As a TCS assistant professor from Eastern Europe, I always am a little jealous of the biggest names in math having such an easy access to the expensive, long thinking models.
Paying for Pro from any of my current academic budgets is completely ouf of the field of reality here -- all budgets tend to have restricted uses and software payments fit into very few categories. Effectively, I'd have to ask for a brand new grant and hope the grant rules allow for large software payments and I won't encounter an anti-AI reviewer; such a thing would take one year at least.
As a nail to the coffin, I was "denied" all Claude Opus recently as part of Microsoft's clampdown on individual (and academic) use of Copilot.
(Chagpt 5.5 Plus does not seem sufficient for any deeper investigations into new research topics, I've tried.)
The point is not that professors are poor. The point is that if this is used for research, it normally needs to come from an academic budget, not personal money.
And $200/month may look small from a U.S. perspective, but I looked up some average figures for Eastern European assistant professors. In Poland, for example, assistant professor base pay is around 73% of a professor’s base salary, roughly PLN 6,840/month gross, or about €1,500–1,600/month gross. At that level, a $200/month subscription can be around 10–15% of personal monthly income after accounting for taxes and local conditions.
I also work as a freelancer and sometimes work with professors. In my experience, academic budgets are often much tighter than people expect.
There is a significant gap between what academics are paid across European countries, and since most top universities here are public institutions, you are right -- Eastern European government employees tend to be on the poorer side.
There are several other philosophical arguments against what you propose but I do not wish to go down that route.
That’s what most people spend on their phone and Internet connections per month in the US. That’s what the average American family spends on just five days of food.
Bruh, $200/m for most people in the US is also a hard "no!". That's a lot of money. Plus Anthropic isn't doing good deals with orgs that spend less than 250k a month. It's ridiculous.
It's a very long post with a mix of technical (math) and philosophical sections. Here are the most striking points to reflect upon IMHO.
> It seems to me that training beginning PhD students to do research [...] has just got harder, since one obvious way to help somebody get started is to give them a problem that looks as though it might be a relatively gentle one. If LLMs are at the point where they can solve “gentle problems”, then that is no longer an option. The lower bound for contributing to mathematics will now be to prove something that LLMs can’t prove, rather than simply to prove something that nobody has proved up to now and that at least somebody finds interesting.
Training must start from the basics though. Of course everybody's training in math starts with summing small integers, which calculators have been doing without any mistake since a long time.
The point is perhaps confirmed by another comment further down in the post
> by solving hard problems you get an insight into the problem-solving process itself, at least in your area of expertise, in a way that you simply don’t if all you do is read other people’s solutions. One consequence of this is that people who have themselves solved difficult problems are likely to be significantly better at using solving problems with the help of AI, just as very good coders are better at vibe coding than not such good coders
People pay coders to build stuff that they will use to make money and I can happily use an AI to deliver faster and keep being hired. I'm not sure if there is a similar point with math. Again from the post
> suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
> Here’s a thought experiment: suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here.
As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.
Sorry, I'm reposting a comment I made yesterday that seems fitting:
> This reminds me of Antirez's "Don't fall into the anti-AI hype". In a sentence: These foundation models are really good at optimizing these extremely high level, extremely well defined problem spaces (ie multiply matrices faster). In Antirez's case, it's "make Redis faster".
>So if your aim in doing mathematics is to achieve some kind of immortality, so to speak, then you should understand that that won’t necessarily be possible for much longer — not just for you, but for anybody.
I saw Tim Gowers give a talk at the AMS-MAA joint meeting in Seattle about ten years ago where he predicted that in 100 years humans would no longer be doing research mathematics. I wonder if he’s adjusted his timeline.
At the time I thought the key missing tool was a natural language search that acted like mathoverflow, where you could explain your problem or ideas as you understood them and get references to relevant literature (possibly outside your experience or vocabulary).
As a graduate student, this piece made me sad. I always believed that my work speaks for itself and transcends beyond my limited time on this cosmic experience. This notion of immortality was just a small intangible bonus I hoped for when I jumped into grad school. AI is making me feel less worthy.
You are worthy. You will hone your skills in grad school and be able to command these AIs better than somebody who hasn’t struggled with hard problems for a long time.
