> 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.
I think what I’m finding interesting is this is the same guy who the AI industry was so jubilant when he was saying [AI is ready for primetime](https://academy.openai.com/public/blogs/terence-tao-ai-is-re...) in March and now he’s AI enemy no1 the moment he suggests some ways of using AI that aren't “turn brain off and let the tokens rip!"
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.
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?
Brace for impact.. OpenAI are going to dump their load
Looks like they are betting the downer from AGMAI is not going to hurt their cred where it matters (investors, and whales-- a mix of b-tier profs, postdocs, uni admins, and wealthy crackpots)
My own is there won't be prompts, traces, whatever, like AGMAI asked for. Same old style. Navier-Stokes "worked". People outside unglamorous analysis swallowed it.
One hope is that everyone will know someone whose years of work went for nought. By hearsay, the pipeline of whales will be broken (only hitting openAI revenues in a couple of years postIPO, however)
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’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 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.
I’ve left everything (Facebook, Instagram, I’ve even deleted the YouTube app from my phone, etc.) apart from HN. I occasionally look at Twitter, but only when someone sends me a link.
Me too, except for YouTube. I'm still hopelessly addicted to YouTube, but I'm working on it. I also ditched my smartphone eight months ago and going strong, zero desire to return to it.
Seriously, fuck all this shit. Some people love to say that love of the old web is just nostalgia and they are free to think what they want.
What really helped me to go through the YouTube backlog quickly was a user-script sending closed captions to an LLM to summarize, with some custom instructions of what I want. Occasionally I will ask a follow-up question. Now, I can read the summary of an hour-long video in 3 minutes and close it. I only watch or listen to videos that I really want to hear in full.
As another option, I use the Redirector browser add-on to automatically take me from /shorts/{videoid} to /watch?v=$1. Its amazing how manipulative the shorts interface is because if you're not in it, the temptation is SO massively reduced. Shows how much money they obviously spent on psych profiling for shorts to get that first click. We are just meat puppets to them.
My plan is to sell my laptop so that I only have a desktop and can't just watch willy-nilly wherever I am in my apartment. But it's a tough trigger to pull.
I’ve learned a huge amount from YouTube and am very thankful for its existence. It’s the absolute insistence on showing me idiotic ‘shorts’ that made me leave. I didn’t want to.
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.