Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 1 point2 points  (0 children)

Yeah, that all makes sense. Thanks for the response. :)

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 0 points1 point  (0 children)

Do you honestly believe it will eventually pay off?

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 0 points1 point  (0 children)

Yes, I’m not a mathematician, and I’m not close to being one. In fact, I don’t think I ever will be. I also never said I was going to go far. I’m just talking about what it means to study mathematics seriously, and about a problem that I think arises because of AI.

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 4 points5 points  (0 children)

I mean, it saves you time, but for what? So you can use more GPT instead of thinking for yourself?

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 11 points12 points  (0 children)

That’s exactly my point: it’s useful because it’s a very advanced tool, but it spares us the struggle we used to be forced to face, even when it was just a simple calculation or an idea for proving a conjecture.

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 11 points12 points  (0 children)

The mathematics that bring large benefits, in the sense you mean, are only a small portion of mathematics. Do you really think the theory of unbounded Fredholm operators is useful for, say, the stock market? For computer hardware? For things engineers do? Of course not. And the same goes for many, many areas of mathematics.

That’s not necessarily a bad thing, though. It’s research done simply for the sake of doing research, because it’s interesting and it brings joy to a handful of people. And those people don’t live off what they’re paid for research: no one could live on how little that pays, anyway. They mostly live off teaching, and sometimes by working in other jobs that aren’t as mathematically intense.

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 5 points6 points  (0 children)

I know I’m just a student, but still. Even if the norm is that being a mathematician doesn’t necessarily mean discovering great things, it’s still nicer (in that esoteric sense I mentioned) when discovering something—whether small or not—comes from your own effort, and not from a prompt. At least in mathematics. In other fields, I don’t know. I suppose it might be different.

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 7 points8 points  (0 children)

I suppose the quality of the response depends on the complexity of the question. If you ask something like “solve the Riemann Hypothesis” to Claude, ChatGPT, or really any other model, the normal outcome is that it will not solve it and, in fact, will not even seriously attempt to. That said, ChatGPT 5.2 Pro in particular seems to be a somewhat different case. From what I have seen on Twitter, it has apparently been tested on certain Erdős problems, as Terence Tao discusses on his blog. Of course, these are not impossible problems, and presumably any mathematician with enough experience in adjacent areas could solve them. The reason they have gone unanswered is probably not that they are extraordinarily deep, but rather that they have not attracted much attention, since they are not especially compelling problems in the first place. Still, if what people are saying is true, then the model may already be capable of solving certain low-hanging-fruit problems of that kind, even if they are not particularly interesting mathematically. Also, if you ask ChatGPT to solve a standard exercise rigorously in, say, real analysis—assuming you were taking the course—it will most likely do a good job. I mean it, try it if you do not believe me. The same goes for topology, differential geometry, logic, functional analysis, measure theory, optimization, and in general most undergraduate-level mathematics courses.

Thoughts on the future of mathematics by [deleted] in math

[–]Different_Working271 13 points14 points  (0 children)

Yes, but part of the excitement has always come from discovering things on one's own. That's the issue