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Tao: Open math problems being non-renewably mined by AI
331–340 of 346 posts
Re: Tao: Open math problems being non-renewably mined by AI
#332Earlier quoted context omitted.
One related problem I see is the pipeline for producing working mathematicians seems to have been completely and irreversibly decimated. What’s the point of doing a long and arduous PhD when all PhD level research problems that used to take months to years can be solved by far less talented people with $100/$1000/$10,000 to spare? How do you even select people into your program (this part is likely hypothetical, clas…
Here most local STEM PhDs try to get into finance. This is largely due to lack of funding for science and poor opportunities for PhDs. Why be a poorly paid postdoc when Jane Street is offering a million USD signup bonus ? PhDs from poorer overseas do try to get related jobs here, mainly to be able to get a permanent resident visa.
> Why be a poorly paid postdoc when Jane Street is offering a million USD signup bonus?
One reason is despising that line of work. Quant firms were pummeling my @prestigious.edu inbox throughout my PhD and I fucking hated those parasites. Well, jokes on me if AI shatters my current career.
Btw a former classmate Caroline Ellison who went to Jane Street eventually landed in prison, lol.
Re: Tao: Open math problems being non-renewably mined by AI
#333Tao's central point seems to be : "In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained. " I am no mathematician, may have misunderstood his point and would be delighted to receive any corrections.
I definitely see what he is saying.
In my work as a graphics programmer I often find that I look at a problem and will immediately see how to solve it, more or less. But the devil is in the details and often nothing works unless you get every detail right. So you spend a lot of time coming up with complex solutions, then boiling them down to simpler versions. In the end you often end up with a fix which is short, simple, and seems obvious. But it gets a lot of subtle details just right and avoids countless potential issues you wouldn't know if you hadn't failed a lot getting there.
And that is actually how you learn and master the craft.
Now, imagine you describe how you sort of solve it to a machine and it spits out the simple, correct implementation and you nod approvingly, never knowing all the ways it could have gone wrong. If this is how mathematics - or programming - is done from now on, no one will actually master their craft. I definitely see why this would worry someone whose career is built on mastery of the craft and a legacy meant to teach the next generation.
Re: Tao: Open math problems being non-renewably mined by AI
#334Earlier quoted context omitted.
The "proof" is merely an appeal (unreadable program) submitted to a different oracle (Lean).
What do u think lean is? That's like saying a program that works, is inscrutable because it appeals to the oracle of "code test cases" to prove itself correct. You're either being intentionally obtuse, or unintentionally ignorant.
Have you tried to read the Lean proofs produced for any of the recent high-profile results? They're extremely long, terribly structured, and don't indicate which parts are restating known results from literature and which are unique to the proof at hand. That's what makes them inscrutable.
It's similar to Mochizuki claiming to have proved the ABC conjecture, with a proof depending on ideas developed over a large number of obscure papers, that required mathematicians to spend a lot of time before they felt they understood it well enough to point out flaws.
If AI solves all famous open problems and the non-famous ones, too, without advances in the readability of their output, there'll still be some work to do to digest and rearrange the proofs for human consumption. During that process, the mathematician may well get some new ideas...
Re: Tao: Open math problems being non-renewably mined by AI
#335Earlier quoted context omitted.
Pure math is practiced mostly for the intellectual thrills and recognition among a very small group of peers. There's little else to it. You don't become rich, you don't become a celebrity. You teach students, write papers, and probably know most other people who work in the same subfield as you. Tao is a sort of a celebrity of the quarter on HN, but I promise you that outside this forum, almost no one has ever heard…
> Now, Tao is a sort of a celebrity of the quarter on HN, but I promise you that outside this forum, almost no one has ever heard of him. This is an absurd thing to say. Hacker news is not the only place that knows about the most famous mathematician in the world. Glancing at Google Trends he seems to be roughly as famous as Linus Torvalds. Not exactly a household name but by no means obscure.
Go to a busy main street.
