In a word, the job of the mathematics department is not only to produce mathematics, but mathematicians.

Similarly, the output of programming is not only a program, but also a programmer. It is you.

Outsourcing the work deprives you of who you become by writing it.

Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question.

The annoying thing about recent AI advances is that they target questions on the wrong end of the spectrum: Erdos problems are exactly the sort of "useless" questions that people might answer purely for the love of the game. The sort of questions that a young person might cut their teeth on and gain confidence.

Solving questions like these automatically, I think, is not good for the long-term health of research. At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.

Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension.

In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.

There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

AI makes the math world more accessible than before. If you have a question about a proof in the lecture, you can just ask it. Of course, one can't trust it blindly, but fundamentally it's amazing.

I think that's a good thing, but of course this means that a lot has to change in culture and behaviors, also in the research world.

The software engineering world is more or less in the same situation, it's also changing. But for now I think it still holds true that someone who knows maths plus an LLM is better than someone who doesn't know maths plus LLM. At least in software it does.

As a former physicist and current data scientist/engineer, I know for a fact that commercial utility drives math research and researchers.

Math is a tool to solve problems. Some mathematicians might only love the process of using the tool, but commercial logic absolutely drives mathematician attention to develop commercially useful tools.

It sounds plausible that LLMs help generate insights that humans have missed. But there are many open questions, eg the rate of generating insightful vs uninsightful but plausible statements, which can affect how useful they will be, and of course "open"ai has no incentive to share how much effort/cost (tokens and/or human-review) had been put into investigating erdos problems before coming up with this solution.

This excessively pro-AI article brought to you by private equity.

That's why there's a disconnect when you go from math for engineers to the stuff above it. It feels less useful and very different

AI is simply not able to innovate, only combine.

They learn how to read papers and literature rigorously. They get low-hanging fruits to practice on, which can take months. Their funding doesn't come from thin air either.

So what happens when the group leaders would rather spend money on compute, and get models to solve the low-hanging fruit? Which the models could very well do in mere hours, compared to months.

Nor does it help that publishing is the number 1 measure in academia. Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups.

It is basically the "junior problem", but even more severe.

Except when someone hands you a magic button that just gives you knowledge?[at least in the framing of this "warning"] Then it's about peoples' livelihoods, about "culture", etc?

"Computer" used to be a job. Did science on the whole lose or gain by making these clerks obsolete?

At this stage, the current wave of AI is not reliable enough that it would be safe to lose the abilities it can replace.

The failures modes are often turned into memes and jokes, but they are the thing we should really pay attention to, IMO.

That's not a problem unique to math, or even to academia. It's a problem in every context in human life where people communicate via written documents.

Mathematicians of all people should be free from such emotion-driven thinking. I guess people’s self interest in continuing to make an income trumps all.

I will note that the average corporate mathematical modelling is usually a fucking circus so adding AI might make it better.

If you love mathematics so much, and it's not the prestige and accolades that drive you, then what stops you from just solving problems on your free time even if they are already solved by AI?

Why does your field have to remain economically viable for you, why does this not apply to textile manufacturing or something? Someone's positions in society is owed to textile manufacturing too, and it has a culture that some people would lament the loss of and so on.(See guild system, craftsmanship in Europe).

I can't predict whether this will be a good thing in the long run, but this is literally the same complaint that every industry affected by automation ever had, and many who are now complaining would dismiss it if it were about something they personally do not care about or isn't sufficiently "noble" or intellectual.

I know it hurts, but the core complaint is just economic displacement, many have had to deal with that before. Most people who have something they love have to do that on their free time because it's not economically viable as a job, tough luck.

I mean, what field doesn't? Everyone works to make money.

Slightly unrelated, but, their website "https://leidendeclaration.ai/" itself gives an eerie feeling of being built by Sonnet. That color scheme and the layout is what Sonnet chooses by default most of the times.

He states that he struggled to come up with problems which would be challenging for AI to solve (at the below site) and thus forced to accept that mathematicians have to rethink their profession.