This is certainly interesting, though I would say that based on my understanding of how the current models work combinatorial problems would be an area where they could be particularly successful. They are pretty good at combinatorial creativity - its the exploratory and transformational aspects that are still pretty tricky, and I expect would come to bear in other areas of mathematics.
After reading this post, I have to admit that I could not understand the mathematical parts at all because they are beyond my current knowledge.
But one thing seems clear to me. If I try to describe the situation in mathematics presented here, it sounds like there were already precedents or existing pieces of knowledge, but humans had not thought to connect them. AI seems to have helped make that connection.
If AI can connect different fields in this way, then perhaps something even more significant could emerge from it.
That said, I could not understand most of the article. And if using LLMs properly requires this level of background knowledge, I honestly worry about whether I can really use them well.
On complex problems with lengthy proofs, the first step that I would have done is to ask 5.5 pro in a new, unrelated, session, to be very critical, to try to find flaws in the arguments.
And certainly not to send it to a fellow colleague to ask its opinion first.
LLMs are certainly becoming capable to code, find vulnerabilities, solve mathematical problems, but we need to avoid putting their works in production, or in front of other humans, without assessing it by any possible mean.
Otherwise tech leads, maintainers, experts get overwhelmed and this is how the « AI slop » fatigue begins.
To be clear I’m talking about this step:
> That preprint would have been hard for me to read, as that would have meant carefully reading Rajagopal’s paper first, but I sent it to Nathanson, who forwarded it to Rajagopal, who said he thought it looked correct.
> but we need to avoid putting their works in production, or in front of other humans, without assessing it by any possible mean.
I think this is good advice in general, maybe with an emphasis on public vs. private, friendly contact. Having 0 thought AI slop thrown at you out of the blue is rude. "could have been a prompt" indeed. But having a friend/colleague ask for a quick glance at something they know you handle well is another story for me.
If I've worked on a subject for a few years, and know the particulars in and out, I'd have no trouble skimming something that a friend or a colleague sent me. I am sparing those 5-10 minutes for the friend, not for what they sent. And for an expert in a particular domain, often 5 minutes is all it takes for a "lgtm" or "lol no".
Undergraduate? No. We've had calculators able to solve undergraduate problems for decades. AI doesn't change the need to understand how calculus works any more than calculators did. The foundations remain valuable.
90% of the final grade are in room examinations with proctors, maybe two sets of exams of midterms and finals that the vast majority of the final grade comes from. This is already how most of East and South Asia does it anyways and it’s probably the best.
For publications and theses, as long as the final results hold and can be replicated and validated, I don’t see why we shouldn’t allow the wholesale use of LLMs
I don’t think it’s just mathematics. We don’t hear enough about this, but if I think back to my undergraduate years, which were less than 10 years ago, every homework assignment and every take-home exam I had would be trivial for LLMs to solve at this point I wonder what is actually happening on the ground.
> producing a piece of PhD-level research in an hour or so
Sure sure sure ... PhD slop. It is fascinating how people
who think they are clever, suddenly operate in the AI skyne
slop bubble. Copy/paste is not really AI, yet this is the
most common way of operation of AI slop. I've noticed this
again recently when looking at grok-media-slop. There are
so many smaller mistakes if you know a specific topic and
look at it. The hallucination is wild through AI slop.
Paying for Pro from any of my current academic budgets is completely ouf of the field of reality here -- all budgets tend to have restricted uses and software payments fit into very few categories. Effectively, I'd have to ask for a brand new grant and hope the grant rules allow for large software payments and I won't encounter an anti-AI reviewer; such a thing would take one year at least.
As a nail to the coffin, I was "denied" all Claude Opus recently as part of Microsoft's clampdown on individual (and academic) use of Copilot.
(Chagpt 5.5 Plus does not seem sufficient for any deeper investigations into new research topics, I've tried.)
Apologies for the rant.
And $200/month may look small from a U.S. perspective, but I looked up some average figures for Eastern European assistant professors. In Poland, for example, assistant professor base pay is around 73% of a professor’s base salary, roughly PLN 6,840/month gross, or about €1,500–1,600/month gross. At that level, a $200/month subscription can be around 10–15% of personal monthly income after accounting for taxes and local conditions.
