one of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance.
we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00001% or 800/8B).
we are also seeing incredible advances in software performance. open ai announced like 15% improvement by fixing gpu kernel issues.
these are clearly linked in the sense of scaling laws and generalization of intelligence: a huge model gets capabilities in both math and software engineering that isn't possible at smaller scales.
but it seems less likely to me than before that the types of math/science discoveries will explicitly unlock better software performance. in some sense this fits our intuitions. when top tech companies use math PhD type employees, they have them stop doing pure math research and instead focus on software engineering. these people are often very good at software engineering but not due to recent discoveries in academic mathematics, it's due to their general intelligence.
to me, this is evidence that the models are getting better but does not make me think we are on the cusp of a foom style fast takeoff enabled by revolutions in frontier math
(i also posted this on twitter @mlipman13)
This makes no sense. To believe this you have to think that the models are somehow being overfit explicitly on academic mathematics and it doesn’t carry over at all to more practical software engineering. I wouldn’t make that bet.
For example, pi can be computed to arbitrarily many digits, but could only even in principle be accurately represented with physical objects to a precision that many humans could memorize easily. This is thanks to physical constraints such as "diameter of the observable universe" and "Planck length", at a minimum.
Even if pi is an approximation, it is still representable mathematically. Floating-point arithmetic is an algebra (in this case, a magma [1]), which can be studied mathematically.
Some of the problems solved here, at least in CS, have been open for decades, and have been worked on by very smart leading researchers in the field, including Turing Award winners.
Like, these would be best-paper awards at many top CS conferences.
Or, that the mathematical formalisms that model the limits of software performance are firm enough that barring P==NP, nothing much will change despite proofs of beautiful math.
I don’t really like AI but let’s stop kidding ourselves, no human mathematician could make progress on a dozen major open problems in a week or two. If you’re measuring it against humans then it is by far the best mathematician to ever live.
I guess it depends on how to measure a single "person"? If you spun up 2000 copies of Terrance Tao, I wouldn't be surprised if you found a few new discoveries at the end of it.
> I don’t really like AI but let’s stop kidding ourselves
If I had to create a tagline to describe my opinions about AI in a single sentence, that’d be it.
It’s possible to both hate AI and be impressed by it at the same time. Lying to ourselves about its capabilities does us no good. It’s emotionally difficult to do, but people need to come to grips with what’s happening and shake themselves out of a state of denial.
How much investment has gone into OpenAI versus mathematics research in 2025 for example? Probably 100x?
The AI results are clearly impressive. But these sorts of things are also in the ballpark of what human effort could solve given enough attention and time. Though it is hard to say.
15% improvements are usually called “fixing a mistake in the code” or “getting to that task in the backlog for optimizing that code we had to ship on a deadline”. They’re more likely the bigger the company: more contributors working in disparate areas means more low hanging fruit is probably lying around.
This is untrue. It is very ordinary. How much do you know about GPU drivers that you state this so assuredly?
Drivers are software. Software can be improved. Do you believe there are no prior examples of GPU drivers being improved such that particular compute patterns go up in performance by more than 15%?
This driver improved Total War performance by 71% https://www.nvidia.com/download/driverResults.aspx/74714/en-...
Also note you can go ahead and improve any open source driver right now, most likely. Compile it for your specific card and remove all other architecture specific if-cases and you can get an improvement.
Correct me if I'm wrong, but all of the aforementioned advances were made in the last year? Until very recently few people had access to these tools. Most people still don't know how to use ChatGPT, and very few use tools like CC regularily. If in a few years these frontier tools become commonplace and people upskill we would should see a network effect?
> but it seems less likely to me than before that the types of math/science discoveries will explicitly unlock better software performance.
You seem to overlook a simpler barrier. To make these advances, they have to be possible. A 15% improvement in GPU kernels doesn't evidence that significantly more improvement has been left on the table.
Google has also invested a lot of time into developing new hardware and new algorithms with AI (other types of AI, not LLMs). I don't know if it's paying off (haven't followed it closely) but they seem to think it's worth the effort.
This will depend on the problem; I expect big algorithmic performance improvements in AI since the algorithms are still new, inefficent, and constantly being improved. But maybe not for sorting, fast fourier transforms, or other well-studied basic algorithms?
A lot of algorithmic improvement in AI is ultimately bottlenecked by compute. It is very easy to come up with ideas that could improve models! But to prove that they do, especially at scale, is expensive and takes a long time.
> we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00001% or 800/8B)
i think you have misunderstanding of what mathematicians do
> i think you have misunderstanding of what mathematicians do
They get to make cool 3D plot visualizations of functions so obscure to me that they’re named after someone who is still alive - and/or get to work on cryptography for the NSA - I think?
but it seems less likely to me than before that the types of math/science discoveries will explicitly unlock better software performance. in some sense this fits our intuitions. when top tech companies use math PhD type employees, they have them stop doing pure math research and instead focus on software engineering. these people are often very good at software engineering but not due to recent discoveries in academic mathematics, it's due to their general intelligence. to me, this is evidence that the models are getting better but does not make me think we are on the cusp of a foom style fast takeoff enabled by revolutions in frontier math (i also posted this on twitter @mlipman13)