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A lot of math research is like that. And, like the blog post suggests, problems one gives PhD students are 95% like that.
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 gr…
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> it sounds like there were already precedents or existing pieces of knowledge, but humans had not thought to connect them 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.
Earlier quoted context omitted.
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. Graduate? Yes.
How should graduate school be changed then? Specifically for mathematics
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
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.
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 “gentl…
> 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".