FrontierMath: Benchmarking AI against advanced mathematical research by Epoch AI - https://epoch.ai/frontiermath

As a follow up to the above, see "First Proof: Mathematicians Putting AI to the Test" featuring eminent mathematicians - https://www.youtube.com/watch?v=AaICCTpkI7Q

> However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration, and the pursuit of knowledge for its own sake.

Generation X was the last generation that had 'general knowledge', as in an abundance of fairly useful information stored in 'grey matter' that could be recalled quickly. When search engines came along there really wasn't much need to know anything since most things could be looked up. However, you still had to think.

With LLMs, thinking is kind-of optional. This really is an existential threat to our intelligence since 'use it or lose it applies'. I am glad these mathematicians are doing their duty as canary in the coal mine.

So, why would they be advocating for limitations on arriving at solutions?

The issue is, how is a group of intellectuals, whose identity derives from their ability to do something rare, useful, and requires many years to get good at, react when a machine can produce all of their useful output nearly automatically, can verify its own outputs, and is getting better exponentially? It is the complete annihilation of one's sense of value and purpose when the binding element to your culture is commodified.

I think there will be a lot of arguments trying to claim that the point of mathematics is curiosity, or that there is always some ineffable human element that AI can't replicate, but I fail to see how somehow these wishy-washy human centered values somehow mean anything compared to the amoral pursuit of mathematical truth, which has nothing to do with humans.

It's just that we humans happened to be the only beings in the universe good at math until ~2025. Now there is another species which can do many of the things we do, and it is not bound by the size of the human brain, our short term memories, or the architectural limits of biological computation. To imagine that humans would retain supremacy in this very un-human like discipline seems like wishful thinking.

I briefly studied at a pure math department. We were learning linear algebra and I found the symbol heavy, proof oriented approach very difficult and unintuitive. But when I squinted at the diagrams I realized, oh wait, this actually has dozens of practical applications! Across dozens of different fields! How fantastic!

And the textbook, for some reason, chose to mention precisely none of them. Which I found quite disappointing, because it made the whole thing seem quite abstract (which it actually wasn't), and made it harder to understand.

I mentioned this to my colleagues, who became extremely upset, and informed me that I was in the wrong department.

For years?

https://leidendeclaration.ai/

Far more interesting as it's outlaying a set of principles for using AI to augment human involvement and science, rather than replacement.

I understand that the "language interface" of a "maths AI" could be some specialized trained LLM (Large Language Model) that to convey, with human language, "high level" mathematical mental contructs and intuition.

But then, you would need some models which does the reasoning using formal mathematical solvers (and probably a ton of "scratch" memory, it would be interesting to see how those models end up storing "mathematical" lema data). I guess you can have ML (Machine Learning) for those models on 'general maths', but also we can think about more mathematically focused ML for a specific problem, area, etc. And in the end, ML for maths, would it be mostly permutations of truth statements fed to a neural net?

When we were talking about "AI", one decade ago, that was what most had in mind (it may help a bit in physics, but it seems less likely, because reality/experiments are hard to teach to "AI"s).

If that becomes a reality (aka easy hardware access, and some "working" models), mathematicians will have to be as good in maths than in maths ML. And this is were there is an issue: training honestely good mathematical human brains may become very hard with some broad availability of good general maths reasoning "AIs".

Every time I ask ChatGPT to make a table for a subject I know well, I will find an error in one of the results and it is very confident about it until I question it in detail

Every time I ask ChatGPT for nutritional breakdown of some dense food source and give it a quantity like 8 ounces and ask for the weight of each ingredient, the weights will be wrong and add up to more than the original weight of 8 ounces

These are variations of the old "how many Rs in strawberry" problem, it's still not solved, "AI" cannot reassemble a complex problem properly

A lot of what it tells me in detail about some subjects sounds suspiciously like Reddit posts reassembled out of order

The ability to clearly outmatch trillion dollar machines is a very unique satisfaction. I even write ordinary internet comments with an intention to make them clearly better and more fun to read than boring Claude output.

The barrier to entry just got lowered. This has happened many times before in history. We just end up with fewer of what David Graeber would call "bullshit jobs."