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- Maybe the Hitchhikers Guide to the Galaxy series was predictive in pointing out the problems of ill defined questions (The Answer to the Ultimate Question of Life, the Universe, and Everything).by tocs3
- AI also can replace a lot of expert attention too. Why not? What is useful or what is not useful is based on the expert's narrow opinion. An AI system can do much more and deep value comparison. It looks like if our current technological advancement continues, in the space of what is possible (or even impossible), AI can find the optimal solutions better than any human or human organizations. But I think there is only one think will remain for humans to go for these solutions: what we value. that will be the last resort I believe and hopefully ai systems won't start manipulate us too as we are very fragile on manipulation.by caglaroktay
- But how would „what we value“ still be relevant?by mmoll
- Terence Tao sees a role for AI in science. I'm no genius but he basically described what I've thought all along... We don't need to be "all in" or "all out".
It's the old cliche of "if you only have a hammer every problem looks like a nail". Let's not fall into the trap of thinking that our life needs to be 100% about AI or completely devoid of AI. We can really use this thing to make our lives better.
Instead of wasting time on the question of whether we should use it, let's focus on HOW we'll use it.
And one thing about Tao: it's really refreshing to have an influential genius "around" who isn't a egomaniacal psychopath trying to rule the world through their XYZ corporation but, instead, being a reasonable and well-balanced person. Big fan.
by glimshe - I think it's impossible to be half in. AI will eventually be better at things than people, and people will simply be rocks in the gears of progress.
The only thing to do is to be all in, or get run over.
by a2ff6eeb0 - I think it’s more that he seeks to preserve and promote human understanding of mathematics, and sees that grappling with this new technology is necessary. One reason is that for human mathematical practices and institutions to retain legitimacy, they need to justify their value. As Tao explains, one obvious answer to that is made less obvious now with AI.by GPerson
- Anyone else print their white papers before reading? (At least the short ones)
- When I was in academia and had easy access to a good printer, I always did. I miss it now that it's easier to just read on my screen.
- Absolutely. I feel I gain at least 10 IQ points when reading something on paper.
This is also the strategy I use for editing drafts of my books. I bring a printed draft to someplace nice (e.g. coffee shop or park) and read it all carefully, then I transfer the edits back to the .tex sources. I do several passes of this, until I feel the text + explanations are solid.
Reading on screen just isn't the same...
by ivansavz - The chess analogy doesn't quite work for me. In chess, an engine's move is useful because it helps you win. In math, a proof is useful because it helps you understand something - and from that, you can build more. If a proof is incomprehensible, it's like a chess move that only works in that one specific position. Useless. The ABC conjecture is a perfect example - Mochizuki's proof might be correct, but no one can follow it, so it's basically dead. AI proofs are going to be like that, but way more of them. Tao's essay is a great starting point
- Terence argues that explanation of results ("understanding") will be the new bottleneck in math research but I am not sure this is the real bottleneck for progress.
Understanding was critical for the field to progress when only humans were involved but if humans are not needed to make progress, I wonder if we split into two worlds: an AI math-world where amazing new results continue at a rapid pace bottlenecked only by compute/cost and a human math-world where we understand a subset of the AI math-world as a hobby (similar to Stockfish vs human chess).
by rramach - How is either of those situations more or less like a hobby than the other?by GPerson
- It will be the same as before: some effort will go into checking proofs and the other into creating them. AI speeds up both.by paulpauper
- Somehow, I feel that progress, in your understanding of what progress is, loses all meaning.
- In some sense "understanding" (understanding if it is true, if it is important, how to use it) is about the only bottleneck in math. Any theorem that you can write down or imagine is already true, false, not provable already. In some ways we can already start iterating through all the theorems. We will never get to the end (or really get very far down the line) and most all of them be trivial (I think the Busy Beaver[1] project is a fascinating example, ymmv).
I am wary of AI in all aspects I am seeing it in but in many ways in mathematics seems to me the least troubling. It will change things in and the field will not be the same. Blacksmithing has not really gone away. You can still work as a farrier, if you like that sort of things. The tools that replaced a man working over a forge with a big hammer are part of a giant industry that is still producing works for the modern world.
by tocs3 - If you're having dinner like me and prefer to watch: https://www.youtube.com/watch?v=M0--ZH1lOzgby piker
- What is being made is "what are our core values?" argument. One does not need to be a mathematician to know how poorly this worked for large communities when incentives are misaligned...
