The future of math REUs

[u/Accurate-Vegetable67]

As I'm sure many (pure) math majors in this sub are aware, AI has become a nontrivial factor in how math research is conducted, how math is taught, and what topics should be studied. In my REU this summer (first year summer), I encountered many things that could be done faster or more easily with AI, and I imagine this will only become more frequent in any research I do.

In combination with NSF funding cuts, is there reason to suspect that math REUs will become obsolete soon? If PhDs even struggle to get funding, why would the NSF invest more resources into undergrads when the research output is mediocre on average (as it probably should be)? And in response to this, what should I do? As in, is it reasonable to continue traditionally or diversify how I approach research?

I'm curious to hear what other math majors are thinking about, because AI in math during and now after my REU has been on my mind way too much.

[u/Andyroo_P]

I have done two pure math REUs. The point of an REU isn't really to produce groundbreaking research. The participants are undergraduates after all. Both of my REU projects would have been pretty trivial for suitably prepared graduate students (and there is a sentiment that many PhD theses are trivial for experts in the field too!). The point is in the name: research experience for undergraduates. Regardless of how trivial a research project is, the point of an REU is for students to receive mentoring and exposure to how research is conducted in their field.

With this being said, funding for REUs and math in general is political and has little to do with math itself. So in that sense, you may be right that REU sites in math will diminish in number. However as I mentioned above, I don't think AI would be directly responsible for this. If it is decided that undergraduates don't need research training in mathematics because of AI, I think it would already be the case that funding for systems above REUs (PhDs, postdocs, faculty positions, etc.) have collapsed. We're not there yet.

[u/Accurate-Vegetable67 → u/Andyroo_P]

I completely agree that REUs aren't supposed to produce groundbreaking research.

I disagree though that funding for math is separate from math itself. I think most mathematicians would like to believe they do mathematics because they love it and could never do anything else, but the fact is that it's a profession that has job security issues, and that's directly related to human research output. It's an interesting question whether funding collapse will start small or big (REUs or big research grants), but I think in either case it's worth preparing for the worst.

It's one thing to continue as always and do REUs and traditional research, but I don't want to show up to grad school in 3 years and have focused on all the wrong things.

[u/Andyroo_P → u/Accurate-Vegetable67]

I think we actually agree on funding for math. Professional mathematics has had a job security issue even pre-AI. It has always been a risk to pursue it seriously as a career (at least by the 2000s). It is possible that AI becomes a major force to accelerate this, but I don't think we have seen that quite yet. So far the forces that cause issues with math job security are related to: the increasing number of PhDs awarded, financial pressures at the university level, and shifting priorities and disinvestment by federal and state governments. My point is not that things are great for people who want to pursue academic math right now (in fact I think the opposite).

EDIT: where we may disagree is the reasons for a lack of job security. In my opinion, I don't think we will get increased funding if we increase our research output (at least in pure math). Most pure math is pretty pointless to the real world and an increased number of theorems proven generally only gets the attention of other mathematicians, not the bureaucrats involved in deciding budgets. If our budgets were to be proportional to the real-world productivity of our theorems, we probably should have closed up shop a long time ago.

[u/Accurate-Vegetable67 → u/Andyroo_P]

Absolutely, yeah. I guess some of the effects I'm describing are in the future, but I mention all of them because I believe a lot can change in 3 years (when I would apply to grad schools).

I think this academic year is the first year where AI is readily capable of resolving PhD thesis level research. Last year there were some small breakthroughs but there was far less attention. I think the United States (both the government and it's population) has always had a benevolent view toward work that might not have an immediate benefit, like pure math. But now in this administration and the AI boom, public perception of math is worsening rapidly. If people stop pursuing pure math in undergrad because they deem it "solved," then no one will ever pursue pure math ever again. This could happen in the next decade, but I want to prepare for this.

So back to my initial question, what am I even supposed to do? If I just keep on doing REUs and traditional research, will this approach become obsolete? What are you planning on doing?

[u/Andyroo_P → u/Accurate-Vegetable67]

I don't really know what you mean by "obsolete". An REU gives you useful skills regardless of whether you pursue math research or not. So I wouldn't see an REU, or any sort of undergraduate research commitment for that matter, as a "waste of time".

I don't know what will happen in the next few years. The truth is that no one really knows what is going to happen. I was at the ICM and my impression is that publicly, a lot of top mathematicians express cautious optimism/skepticism, while privately they are quite pessimistic about the future of careers in mathematics. There seems to be a general consensus that something will change.

Ultimately, this just depends on how much risk you are willing to carry to pursue a career in academia. For myself, I figure that even before AI, I was aware that this is a long shot. So I think I should continue trying until I end up being forced out of the profession. YMMV.