Mathematics and AI

[Ves]

I am a math PhD student. Because of this, I thought I'd talk about the recent achievements of AI from the perspective of someone within the mathematics community. I was originally going to type some kind of essay, but I don't think I can do better than the open letter to the Mathathon signed by a large number of mathematicians:
https://docs.google.com/document/d/1IL0b2oG2KvvSnxn_DuXsNxuHaCefDJ9hNY1k9BP3kKQ/view?tab=t.0

There are also good talks given by Terence Tao on this subject. Here is one at the ICM:

And here is a talk intended for a more general audience:

The basic idea, which applies to many fields, such as math and software engineering, is that the real bottleneck is human understanding.

For math, that is essentially the entire point of the field. If you have a machine that can generate a proof of some result by cobbling together existing knowledge, especially if it's done in an inelegant way that is difficult for humans to understand, then human understanding is not advanced very much, and no new mathematics was developed. That will only happen if someone reads the proof, takes time to extract the methods that were used to solve it, communicates them to others, and passes along the knowledge to "the next generation."

For software engineering, the bottleneck is not in writing code (once you're sufficiently experienced with this), it's in understanding the problem you're trying to write code to solve and understanding the current state of your codebase so you know what changes to make and how to design your software on a high level. Even if you use AI to write code for you, you have to read the code the AI has generated and understand what it does, which takes time.

Now, this is assuming we actually care about human welfare, that we want to have the humans understand what the AIs are doing, and that we want to have humans "directing things". It seems like many of the people at top AI companies assume that humans are not going to be in charge of the future in the next decade, but they're all in a race to the bottom and so they can't help but destroy everything (from their POV). I know people at some software companies in the bay area where everyone is just using AI to write thousands of lines of code each day, and nobody can peer-review the code because nobody knows what's happening anymore.

I also have concerns for the funding of math. If funding primarily comes from people with money who only care about math for new applications that can make them more money, and if AI can give them results with none of the human understanding (since they don't care about that), the field as a whole could dry up if there are no resources provided for it. One practical way this would be bad (if we care about humans knowing what is going on) is if we lose a huge number of people that understand math well, we lose a huge number of people that can understand what the AIs are doing when they are doing math. Personally, though, it would also be very sad to see the field die.

I could say more, but maybe I'll just leave it at it seems the field of mathematics is going to have to undergo a huge paradigm shift, but nobody exactly knows how.

[Ves]

Update: It seems the open letter partially worked!

https://www.businessinsider.com/openai-caltech-ai-math-hackathon-backlash-anthropic-2026-9

[Xonas Pitfall]

On 11/09/2026 at 0:07 AM, Ves said:

I also have concerns for the funding of math. If funding primarily comes from people with money who only care about math for new applications that can make them more money, and if AI can give them results with none of the human understanding (since they don't care about that), the field as a whole could dry up if there are no resources provided for it. One practical way this would be bad (if we care about humans knowing what is going on) is if we lose a huge number of people that understand math well, we lose a huge number of people that can understand what the AIs are doing when they are doing math. Personally, though, it would also be very sad to see the field die.

Super interesting! Although I doubt the companies would actually want people who understand math to disappear. Most likely, they’ll just end up working more on correcting, evaluating, and guiding AI. I have a feeling that’s where a lot of jobs will be heading in some form.

For example, with coding/software development, systems design and having good "taste" in UI/UX/design seem more important than ever as AI gets better at actually writing the code. I’d imagine something similar could happen with math.

But I know very little about this subject, so it’s really interesting to hear about. Thanks for sharing!

I’d love to hear more of your thoughts in future threads if you feel like sharing more 

[Leo Gura]

On 9/10/2026 at 3:07 PM, Ves said:

nobody knows what's happening anymore.

Tagline of the 21st century

[Leo Gura]

A few serious points:

1) AI can be used to find interesting correlations between all the math humans know so far. There are probably interesting low-hanging fruit to pick just from connecting unconnected dots in existing knowledge. But at some point this easy fruit will run out.

2) Some kinds of math problems can be solved with a brute force approach. Not nearly all, but some. So AI could play a role there, similar to how it did with the protein folding problem with AlphaFold.

3) AI companies are definitely betting that humans won't even need to understand things anymore in the future because AI will magically handle everything. However, my position is that this is a sci-fi fantasy, not how it will really work. There is no good evidence yet that AI can replace human understanding. If it can, that is the paradigm shift, but it may never come.

Edited 3 hours ago by Leo Gura

[JTL]

Have you seen this? @Leo Gura I just saw someone mentioning it on reddit, but I found a article aswell so I think it is legit. This is insane.

https://futurism.com/artificial-intelligence/drama-openai-supposed-mathematical-breakthrough

https://www.reddit.com/r/singularity/comments/1wafkt4/breakthrough_for_navierstokes_from_tristan/

It seems openai reached out to him and offered him that he could be lead author on a rewrite of OpenAI’s Navier-Stokes proof.

 

Edited 12 minutes ago by JTL

[Butters]

9 minutes ago, JTL said:

Have you seen this? @Leo Gura I just saw someone mentioning it on reddit, but I found a article aswell so I think it is legit. This is insane.

https://futurism.com/artificial-intelligence/drama-openai-supposed-mathematical-breakthrough

https://www.reddit.com/r/singularity/comments/1wafkt4/breakthrough_for_navierstokes_from_tristan/

It seems openai reached out to him and offered him that he could be lead author on a rewrite of OpenAI’s Navier-Stokes proof.

 

You shouldn't take those things seriously. OpenAI is a commercial operation run by a scam artist, not some sort of scientific institution lol.