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One of the awesome things about LLMs is they make it quick and easy to make PoCs, so yes. Proving that an approach will work before spending a bunch of deep des

One of the awesome things about LLMs is they make it quick and easy to make PoCs, so yes. Proving that an approach will work before spending a bunch of deep design effort is absolutely valuable. Your exact scenario is something I've literally done: give a half-completed design to a team member and asked them to vibecode a PoC to prove the approach will work and figure out some of the details, explore scaling and failure characteristics, etc. Or I do the PoC vibecoding myself too. LLMs have been a gamechanger here.

SpicyLemonZest 7d ago
It's valuable for you, the person who's going to spend a bunch of deep design effort, to make POCs. Is it valuable for someone else to drive by, dump some POCs on your lap, and then leave you to do the deep design effort while they run away to study AI? If that person then runs around telling people that they're the real author of your project, because they generated the original POC, would you consider that an accurate assessment?
- ndriscoll 7d ago
  Your analogy is far enough away from the way that the real world works that I'm not sure that I can really even strain my experiences to fit within it. Sure, I guess that would be annoying? But mathematicians define their field. They're smart people. They're capable of recognizing when someone just did a vibecoded throwaway PoC and when someone has a well structured proof. Actually even before LLMs they'd publish new, clearer or more elegant proofs of old results. They can say that inscrutable proofs are exactly as valuable as they are, and that the first explanation people can actually understand carries its own prestige.
  - SpicyLemonZest 7d ago
    It's a real example that's happened to me twice in the past year, so I'm not sure what to make of the idea that it's far away from how the real world works. I'm also not sure I understand what you're objecting to if we agree that mathematicians define their field. The source link is a declaration from 25 Fields Medallists with precisely that goal. They believe/define/declare that the type of AI-generated proofs we've seen are vibecoded throwaway PoCs; they feel that a well-structured proof must include factors such as "a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others", and the success criterion is not a true/false conclusion but rather "development and integration into the mathematical canon".
    - ndriscoll 7d ago
      Maybe your management has no idea what you work on. If so that's its own issue. Or maybe they do, and the person trying to take credit for more than they did just looks like an idiot. Like I said, I intentionally give throwaway PoC creation as a work item to people and it's fine. And if e.g. someone randomly made a drive-by PoC that proved that the approach I was exploring couldn't work and had some fundamental flaw, well, oddity of a random person doing it aside, I'd want to know that, and they'd deserve credit for saving us from a bad approach! My objection is characterizing things like AI slop proofs as not valuable. Obviously it's valuable to know that: 1. NS has solutions that blow up in finite time. 2. This fact is provable, and we have a proof. I don't think anyone anywhere is saying that these will replace mathematicians as they are now. I also think "a proper write-up, the isolation of new methods and ideas, and citing relevant previous work of others" is frankly not necessary or even desirable before we publish a computer generated result. We have a machine now that can spit out answers that we have good reason to believe are accurate, but they're perhaps inscrutable. There's no need to first decode the why and figure out proper attribution before simply posting the proof online. The proof itself does add value as it stands, even if it's not the ideal. Hoarding it until you can do a proper write-up would be silly.
  - qlte 7d ago
    Yes, mathematicians will clearly need to rewrite the qualifying criteria for prizes to better align with the actual goals and value they were hoping to get from a solved problem. The field as a whole assumed good faith actors and collaboration, not expecting a few trillion dollar companies to walk in and start turning in piles of Lean no human understands to be able to claim "first". This letter includes someone like Terrance Tao who publicly expressed a lot of optimism about AI for solving novel math like with the Erdos problems. It's not sour grapes but the first steps to define those new expectations for the future to reduce the perverse incentives. And yet, predictably, people are accusing him of "gatekeeping" and ignoring the arguments he has made here and elsewhere about the benefits vs. harm in different ways of using AI.
    - ndriscoll 7d ago
      I don't see turning in piles of Lean as bad-faith somehow. They were first, and they did prove the result (assuming no hidden exploit deep in the middle). The thing they produced is just different, and both giant raw proofs and distilled human-understandable proofs are valuable. Before we couldn't make giant raw proofs, so we didn't need to understand their place. Now we can. It makes sense to just incorporate that into what "math" is (at least until the machines are smarter and can make elegant proofs from the start).

