If you’re not a mathematician why are you chiming in to contradict one of the best mathematicians in the world? I don’t understand the lack of humility on this website.

Because that's an appeal to authority, which is a fallacy. Things aren't true or false because one expert says they are, they're true or false on the basis of arguments and evidence.

There's no lack of humility here. I'm stating an opinion and giving my reasons for why I think it's true, while acknowledging my limited perspective. If I heard a convincing argument, or saw data that 90% of research mathematicians think we're at risk of running out of problems, then I would update my beliefs accordingly.

No one’s saying you have to believe whatever the famous mathematician says — that would be stupid. They’re saying that there’s a difference between the opinion of an expert and some random outsider.

This is true of all subjects, but it’s hard to think of a subject where the gap is as stark as it is in mathematics — even intelligent outsiders have no idea what the subject is really about, and, even worse, they think they know (mainly because we all studied something also called ‘mathematics’ as children and assume that research mathematicians probably do something similar).

By the way, I agree with your original comment.

I dunno, it's a weird take on a website dedicated to casual discussion of technical subjects to say that I shouldn't chime in because I'm not an expert. I stated an opinion, and I don't see anywhere that I presented myself as some sort of authority. Also, it's beside the point, but for what it's worth I have taken upper level undergraduate courses in pure mathematics (real analysis and two semesters of combinatorics), so I have at least some idea of what research-level mathematics looks like.

I’m sorry you feel like such a victim but it’s a topic in which having an awareness of how the mathematics culture works matters, which honestly should go without saying. You’re pitting yourself, someone with no understanding of the system, in direct contrast to someone who understands the system very well. You have no evidence for your view either. You’re just contributing noise.

I provided an argument: mathematics is a discipline where we invent axioms and try to find interesting consequences of those axioms. By its nature, there are an infinite number of possible problems. Even if there is a finite number of problems interesting to humans (which could itself be questioned), we don't have any reason to think that we are anywhere close to running out of them. Saying there is "no evidence" for my view is a non sequitur; the burden of proof would be to establish that there's a finite number of interesting problems and that we've, say, exhausted 80% of them.

I don't think I'm the one adding noise here. You've done nothing but put words in my mouth, attack me personally, and use argument from authority instead of responding to the substance of the debate.

You’re free to generate an arbitrary set of axioms and study the consequences. Zero people will care. People care about doing mathematics in a community, working toward recognizable goals.

The infinitude of mathematics doesn’t matter. What matters if mathematics doesn’t change radically is the size of the database of AI results relative to the potential output of a human lifetime.

You don’t actually understand what argument from authority is. There’s an actual reason the “authority” here is being appealed to which is not just their authority. You don’t respect people who know more than you, but you should still read Terence Tao’s mathstodon posts on stripmining mathematics.

I agree, though it might not be what you mean!

I get pissed off reading the ‘weird takes’ on mathematics from people who come from the tech world and don’t know what they’re talking about (but for some reason think they do). Not only is it just painful to read; it’s actively harmful.

Mathematicians are largely ignorant of software and are aware of and will freely admit to their own ignorance, but for some reason the software engineers here are largely ignorant of mathematics AND think they know it inside out.

It sounds like you’re actually more well informed than most. Don’t take my comments personally, in any case.