4 ms·

If it’s an oracle and we know it’s an oracle then it’s not useless. Humans make mistake and there are examples of published results that were widely believed

by czgov 1mo ago

If it’s an oracle and we know it’s an oracle then it’s not useless. Humans make mistake and there are examples of published results that were widely believed to be correct by experts that later proved to be wrong. Why do you think human verified proofs are better than machine verified proofs? Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form: If RH is correct then A. It would be very useful to have an oracle tells us whether or not RH is correct.

Jensson 1mo ago
> It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?
- czgov 1mo ago
  You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.
  - deleted 1mo ago
    [deleted]
  - Jensson 1mo ago
    The whole point why anyone cares about these proofs is that the things we learn as we make the proof might add value, proving p = np itself isn't interesting, that knowledge has no application and therefore no value in itself. I have published mathematics so I do value knowledge, but for most of mathematics the value of the knowledge isn't the thing you try to prove it is all the things you learn as you try to prove it. p = np is one such thing. So the whole interesting bit about it is the proof, not the fact.
    - czgov 1mo ago
      You are wrong as far as most mathematicians believe. The fact is important. The proof of the fundamental theorem of algebra is interesting and important but the theorem itself is also important. For what? Which product becomes better if it is correct? This sentiment is anti-thetical to the whole point of pure math and theoretical science. No product became better when Euler proved the fundamental theorem of algebra.
  - customguy 1mo ago
    Someone claimed it would be "useful", without saying what for. Hence the questions "what for?". To try to shame people for that question in the name of science of all things is wild.
    - czgov 1mo ago
      Which product becomes better if it is correct? Tying the worthiness of theoretical knowledge to the whether or not it improves a product is asinine in my opinion.
      - customguy 1mo ago
        I generally[0] agree, but IMO that should be taken up with https://news.ycombinator.com/item?id=49369458 https://news.ycombinator.com/item?id=49369458 more than with people who ask for examples for that claim. [0] and am only adding that "generally" because I can think of examples where I'd disagree, e.g. a kid that wants to count all stars in the night sky before it has dinner would just starve and then not be able to count stars, either.
HWR_14 1mo ago
I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?
- czgov 1mo ago
  If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.
  - mahdi7d1 1mo ago
    In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?
    - czgov 1mo ago
      There is no actual oracle. In this discussion oracle means Lean.
  - saithound 1mo ago
    > If it is known that A is provably true then one can study the consequences of A being true But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that. Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.
    - czgov 1mo ago
      Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. In the present discussion it’s not about letting me do something I can’t do now but about whether or not the endeavor is worthwhile. A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.

by czgov 1mo ago

Jensson 1mo ago

> It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?

czgov 1mo ago
You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.
- deleted 1mo ago
  [deleted]
- Jensson 1mo ago
  The whole point why anyone cares about these proofs is that the things we learn as we make the proof might add value, proving p = np itself isn't interesting, that knowledge has no application and therefore no value in itself. I have published mathematics so I do value knowledge, but for most of mathematics the value of the knowledge isn't the thing you try to prove it is all the things you learn as you try to prove it. p = np is one such thing. So the whole interesting bit about it is the proof, not the fact.
  - czgov 1mo ago
    You are wrong as far as most mathematicians believe. The fact is important. The proof of the fundamental theorem of algebra is interesting and important but the theorem itself is also important. For what? Which product becomes better if it is correct? This sentiment is anti-thetical to the whole point of pure math and theoretical science. No product became better when Euler proved the fundamental theorem of algebra.
- customguy 1mo ago
  Someone claimed it would be "useful", without saying what for. Hence the questions "what for?". To try to shame people for that question in the name of science of all things is wild.
  - czgov 1mo ago
    Which product becomes better if it is correct? Tying the worthiness of theoretical knowledge to the whether or not it improves a product is asinine in my opinion.
    - customguy 1mo ago
      I generally[0] agree, but IMO that should be taken up with https://news.ycombinator.com/item?id=49369458 https://news.ycombinator.com/item?id=49369458 more than with people who ask for examples for that claim. [0] and am only adding that "generally" because I can think of examples where I'd disagree, e.g. a kid that wants to count all stars in the night sky before it has dinner would just starve and then not be able to count stars, either.

HWR_14 1mo ago

I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?

czgov 1mo ago
If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.
- mahdi7d1 1mo ago
  In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?
  - czgov 1mo ago
    There is no actual oracle. In this discussion oracle means Lean.
- saithound 1mo ago
  > If it is known that A is provably true then one can study the consequences of A being true But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that. Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.
  - czgov 1mo ago
    Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. In the present discussion it’s not about letting me do something I can’t do now but about whether or not the endeavor is worthwhile. A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.