OpenAI says its unreleased next model has made ten mathematical advances.
And each successful runs cost about $2,000.
So: maths is basically solved right? We’re done here. Pack it up.
Yes and no.
Fair warning before we get into this: I am NOT a mathematician. If you see people like me talking about research-level maths, don't trust us on the maths! Go and listen to the mathematicians. They, funnily enough, know more about this! Terrance Tao (more on him later) is a good source here.
What I can do is show you what OpenAI released, what the $2,000 includes and why the whole thing is getting serious attention.
And why, most importantly, this isn’t just about maths. This is much wider.
Astra is still locked away
First up, the model used to make these advancements is in the ChatGPT Astra family.
Read: GPT-6. The next generation.
I need to start here: Astra is not out. We cannot use it, there is no public model card and we cannot throw our own problems at it to see how often it falls over. So we have to take news about Astra with a pinch of salt as always with new models.
Howver, OpenAI did publish a 249-page collection of papers, 62 pages of the model's discovery notes and ten public Lean certificates.
OpenAI published the research artifacts. Astra itself remains unreleased.
That is a hell of a lot more useful than the normal "our model is amazing" bar chart that we get. Mathematicians can actually get their hands on the work and start checking the work.
Here’s the original tweet that kicked all this off:
Note the 10 different areas. These are across a broad swathe of mathematics and computer science, perhaps to show the model’s versatility.
Also not Noam uses the word “solved”. That’s the social media spin on it - a bit overblown!
OpenAI's own article calls these ten advances. Four improve mathematical bounds. There is a new construction, two counterexample results and several theorems, including three numbered Erdős problems. One improves a sphere-packing bound for the first time since 1978. Advances is much more honest that “solved” so we’ll stick to that - but I do understand why Noam used “solved” otherwise no-one would have paid attention!
$2,000? Sort of.
OpenAI priced the tokens used to find the successful solutions at roughly $2,000 using Sol API rates.
Let’s be a little careful here.
That figure does not include training Astra (hundreds of millions), paying the researchers, building the tools, choosing the problems, preparing the papers or checking the results.
The quoted $2,000 is successful solution-finding inference, not the project cost.
We also do not know the denominator.
Did Astra have ten goes and nail all ten? Did OpenAI run 100 problems? 1,000? 10,000? How much did they spend chasing work that went nowhere before choosing these results?
No idea. OpenAI has not told us. Probably because it undercuts the headline lets be honest.
BUT…let’s not be too cynical here. Once the model and workflow exist, they can run another ten problems. Then another 100. Then another 1,000. The extra marginal inference of each new run is small.
Especially compared to academic funding, grants and labs….
Mathematicians (and scientists) are in a weird position now. Suddenly problems they may have dedicated years or decades too are just being solved.
A really useful term here is agency rupture. You’ve probably felt this yourself - it’s when AI finally does a task you thought you were required for. Previously maybe you had to use AI. Now you actively hinder the AI with your input:
Genius at maths. Shit at strawberry. Still.
These models are ripping their way though problems at the edges of mathematics and science.
So…why can’t it count the Rs in “strawberry”?
This is a (I think fair, if overused!) criticism of large language models.
It’s still an issue!
There’s a single word answer for why this happens: Representation.
Language models normally receive token chunks rather than a tidy row of letters. Depending on the tokeniser, "strawberry" can arrive as something like STR + AW + BERRY. The model has to reconstruct the individual letters before it can count them.
I’ve written a whole beginner’s guide on tokenization here.
This remains an issue in pure large language models.
But we’ve moved beyond that. For the most part we don’t just use the model. We also (increasingly) don’t even use the basic Chat app version of models. Nope - for higher level tasks we use, funnily enough, higher level tools. Claude Codex, Codex etc.
The harness is the thing.
So when running maths problems we can give the model a much nicer setup: symbols, long reasoning time, lots of candidate approaches, tools and a precise verifier at the end. It’ll use code to work out “counting” problems like how many Rs in strawberry, not the large language model itself.
This leads to AI tools being very good at some areas of maths (formulating new proofs) and very poor at others (counting!). Which to use humans feels weird. We find counting easy and discovering new proofs difficult. And so we ascribe the same difficulty scale to AI. That’s our anthropocentrism seeping though!
This is also why some people believe that AI is still terrible. It might be for the type of task they use it for! This uneven boundary is the jagged frontier. Two people can use the same model and one says it is useless whilst the other says it has transformed their work. They may simply be giving it very different jobs.
55,000 lines of checking
The most important part of this story is that OpenAI released their working.
It’s a bit like when we did maths exams at school and had to show our workings. You can’t just have a stab at an answer. You need to show how you got there!
In this case they released Lean files. The public Lean files contain roughly 55,000 lines of formal proof. A mathematician can run them through Lean and check whether each logical step follows from the definitions and assumptions in the file.
Lean checks the formal proof. Experts still have several other jobs.
Importantly, Lean cannot tell us whether OpenAI encoded the right theorem, whether the assumptions are sensible, whether the result is new or whether anybody should care about it. All is tells us is that the chain of logic makes sense.
People are already pushing back on one of the ten results. Good. OpenAI has put the work out, specialists can tear it apart and the result will either survive, change or die.
Compared with a chatbot checking its own homework, Lean gives other people something they can actually rerun. AI hallucinations do not disappear, but a polished wrong answer is much harder to sneak through 55,000+ lines of formal checks!
And remember, OpenAI could have kept all of this behind a launch post. They published the papers and the checks instead. Good on them!
The human queue could get very long
Why does all this matter? It’s another case of humans being pushed further up the chain.
If OpenAI can cheaply run another 1,000 problems, somebody still has to choose useful questions, inspect the proofs and explain the results in a form that other mathematicians can use.
Answers get cheaper but judgement gets scarcer.
And candidate papers could arrive much faster than journals and researchers can review them.
This is what’s happening across the board with AI.
AI increases output but we still need to manage it, delegate, check the work. Our judgement and discernment is valuable.
In fact it is ALL that is valuable.
The grunt work. the labour. The “work” that we have been doing for centuries. That stuff is going away. It’s going to be devalued.
The value shifts upstream to the people who can manage the process.
That is you.
To the task,
Kyle