If a subset of mathematicians, use AI to condense timelines focusing on goal 6.2 exclusively and make rapid progress and reach a proverbial inflection point — one where value proposition of the using this new normal is too enticing to give up — everyone will ask: "This thing is so awesome. Why should I care about your values?"
by itissid - I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are banned from publishing until their cats understand the theorems.
If Amazon uses AI math to come up with better routing, the cats can benefit from cheaper delivery fees just as much as humans can. No understanding needed.
The human brain is being obsoleted, soon thinking is going to be a recreational activity like weightlifting. If you want to think as a hobby, that's fine, but most people will be free of that toil of unwanted brain labor.
by a2ff6eeb0 - I’m not anti AI but thinking the human brain is obsolete and using it will become a hobby is a dystopian view of the future where no one has any agency anymore. By your logic since our brains provide no value why not just shoot ourselves in the head while we’re at?by TSiege
- What if the better routing leads to an outage that the AI can't explain or fix and all the humans who might have understood it were laid off or otherwise unavailable?
- If a result has a real-world application, then it can easily be published in an engineering or applied scientific journal in which it is already the norm to present methods that work empirically with little to no understanding of how.
- Your analogy is great.
What happens when it's the cats who get to decide what's published?
Not an ideal scenario, but that's exactly the situation here. Mathematicians decide what gets reviewed and published in a a top journal.
In the long run, this can and should make journals obsolete.
by fooker - > If Amazon uses AI math to come up with better routin
Most research mathematics is pure mathematics which is completely useless. No routing algorithms. It's only relevant because we (or at least mathematicians) are interested in it. So an AI producing incomprehensible proofs would be completely pointless. That's why Tao insists on the importance of human understanding.
by cubefox - > I don't know why anyone should care about understanding the results if the AI is better at math than us
This is a big if, right? AI can still generate subtle or even silly mistakes that any normal human, let alone a mathematician, wouldn't make. Besides, math is more than just getting a conclusion but to understand and to generalize new ways of solving problems. After all, mathematicians are a curious bunch. To quote Hilbert's epitaph: We must know. We shall know.
by hintymad - If you are free from physical and mental labor, you are in fact, not supplying labor, and are therefore surplus to requirements.by FuckButtons
- The essay On Proof and Progress in Mathematics by a Field's medalist is worth reading:
https://arxiv.org/abs/math/9404236
He wrote it in 1994.
He writes about how he almost "destroyed" a subdiscipline in mathematics by becoming so good at it that he outclassed everyone. PhD students were advised to stay away from the whole field.
When he discovered this, he realized his error was that he was focusing on producing results, and not focusing on explaining his thought process. It's that thought process that is valuable in advancing the frontier - results alone won't do it. It didn't matter how many theorems he proved, if he was the only one who had the mental framework in mind on how to think about the whole field.
I'm sure we've come across abstruse books where every theorem has a rabbit being pulled out of a hat, whereas other readers find it intuitive. It's because the latter has developed a mental model for the discipline, and you haven't.
So he set about slowing down, and focusing on holding lots of seminars where he worked with other mathematicians to explain the thought process. Eventually others started publishing proofs of key theorems.
When people publish in a journal, they are not merely doing it to show the result. They are having a conversation with other mathematicians. If they cannot explain their own proof, they're not having a conversation.
This is why even decades after the Four Color Theorem was proved, plenty of mathematicians don't consider it "mathematics".
by BeetleB - Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."
- Similar to Ai writing. Lots of bloat.by paulpauper
- That's also true for regular math proofs.
No one talks about why the proof works, but they will happily spend thousands of pages explaining how it works.
by noosphr - Someone just brought up this point to me a few days ago on here, I'm definitely increasingly convinced that it's one of the main reasons (maybe even the main reason?) AI prose is so annoying to read through, and so rarely seems able to convey true understanding. It assigns the same narrative importance and dramatic tone to everything (the load bearing whatever, the crucial insight, the smoking gun) even when it's trivial.by ipdashc