[nonethewiser]

>But I don't see any particular reason things would have to stop there: why couldn't some model also spit out nice, beautiful explanations of why the result is true?

Oh… I didnt anticipate this would bother you. Would it be fair to say that its not that you like understanding why its true, because you have that here, but that you like process of discovering why?

Perhaps thats what you meant originally. But my understanding was that you were primarily just concerned with understanding why, not being the one to discover why.

[nicf]

This is an interesting question! You're giving me a chance to reflect a little more than I did when I wrote that last comment.

I can only speak for myself, but it's not that I care a lot about me personally being the first one to discover some new piece of mathematics. (If I did, I'd probably still be doing research, which I'm not.) There is something very satisfying about solving a problem for yourself rather than being handed the answer, though, even if it's not an original problem. It's the same reason some people like doing sudokus, and why those people wouldn't respond well to being told that they could save a lot of time if they just used a sudoku solver or looked up the answer in the back of the book.

But that's not really what I'm getting at in the sentence you're quoting --- people are still free to solve sudokus even though sudoku solvers exist, and the same would presumably be true of proving theorems in the world we're considering. The thing I'd be most worried about is the destruction of the community of mathematicians. If math were just a fun but useless hobby, like, I don't know, whittling or something, I think there would be way fewer people doing it. And there would be even fewer people doing it as deeply and intensely as they are now when it's their full-time job. And as someone who likes math a lot, I don't love the idea of that happening.

[zmgsabst]

CNCs and other technology haven’t destroyed woodworking. There’s whole communities on YouTube — with a spectrum from casual to hobbyist to artisanal to industrial.

Why would mathematics be different than woodworking?

Do you believe there’s a limited demand for mathematics? — my experience is quite the opposite, that we’re limited by the production capacity.

[dinkumthinkum]

HN has this very unique and strange type of reasoning. You’re actually asking why would mathematics be any different than woodworking because CNC machines? It’s like aby issue can be reduced to the most mundane observations and simplicity because we have to justify all technology. Professional mathematics requires years of intense and usually, i.e. almost always, in graduate schools and the entire machinery of that. You’re comparing something many people do as a hobby to the life’s work and f others. of course you can have wave all this away with some argument but I’m not sure this type of reasoning is going to save the technocrats when it he majority of people realize what this app portends for society.

[zmgsabst]

No Im not — I’m comparing two fields that range from hobby to professional, both of which I’ve worked in professionally. But for which automation occurred at different times.

> You’re comparing something many people do as a hobby to the life’s work and f others.

You’re denigrating the talents and educational efforts of artisanal woodworkers to make a shallow dismissal of my point.

[nicf]

This is actually a metaphor I've used myself. I do think the woodworking community is both smaller and less professionalized than it would be in a world where industrial furniture production didn't exist. (This is a bizarre counterfactual, because it's basically impossible for me to imagine a world where industrial furniture production doesn't exist but YouTube does, but like pretend with me here for a moment.) I don't know that this is necessarily a bad thing, but it's definitely different, and I can imagine that if I were a woodworker who lived through the transition from one world to the other I would find it pretty upsetting! As I said above, I'm not claiming it's not worth making the transition anyway, but it does come with a cost.

One place I think the analogy breaks down, though, is that I think you're pretty severely underestimating the time and effort it takes to be productive at math research. I think my path is pretty typical, so I'll describe it. I went to college for four years and took math classes the whole time, after which I was nowhere near prepared to do independent research. Then I went to graduate school, where I received a small stipend to teach calculus to undergrads while I learned even more math, and at the end of four and a half years of that --- including lots of one-on-one mentorship from my advisor --- I just barely able to kinda sorta produce some publishable-but-not-earthshattering research. If I wanted to produce research I was actually proud of, it probably would have taken several more years of putting in reps on less impressive stuff, but I left the field before reaching that point.

Imagine a world where any research I could have produced at the end of those eight and a half years would be inferior to something an LLM could spit out in an afternoon, and where a different LLM is a better calculus instructor than a 22-year-old nicf. (Not a high bar!) How many people are going to spend all those years learning all those skills? More importantly, why would they expect to be paid to do that while producing nothing the whole time?

[zmgsabst]

That’s no different than high-end artisanal woodworking, which I would argue is comparable to self-directed, cutting-edge research:

- apprenticing

- journeyman phase

- only finally achieving mastery

CNC never replaced those people, rather, it scaled the whole field — by creating much higher demand for furniture. People who never made that full journey instead work at factories where their output is scaled. What was displaced was mediocre talent in average homes, eg, building your own table from a magazine design.

You still haven’t answered why you think mathematics will follow a different trajectory — and the only substantial displacement will, eg, be business analysts no longer checking convexity of models and outsourcing that to AI-scaled math experts at the company.

[nicf]

Woodworking is very far from my world, so I don't really have any grounds to judge how comparable the two things actually are. I'll say two things instead.

First, right now presumably the reason a few people still become master woodworkers is that their work is actually better than the mass-produced furniture that you can get for much less money. Imagine a world where instead it was possible to cheaply and automatically produce furniture that is literally indistinguishable from, or maybe even noticeably superior to, anything a human woodworker could ever make. Do you really think the same number of people would still spend years and years developing those skills?

Second, you've talked about business logic and "math experts at the company" a few times now, which makes me wonder if we're just referring to different things with the word "mathematics". I'm talking about a specific subset, what's sometimes called "pure math," the kind of research that mostly only exists within academia and is focused on proving theorems with the goal of improving human understanding of mathematical patterns with no particular eye on solving any practical problems. It sounds like you're focused on the sort of mathematical work that gets done in industry, where you're using mathematical tools, but the goal is to solve a practical problem for a business.

These are actually quite different activities --- the same individuals who are good at one stand a decent chance of being good at the other, but that's most of what they have in common, and even there I know many people who are much more skilled at one than the other. I'm not really asking anyone who doesn't care about pure math to start caring about it, but when I'm talking about the effect of AI on the future of the field, I'm referring specifically to pure math research.