171–180 of 292 posts
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How would the mere knowledge that it holds, without any understanding why, be useful?
Can you explain to your cat how Amazon uses graph theory to deliver their packages of cat food? Is Amazon still delivering food to your cat? Humans don't need to understand what AI generates. We still can get the rewards.
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It could just as easily be the opposite: it could end up being far easier to reasonably direct and evaluate the research direction and output of AI systems than human mathematicians, who are forced to specialize over decades and essentially cannot pivot and often can't even meaningfully evaluate each other's work. Moreover, the disdain you have for low-value output in mathematics is not unique to you. Talented mathem…
Moreover, the disdain you have for low-value output in mathematics is not unique to you I didn't say anything about low-value output. No one actually knows the value of any particular piece of mathematics within that deluge. Mathematicians don't have a magical ability to differentiate high-value mathematics from low-value merely by reading paper titles and abstracts. The dirty secret in the mathematical world -- that…
False. You very plainly did. You simply used the term “junk” instead.
> That's baseless speculation.
It might be speculation (as is much of what you’re writing), but it’s not baseless. Obviously, it’s quite easy to direct AI agents, a single one of which can pivot across all of mathematics, unlike all human mathematicians.
> All indications so far are that LLMs produce proofs far longer and far more complicated than humans are capable of, such that only machines can check the proofs for validity.
I’m unaware of any clear evidence of this. Hence, it appears to be baseless speculation.
> Digesting them into a human-readable interpretation of the results is an open problem.
I’m unaware of any clear evidence of this. Hence, it appears to be baseless speculation. Moreover, and more importantly, to my knowledge there hasn’t been any meaningful result in AI mathematics so far that has posed any kind of blocking issue on understanding it yet.
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Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.
If a magic oracle tells you p=np, that's useless. How would that change anything?
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.
Earlier quoted context omitted.
How would the mere knowledge that it holds, without any understanding why, be useful?
Can you explain to your cat how Amazon uses graph theory to deliver their packages of cat food? Is Amazon still delivering food to your cat? Humans don't need to understand what AI generates. We still can get the rewards.
Earlier quoted context omitted.
Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.
A proof by contradiction that p = np is of no use to anyone, given that it wouldn't help you find any polynomial time algorithms for np-hard problems.
You would need an algorithm that finds solutions, not just a proof they exist. So the value here would almost entirely come from how you proved p = np, since that proof will probably be the first step towards finding the polynomial solutions. But if humans don't understand it good luck finding any.
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If a magic oracle tells you p=np, that's useless. How would that change anything?
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…
For what? Which product becomes better if it is correct?
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If a magic oracle tells you p=np, that's useless. How would that change anything?
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…
We all believe it. It's a magic oracle. Now what?
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Can you explain to your cat how Amazon uses graph theory to deliver their packages of cat food? Is Amazon still delivering food to your cat? Humans don't need to understand what AI generates. We still can get the rewards.
p = np doesn't produce any value though, the stuff you learn solving it might but the fact that they are the same wouldn't be valuable at all.
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Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.
A proof by contradiction that p = np is of no use to anyone, given that it wouldn't help you find any polynomial time algorithms for np-hard problems.
We only compute with two kinds of things:
- small data; or,
- extremely lower power and coefficient algorithms
We lack the power to, eg, use a quintic algorithm in anything but nearly trivial cases.
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I don't think this is a valid counterpoint at all. Math is cooperative, and comprehension is the point : the proof has value exactly because (and only to that extent) it empowers humans to understand an abstract truth. Chess is competitive: the memorized line has value because it makes you incrementally more likely to defeat your opponent.
Math that humans don't understand but nonetheless allows AI systems to develop breakthroughs in various fields of science, technology, physics, engineering, medicine, etc., would have great value to humanity even if it doesn't help humans understand abstract truth at all. Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it, it initially seemed useless, the…
When you have full AGI of course you no longer need humans to understand math.
> Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it
Developing multivariable calculus requires much more than just solving problems though, it requires defining an entirely new system and space. That is not the situation mathematicians face today, modern AI cannot do that.
When talking about mathematicians and AI don't use fictive examples, we can look at what AI can do today and extrapolate that they can do more of that tomorrow, that is what we have to work with.
In the case you posit where AGI exists there is no reason to even discuss what is left for humans to do, since AGI is defined as when humans are no longer needed for anything, the AGI can do every bit of thinking humans can.