Ask 1000 different individuals if Terrence Tao rings a bell. If 5% or less can answer you who Tao is, it is safe to say that Tao is obscure.
I'd be very surprised if you can find over 50 individuals, out of the 1000, who can tell you who Terrence Tao is. Even big names like Euler or Gauss would surprise me.
Re: Tao: Open math problems being non-renewably mined by AI
#336Earlier quoted context omitted.
Doesn't this seem to be where all domains are headed? I get kinda freaked out when I feel like all the AI "utopianists" haven't taken the next logical step of thinking about what society looks like when humans are subpar in every domain (and you may argue this won't happen, though I'm becoming more and more a believer that it will, but my point is the utopianists believe that this absolutely will happen, and that it'…
I don't think humans necessarily become subpar when AI can do most of the work. Taking my own personal example, I have far more intellectual curiosity and improved my skills in programming far more with Claude Code than for 15 years of programming without AI simply because I was bogged down by boilerplate and grunt work. Now that AI handles most of the boilerplate and grunt work and can handle harder and harder probl…
> what society looks like when humans are subpar in every domain
> when AI can do most of the work
You're not really responding to the core hypothetical of his comment
To me it reads as that: for utopians, you may benefit from LLMs now, but they'll still surpass you later, what then ?
Re: Tao: Open math problems being non-renewably mined by AI
#337Earlier quoted context omitted.
I think the problem with AI asking questions is that it will ask questions that are interesting to it but not necessarily us. AI, as a model, will never be a perfect copy of a human. It will always be a simulation, and thus to some extent, will ask questions that humans find irrelevant and solve problems that humans find irrelevant. For anyone facing an existential crisis on AI, your ace in the hole is your humanity.…
>your ace in the hole is your humanity Average HN Poster: [nervous sweating]
Exactly.
My humanity is not paying my bills.
Re: Tao: Open math problems being non-renewably mined by AI
#338Earlier quoted context omitted.
Also Andrew Wiles working in secret for 7 years out of fear of someone scooping him.
I've always found the story of A. Wiles sad and frustrating. He worked in secret for 7 years. He submitted a (incorrect) proof at year 4 or so. Reviewers found a problem, but he decided kept all secret for many years after. He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem... I found this behavior against healthy…
What you’re talking about is his proof of (a specialised version) of the Taniyama-Shimura-Weil conjecture[1] which had been proven to imply Fermat’s Last Theorem. The technique he used to prove this was adopted by his students to prove the conjecture in full generality so it now known as the modularity theorem. Given its importance to the Langlands programme it may be that when history looks back on this it will consider this a more important contribution than the fact that it proved FLT even though that is obviously the thing that grabs the headlines, but there’s nothing at all wrong with proving something that implies your goal rather than proving the goal directly. There’s a reason the words “it suffices to show” often turn up in proofs.
[1] https://mathworld.wolfram.com/Taniyama-ShimuraConjecture.htm...
Re: Tao: Open math problems being non-renewably mined by AI
#339Other mathematicians for the last ten years : Open math problems being non renewably mined by Terrence Tao.
Jokes aside, this seems like a pretty weird take. What's stopping mathematicians to make this renewable?
Why not spend some time and effort (presumably using AI) to pose new open problems that are fundamental in nature?
As a field, math could start crediting the person who comes up with a great question, rather than the AI brute forcing a LEAN proof.
Re: Tao: Open math problems being non-renewably mined by AI
#340Earlier quoted context omitted.
> An AI-generated solution always provides ... proof that there is a solution This is only true in the most trivial sense. A solution is a solution, sure... but how do you know it's a solution, and not an incoherent jumble of words? A human has to review and vouch for it. Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could gi…
> Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could give you the same PDF/Lean code and says it proves the opposite, how would anyone know the difference? > You can't advance human understanding unless you produce things that humans can understand. And you can't advance human understating unless you maintain that understand…
That was exactly my thought - taking out the problems that PhDs and early stage researchers work on kills the pipeline of developing mathematicians