I saw an interview (in French) of Cédric Villani, speaking on behalf of him and other Fiels medalists, who said that in order to advance mathematics we need three things:
- ideas
- students
- problems
Basically, students to bring original ideas to try and solve existing problems and this generates new ideas and possibly new problems for new students to try and solve with new ideas and so on.
And he continued to say that the issue with LLMs in mathematics, is that he's afraid they could run out of problems, and so students wouldn't bother trying, and this could hurt understanding of mathematics as a whole.
It's totally not my field so I'm not sure what to think of it but it seems important
I'm not a mathematician either, but I find it hard to believe we could run out of problems in pure mathematics. Pure math is like a game where if you get bored you can invent new rules. Maybe eventually all fields related to applied problems will be settled, and the value of pure mathematics will be relegated to the status of other games like chess and go. But that's so far away from current reality that I can't imagine it happening in the next century at least.
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).
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 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.
LelouBil · · focus · HN ↗
- ideas
- students
- problems
Basically, students to bring original ideas to try and solve existing problems and this generates new ideas and possibly new problems for new students to try and solve with new ideas and so on.
And he continued to say that the issue with LLMs in mathematics, is that he's afraid they could run out of problems, and so students wouldn't bother trying, and this could hurt understanding of mathematics as a whole.
It's totally not my field so I'm not sure what to think of it but it seems important
fasterik · · focus · HN ↗
GPerson · · focus · HN ↗
[dead]
fasterik · · focus · HN ↗
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.
xanderlewis · · focus · HN ↗
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.
fasterik · · focus · HN ↗
xanderlewis · · focus · HN ↗
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.