xanderlewis

> Can't we get all the meaty goodness by simplifying and generalizing the proofs now we know they exist?

Perhaps, but there is a danger: it is difficult to un-see things. At least for now, AI-generated proofs are likely to be of a somewhat brute-force nature. As each such proof pops into existence, two things happen: (1) it is much harder to maintain an untainted mind and go on to discover alternative, perhaps deeper and more conceptual, proofs that cannot be obtained by massaging and cleaning up a more brute-force approach (think of this as getting 'stuck in a local minimum', if you like), and (2) at a societal level there is thereafter much less incentive to attempt to do so (announcing a proof of a previous unproven result is, for now, far more prestigious than announcing a much better, more elegant, proof of a known result).

One could ask why we prefer conceptual explanations to brute-force proofs; after all, a proof is a proof, isn't it? I suppose one reasonable answer is that conceptual explanations lead more readily to new questions and that there's also intrinsic beauty in such explanations -- though, of course, many outside the field will simply not care.

When it comes to mathematics, you won't find any well-informed commenters on HN. Or, at least, 99% of commenters have no idea what they're talking about. It's infuriating. I try to just ignore it now and let it wash over me.

It's an unbelievably unoriginal statement, and an irrelevant one too.

AI isn't going to stop hobbyists doing anything; no one ever suggested so. We're not talking about hobbyists.

Have you not already heard others make this analogy a million times by now? It seems like I read it multiple times a day at this point.

Mathematics can be enjoyed recreationally as a puzzle like any other, but it isn’t just an arbitrary puzzle. It’s a science where one discovers truth and seeks an understanding of, and dreams up, new phenomena. It’s not chess, or go, or StarCraft. There’s no fixed rule set and the goal isn’t to ‘win’ or beat your opponents.

Let’s stop repeating this nonsense as if it’s a profound observation.

The real value is in advancing the understanding but very few outside academia understand this (it’s counterintuitive, which is fair enough as it’s somewhat unique to mathematics as a subject), so if you want to get funding you frame it as being for solving the problems.

Now that you can solve without understanding this setup is broken. Either the sources of funding will finally have to learn the difference and the value of the latter, or mathematics research ends.

> even if they like doing it as a day to day job, they'd probably be doing something else if they had absolute freedom over their time.

Not the mathematicians I know. They’d happily drop the academic admin stuff, but they’d absolutely keep doing mathematics in much the same way.

You’re (as Claude would say) absolutely right, and I suspect the original commenter has no idea what they’re talking about.

As Kevin Buzzard recently said:

> In a 2020 piece in the Notices of the AMS, I asked the following question: “If one human had an understanding of all of modern pure mathematics simultaneously, how much further would they immediately be able to see?” Six years later we are beginning to understand the answer to this question.

It’s like people think problems are given to us by God.

We make our problems up!

> For some reason there is this virulent strain of anti-human AI rhetoric

It’s just… nasty, isn’t it? Facts aside, one does have to wonder what motivates not the beliefs themselves, but the, well, frankly aggressive, way in which they’re expressed. Bitterness and envy felt towards those who have actually done the hard work and achieved things?

> We've reached the point that it's even started solving Millennium problems.

Since you’re so certain, how long do you think it’ll be before all of the millennium problems are solved by AI (by leveraging the current literature)?

> I don’t open emails anymore i let it summarize draft and handle most of the work and I only talk to Claude and not read/write the emails myself.

I pity the people on the other side.

Just don’t do drugs.

It’s hard though when Google tries to tempt you to do drugs every three seconds.

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.

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.

Listening to him, I didn’t get that impression. I get that academia at large is full of egomaniacs (or so I’ve heard and read online), but the mathematics community is a weirdly non-toxic oasis of reasonable enthusiasts — genuinely, surprising though that may be to those with no experience!

So I have my reasons to weigh his statements more heavily. I certainly don’t take anything for granted.