The question for some is, is whether the original authors would have produced their work without building off from the work of other mathematicians.
(which is somewhat valid).
Though I think a far more interesting thing would be whether AI given the corpus of 19th century mathematics and physics reproduce what Ramanujam or what Einstein did.
IMO that there is any work at all to build from is the result of a long tradition of taking the next step. Professor to student and so on. The danger of AI here is we get to take a leap, say, 10 steps - but then there is no more tradition to have the fortitude and mentoring necessary to continue the progress.
It all gets derailed while betting on RSI and never having to do math research again (but if an advanced theorem is proven, and no one alive is competent enough to comprehend it, does it even matter that we get to call it solved?)
> if an advanced theorem is proven, and no one alive is competent enough to comprehend it, does it even matter
For any applied mathematics: of course it matters if I can use a better algorithm for $PROBLEM. Yes, even if I do not understand it (I'd like a LEAN certificate tho)! As for pure mathematics, it can be argued that it never mattered in the first place.
This is why the AI companies are making money off selling tokens and raking in investments for as long as it will work and is not looking to create the value themselves and making money off it...
They know that value creation is a dead end sooner or later..
If we suddenly skipped 10 generations of mathematical lineage because of AI, wouldn’t it also be smart enough that you could just prompt it to connect ideas from graduate level maths all the way to the proof!
no. That's not a given at all? I think most reasonably people now agree that AI intelligence is spiky, that is to say, there are some areas it is amazingly good, and some areas where it spectacularly fails.
One of these areas it's not good at is sadly it's social ability. It's terrible at explaining things - just try asking ask it to explain code !
I find there is quite a difference between something like "what do I do next" for a specific problem, and actually trying to learn something hard from an AI. The first it is quite good at, the second it is not. Surface level is easy, going into the weeds is difficult
It seems like future models could build off the 10 steps to take 10 more. It's not 10 steps of AI slop, it's a discovery to build off of just like how human scientific progress has worked.
I think the question is rather, what will happen to human beings when any possible personal intellectual accomplishment will no longer be seen as interesting or relevant by other human beings when AI can do most of it?
It's all well and good to say that we should just go on these journeys for our own enrichment, but even so they will just be doing it alone...or else not do it at all because they need a shared human effort surrounding them to do it, and therefore end up depressed and immersed in drugs or media all day.
Of course we're awed at what AI can do now, because all of us observing it have had the luxury of having such opportunities before AI. I got my PhD before AI and I found satisfaction in participating in a shared math community, which I wouldn't have done if I were starting my PhD now, because I would find the current academic environment unacceptable and useless.
Many people still do woodworking for the love of the craft, even though factories exist with machines that can do everything hand tools can but 10x better and faster. If AI gets way out in front of anything humans understand, I expect that mathematicians will probably pick up where their understanding actually is, and carry on.
That analogy is rather poor. Woodworking produces discrete, unique, and physical objects, that can be made, and found use for, as many times as the craftsman wishes. Once you discover a law of physics, you can't discover it again, and it's not yours to do with as you please.
Why not? If I discovered a law of physics that explains superconductivity and could use it to make a room temperature superconductor and kept it a trade secret?
That would be a very exciting experiment. I doubt you could find enough vintage training data to train a LLM enough to do it without it being contaminated by anachronistic data in the weights, but I would be absolutely amazed if it could reproduce that.
Other mathematicians have done the work of writing out and publishing these proofs, OpenAI has published Lean certificates.
The first type of work pushes the field of mathematics further, the second kind strip-mines the sense of discovery and accomplishment and replaces it with math homework for high level mathematicians, because in order for it to be useful, it still needs to be turned into a human readable proof.
It's imho not valid to say OpenAI is "building off" other mathematicians work, in the same way as humans, do.
> Though I think a far more interesting thing would be whether AI given the corpus of 19th century mathematics and physics reproduce what Ramanujam or what Einstein did.
I don't think so, it was a big leap forward in terms of creativity, imagination, rigor and experimentation. Einstein was able to "run" visual thought experiments inside his mind
whether the original authors would have produced their work without building off from the work of other mathematicians.
That's rhetorical, right? Of course mathematicians built on what older mathematicians built and OpenAI's machine built on that. The real question whether OpenAI's machine has contributed something others will in turn build on.
Not saying I agree with the view, but something along those lines popped up when the Naive Stokes conjecture was seemingly solved (and way before when Open AI began solving Olympiad level problems and so on with their older class of models). Personally, I do see both sides of the argument. Though the broader impact remains to be seen.
That's not the real question. Humans make incremental progress and sometimes have a brilliant inspiration that seems to change all of mathematical thinking after it. The question is: is AI making predictable incremental progress? Or is it discovering fundamentally different ways of thinking about math?
The idea that mathematicians progress math by discovering fundamentally different ways of thinking about it is closer to a hallucination than a meaningful statement about mathematics.
Why is that even a question? That's how human mathematics has worked for ages, it's OpenAI breaking that chain, which needs to be severely questioned.
Because the real question is not whether anyone or anything built on other work, but whether any human can build on that work.
And so far, yet again, OpenAI has stopped just shy of that, instead creating math homework for mathematical geniuses while taking away their sense of discovery and accomplishment.
This question strikes me as strange, because it has always been in the nature of the mathematical community to share results as openly and widely as possible. Hong Wang’s work was in the public domain and was meant to be built upon. This is what human mathematicians have been doing for centuries.
And the level of effort required to have these laws applied to false marketers is unrealistic. Unless there is a case of disfigurement or death, it's just caveat emptor.
Teach them how to use tools to solve their own problems; give them real tasks to do, and trust them to do them, without watching over them. I want my kids to be curious about the world, and understand that they have the agency to fix things. The other thing I try to drive home is that failure is a natural part of learning, if you want to get good at something, you have to fail a bunch first. My biggest failure as a parent is completely flying off the handle when they don't eat their food, but I'm trying to be less psychotic about that. You'll have your own problems. Try to get ahead of them and course-correct before it defines their whole personality or ruins your relationship with them.
I used some check marks and x-es in a work chat, because it was easy to do, and so I could highlight the good and bad outcomes, and someone immediately asked me if I was using AI. I was caught totally flat-footed, because I hadn't used AI, but it looked VERY MUCH as though I had.
Was this written by AI? This is just "I automated some things, use skills instead of scripts". Like, what did you automate? How much time did you save? How can I reproduce that?
I too found the article lacking, however I also feel we should have a new HN guideline to not talk about whether or not something was written by AI. It’s rather tiresome, and in this case probably wrong (AIs hate leaving things incomplete).
It’s a useful signal. As the web becomes more full of noise. I am not interested in having my time wasted reading an article that the purported author couldn’t even be bothered to write. If there is a new guideline, I’d propose that it be to not submit AI-generated content.
I think OP was rather suggesting that we have a guideline to avoid comments about whether something was written by AI or not.
Without fail, every comment section will have posts by people talking about how something is AI generated. Yeah we get it. It used to be novel to spot this, but now most people are pretty good at spotting it too and/or don't care.
It's about as meaningful as noting an article is written in English.
100% I picked up shorthand to take notes quicker, but I'm still half-in/half-out of the conversation, mentally deciding what's important enough to jot down. This sounds like a great solution.
I typed in my dentist's full business name and location, "<name> family dentistry <city> <state>", and it was still #5 in the results. I still, out of habit, tapped the first link and called that number instead. It's ludicrous. In 2010 that would have been the top hit, next to the Wikipedia page on dentistry.
