.
And actually, this diversity of strengths
is a really positive sign for the future of AI in mathematics.
How so?
Well, it means we're not limited to just one single approach
to developing AI that can reason mathematically.
There's no one size fits all solution.
Instead, we can have a whole ecosystem of AI models
with complementary strengths.
So instead of trying to create one super AI that can do it all,
we can have specialized AI models that excel
in different areas of mathematics.
Exactly.
And by combining the insights from all these different models,
we can create even more powerful and versatile AI systems
that can tackle a wider range of mathematical challenges.
That's the idea.
That's a really optimistic perspective.
It is.
It's like assembling a team of mathematical superheroes,
each with their own unique superpowers.
I love that analogy.
And frontier math is providing the training ground
for these future mathematical superheroes
to hone their skills.
This is seriously blowing my mind.
Frontier math is so much more than just a test or a benchmark.
It's a catalyst for innovation and discovery in both AI
and mathematics.
It is.
It's helping us understand not only what AI can do today,
but also what it might be capable of in the future.
Right.
And that's what makes this whole project so exciting.
It is exciting.
This has been an incredible deep dive so far.
We've talked about the motivation behind frontier math,
the meticulous process of creating the problems,
and the impressive, albeit varied,
performance of different AI models.
It's been a fascinating journey,
and we're just getting started.
We've focused a lot on the AI side of things.
Yeah.
But what about the human element in all of this?
What are the implications of frontier math for those of us
who aren't AI researchers or field's medalists?
That's a great question.
And it's something we'll dive into right after this.
So we've talked a lot about the technical side of things,
but let's zoom out a bit.
What does this all mean for the average person?
Yeah, that's a good point.
I mean, I'm all for robot solving complex math problems.
But how does this actually affect our lives?
Well, for one thing.
Frontier math is helping to kind of demystify
advanced mathematics.
OK.
By showing that AI can grapple with these really challenging
problems, it makes the whole field seem a little less
intimidating.
So it makes it feel more accessible.
Exactly.
Especially for students or anyone
who might feel intimidated by higher level math.
Right.
Like if a computer can understand it, maybe I can too.
Exactly.
And beyond that, frontier math is also
helping to accelerate the pace of mathematical discovery.
How so?
As AI gets better at solving math problems,
it can become a really powerful tool
for human mathematicians, automating
tedious calculations, checking for errors,
even helping to generate new ideas.
Like a super powered research assistant.
Yeah, exactly.
That's pretty cool.
And this kind of collaboration between humans and AI
could lead to breakthroughs in all sorts of fields,
cryptography, material science, even fundamental physics.
Wow.
So frontier math is having ripple effects,
far beyond the world of pure mathematics.
It is.
And maybe even more importantly,
frontier math is forcing us to rethink what
it means to do math.
OK.
How so?
Well, traditionally, we viewed math
as a purely human endeavor, something
that requires special kind of intuition and creativity
that machines could never replicate.
But frontier math is kind of challenging that assumption.
Yeah.
It's blurring the lines between human and machine
intelligence.
Right.
And that raises all sorts of interesting questions
about the nature of mathematical thinking
and the potential for AI to become a true partner
in mathematical exploration.
So we're on the verge of a new era in mathematics.
Maybe.
Where humans and AI work together.
That's pretty exciting.
It is.
This has been an incredible deep dive.
It has.
We've gone from the nitty gritty details of AI algorithms
to the philosophical implications of machines doing math.
It's been a great discussion.
And for our listeners, if you're feeling adventurous,
we'll include links to some of the frontier math problems
in the show notes.
Let us know if you managed to crack the code.
Good luck.
And remember, even if you don't solve them,
just trying to understand these problems
is a great way to stretch your mathematical muscles.
That's a good point.
The journey is just as important as the destination.
Absolutely.
Especially in the world of mathematics.
So keep exploring.
Keep questioning.
Yeah.
And keep pushing the boundaries of what's possible.
Well said.
And we'll see you next time.