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- Hacker News
- 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.)
Apologies for the rant.
- 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.
- >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.
This made me a little sad
by few - I am a physics professor and often use Gemini to check my papers. It is a formidable tool: it was able to find a clerical error (a missing imaginary unit in a complex mathematical expression) I was not able to find for days, and it often underlines connections between concepts and ideas that I overlooked.
However, it often makes conceptual errors that I can spot only because I have good knowledge of the topic I am discussing. For instance, in 3D Clifford algebras it repeatedly confuses exponential of bivectors and of pseudoscalars.
Good to know that ChatGPT 5.5 Pro can produce a publishable paper, but from what I have seen so far with Gemini, it seems to me that it is better to consider LLMs as very efficient students who can read papers and books in no time but still need a lot of mentoring.
by ziotom78 - > 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.
by mxwsn - A very interesting comment from Baez, I'll just quote part of it.
> Where does the value of thinking and having deep ideas come from? We need to think about this now. If it comes primarily from their scarcity – the fact that having certain ideas is hard – then indeed this value may drop precipitously when the manufacture of ideas can be automated. But if the value comes from the utility of the ideas – the benefit that the idea brings – then the story changes: perhaps creating more good ideas is actually better, not worse. Here I’m using “utility” in a broad sense, not just in the sense of what people often call applied mathematics.
> In other words, mathematicians may need to adjust to a transformation from a scarcity economy to an abundance economy.
https://gowers.wordpress.com/2026/05/08/a-recent-experience-...
- 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.
by pmontra - This jives with what I've experienced in the brief time I had access to 5.5 Pro. It's the very first LLM that I feel like I can wrangle into solving tedious, but straightforward, problems correctly. It still makes a ton of mistakes and needs to be very rigidly guided, but it does a pretty good job of tracing its own reasoning and correcting itself in a way that the other models do not.
The downside (not noted in the article, but noted by others here) is cost. It uses tokens at an insane rate, the tokens cost a lot, and using it with subagent flows that you can use to have it tackle large problems with high accuracy costs even more. It is also much "slower" for large scale problems because of context limitations -- it has to constantly rediscover context for each part of the problem, and in order to make it accurate you need to wipe its context before progressing to the next small part, or launch even more agents. For mathematical proofs like these, where the required context to understand the problem and proof besides stuff that's already available in its training set is small and the problems are considered "important" enough, this might not be a problem, but for many of the tasks I would like to use it for (ensuring correctness of code that affects large codebases, or validating subtle assumptions) it definitely is one.
So I think it will be a while before the impressive capabilities of these models really percolate into our lives as programmers, unless you're one of the lucky ones given unlimited access to 5.5 Pro.
by Jweb_Guru