I also work as a freelancer and sometimes work with professors. In my experience, academic budgets are often much tighter than people expect.
And the situation is better, ten years ago it would have been 80%.
There are several other philosophical arguments against what you propose but I do not wish to go down that route.
> It seems to me that training beginning PhD students to do research [...] has just got harder, since one obvious way to help somebody get started is to give them a problem that looks as though it might be a relatively gentle one. If LLMs are at the point where they can solve “gentle problems”, then that is no longer an option. The lower bound for contributing to mathematics will now be to prove something that LLMs can’t prove, rather than simply to prove something that nobody has proved up to now and that at least somebody finds interesting.
Training must start from the basics though. Of course everybody's training in math starts with summing small integers, which calculators have been doing without any mistake since a long time.
The point is perhaps confirmed by another comment further down in the post
> by solving hard problems you get an insight into the problem-solving process itself, at least in your area of expertise, in a way that you simply don’t if all you do is read other people’s solutions. One consequence of this is that people who have themselves solved difficult problems are likely to be significantly better at using solving problems with the help of AI, just as very good coders are better at vibe coding than not such good coders
People pay coders to build stuff that they will use to make money and I can happily use an AI to deliver faster and keep being hired. I'm not sure if there is a similar point with math. Again from the post
> suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here. As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.
> This reminds me of Antirez's "Don't fall into the anti-AI hype". In a sentence: These foundation models are really good at optimizing these extremely high level, extremely well defined problem spaces (ie multiply matrices faster). In Antirez's case, it's "make Redis faster".
This made me a little sad
At the time I thought the key missing tool was a natural language search that acted like mathoverflow, where you could explain your problem or ideas as you understood them and get references to relevant literature (possibly outside your experience or vocabulary).
Does the author know about CAISc 2026 [0]?
[0]: https://caisc2026.github.io
But one thing seems clear to me. If I try to describe the situation in mathematics presented here, it sounds like there were already precedents or existing pieces of knowledge, but humans had not thought to connect them. AI seems to have helped make that connection.
If AI can connect different fields in this way, then perhaps something even more significant could emerge from it.
That said, I could not understand most of the article. And if using LLMs properly requires this level of background knowledge, I honestly worry about whether I can really use them well.
A lot of math research is like that. And, like the blog post suggests, problems one gives PhD students are 95% like that.
Most of what I do is just assemble things that other people have already built.
And certainly not to send it to a fellow colleague to ask its opinion first.
LLMs are certainly becoming capable to code, find vulnerabilities, solve mathematical problems, but we need to avoid putting their works in production, or in front of other humans, without assessing it by any possible mean.
Otherwise tech leads, maintainers, experts get overwhelmed and this is how the « AI slop » fatigue begins.
To be clear I’m talking about this step:
> That preprint would have been hard for me to read, as that would have meant carefully reading Rajagopal’s paper first, but I sent it to Nathanson, who forwarded it to Rajagopal, who said he thought it looked correct.
I think this is good advice in general, maybe with an emphasis on public vs. private, friendly contact. Having 0 thought AI slop thrown at you out of the blue is rude. "could have been a prompt" indeed. But having a friend/colleague ask for a quick glance at something they know you handle well is another story for me.
If I've worked on a subject for a few years, and know the particulars in and out, I'd have no trouble skimming something that a friend or a colleague sent me. I am sparing those 5-10 minutes for the friend, not for what they sent. And for an expert in a particular domain, often 5 minutes is all it takes for a "lgtm" or "lol no".
Graduate? Yes.
For publications and theses, as long as the final results hold and can be replicated and validated, I don’t see why we shouldn’t allow the wholesale use of LLMs
Sure sure sure ... PhD slop. It is fascinating how people who think they are clever, suddenly operate in the AI skyne slop bubble. Copy/paste is not really AI, yet this is the most common way of operation of AI slop. I've noticed this again recently when looking at grok-media-slop. There are so many smaller mistakes if you know a specific topic and look at it. The hallucination is wild through AI slop.