SpicyLemonZest 7d ago

It's valuable for you, the person who's going to spend a bunch of deep design effort, to make POCs. Is it valuable for someone else to drive by, dump some POCs on your lap, and then leave you to do the deep design effort while they run away to study AI? If that person then runs around telling people that they're the real author of your project, because they generated the original POC, would you consider that an accurate assessment?

ndriscoll 7d ago
Your analogy is far enough away from the way that the real world works that I'm not sure that I can really even strain my experiences to fit within it. Sure, I guess that would be annoying? But mathematicians define their field. They're smart people. They're capable of recognizing when someone just did a vibecoded throwaway PoC and when someone has a well structured proof. Actually even before LLMs they'd publish new, clearer or more elegant proofs of old results. They can say that inscrutable proofs are exactly as valuable as they are, and that the first explanation people can actually understand carries its own prestige.
- SpicyLemonZest 7d ago
  It's a real example that's happened to me twice in the past year, so I'm not sure what to make of the idea that it's far away from how the real world works. I'm also not sure I understand what you're objecting to if we agree that mathematicians define their field. The source link is a declaration from 25 Fields Medallists with precisely that goal. They believe/define/declare that the type of AI-generated proofs we've seen are vibecoded throwaway PoCs; they feel that a well-structured proof must include factors such as "a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others", and the success criterion is not a true/false conclusion but rather "development and integration into the mathematical canon".
  - ndriscoll 7d ago
    Maybe your management has no idea what you work on. If so that's its own issue. Or maybe they do, and the person trying to take credit for more than they did just looks like an idiot. Like I said, I intentionally give throwaway PoC creation as a work item to people and it's fine. And if e.g. someone randomly made a drive-by PoC that proved that the approach I was exploring couldn't work and had some fundamental flaw, well, oddity of a random person doing it aside, I'd want to know that, and they'd deserve credit for saving us from a bad approach! My objection is characterizing things like AI slop proofs as not valuable. Obviously it's valuable to know that: 1. NS has solutions that blow up in finite time. 2. This fact is provable, and we have a proof. I don't think anyone anywhere is saying that these will replace mathematicians as they are now. I also think "a proper write-up, the isolation of new methods and ideas, and citing relevant previous work of others" is frankly not necessary or even desirable before we publish a computer generated result. We have a machine now that can spit out answers that we have good reason to believe are accurate, but they're perhaps inscrutable. There's no need to first decode the why and figure out proper attribution before simply posting the proof online. The proof itself does add value as it stands, even if it's not the ideal. Hoarding it until you can do a proper write-up would be silly.
- qlte 7d ago
  Yes, mathematicians will clearly need to rewrite the qualifying criteria for prizes to better align with the actual goals and value they were hoping to get from a solved problem. The field as a whole assumed good faith actors and collaboration, not expecting a few trillion dollar companies to walk in and start turning in piles of Lean no human understands to be able to claim "first". This letter includes someone like Terrance Tao who publicly expressed a lot of optimism about AI for solving novel math like with the Erdos problems. It's not sour grapes but the first steps to define those new expectations for the future to reduce the perverse incentives. And yet, predictably, people are accusing him of "gatekeeping" and ignoring the arguments he has made here and elsewhere about the benefits vs. harm in different ways of using AI.
  - ndriscoll 7d ago
    I don't see turning in piles of Lean as bad-faith somehow. They were first, and they did prove the result (assuming no hidden exploit deep in the middle). The thing they produced is just different, and both giant raw proofs and distilled human-understandable proofs are valuable. Before we couldn't make giant raw proofs, so we didn't need to understand their place. Now we can. It makes sense to just incorporate that into what "math" is (at least until the machines are smarter and can make elegant proofs from the start).