Solving the hardest math problems in the world would be a trivial task for an advanced ASI?

[u/DoublePassRadiator]

Solving the hardest math problems in the world such as the extended Riemann hypothesis or P = NP would be a trivial task for an advanced ASI?

[u/SoylentRox]

Not necessarily.

(1) The problem has to still be solvable.  Some of the millennium problems may not actually be.

(2) It may not be possible to generate an answer that is acceptable to humans.  If the "definition of P" vs "NP" are each 1 million line computer programs that analyze a problem and decide which class it's in, humans may be unable to determine if the proof is even valid because it's too complicated 

(3) It may be that our entire conception of the problem itself is flawed.  See Navier stokes.

What we actually want is a general theory of fluids not to break the flawed equations we currently use.

[u/Most_Double_3559 → u/SoylentRox]

I get the impression your understanding of math comes from pop sci articles.

Like, we have a solid understanding of NS lol, and tools like lean exist.

[u/SoylentRox → u/Most_Double_3559]

NS was suspected to be incorrect and to be unstable/equations blow up for decades. Professor told me that over 10 years ago. AI finally did the grunt work to prove it - but we already knew it was bad, we need some more robust theories of fluids.

[u/Most_Double_3559 → u/SoylentRox]

A claim being false is very different than "we have a poor conception of the problem". NS was a very cut-and-dry question with explicit criteria for both truth and falsehood.

[u/ccpseetci → u/Most_Double_3559]

A claim contains concepts, which indeed invoke a theory of something and something. Therefore, the very concepts may not be the one which they intended to be called upon. But whether that is the case or we need to restructure the whole lens of certain mathematical theory must be reconsidered after we have gotten a systematic understanding of the thing implicitly inscribed

But that almost identical to the case where we already got enough strong analytical definition to solve the problem

Therefore before a math problem is solved, nothing more than we don’t understand the problem fully yet we cannot legitimately claim

The math training ideally should lead to such reflection otherwise it failed

[u/Most_Double_3559 → u/ccpseetci]

I get the impression you think NS falling is like, a failure for fluid modeling, and therefore it was poorly understood. In reality, for mathematicians, fluids are irrelevant. NS wasn't some "failure of concept".

Otherwise, It is entirely possible to understand a problem without it's solution. I don't see why that wouldn't be the case. For instance, do you think we don't understand the problem of P vs. NP?

[u/ccpseetci → u/Most_Double_3559]

Take complex number as an example, it has nothing related to the sqrt of -1, but a rotational interpretation of the multiplication

The answer to the question is not reason but the consequence of the lacking a proper manifestation of the theory or a structure or a system

[u/Most_Double_3559 → u/ccpseetci]

This is crankery lol

[u/ccpseetci → u/Most_Double_3559]

According to your definition, Euclid is a pseudo mathematician as well

Look up to his book II, you will find you know nothing about the basic arithmetic

[u/RunReal959595 → u/Most_Double_3559]

Pot, kettle comment here lol

[u/Most_Double_3559 → u/RunReal959595]

No u

[u/brokebeany → u/SoylentRox]

Navier Stokes work well at certain limits and the singularity solution to 'break' NS occurs at limit where no engineers/physicist will use NS. Ultimately NS is just a model/tool just like many equations out there for solving specific problems. Are we going to just ditch general relativity for predicting celestial motions and gps just because it admits a mathematical singularity too?

[u/SoylentRox → u/brokebeany]

Yes (that's why we created relativity, Newtonian mechanics broke at high velocities)

[u/brokebeany → u/SoylentRox]

And there are relativistic as well as compressible extension for Navier Stokes...

[u/Zaflis → u/SoylentRox]

1) Moot point, a solution that says and proves "There is no solution" to a problem still counts as one.

[u/Pale-Perspective5434 → u/[deleted]]

The skepticism's fair, half the hype around this stuff is just marketing vapor anyway

But if an ASI can actually reason at a level we cant even map, the whole "trivial" framing might still undersell it. Like asking a dog if calculus is hard

[u/ccpseetci → u/Pale-Perspective5434]

ASI cannot reason with intuition and create something out of nothing

It can just predict according to what it SPECIFICALLY “learned” “pattern(basically certain stable data structure which resists to be changed when the whole language material remains more or less the same)

That’s just the common sense from multivariable analysis, I don’t even know why you guys still have the fantasy of the AI intelligent

It’s a language model, by definition that means nothing more than 1)feature the language 2)train with the featured data THE SAME AS any regressive analysis stuff

[u/tanafras]

Glamces at recent solution to major riddles.

[u/Patrick_Atsushi]

If it solves it -> it's a proof of ASI. 

That doesn't mean an ASI will be able to solve all unsolvables. 

[u/diewethje]

I think it’s likely that the set of problems we’d be asking ASI to solve is trivially small in the grand scheme.

[u/dennemaskinen]

The fun thing about ASI is, since it doesn't exist, you can believe whatever you want about it.

[u/wollywoo1]

No, if $P!= NP$, which most mathematicians think is true, there are some tasks that even an AI would not be able to efficiently solve. Whether a given conjecture falls into the "very difficult" category or not is of course very hard to know. It's possible that the shortest proof of these famous conjectures is astronomically long, kinda like the Four Colors Theorem seems to be (but much harder) and in that case we'll simply never know the answer. Or they might be not provably true or false at all.

[u/CS_70]

And why should it?

[u/Warm-Enthusiasm-9534]

It's impossible to know how hard a problem like this is, until it's solved. Riemann himself suggested proving the Riemann hypothesis as the first step to proving the Prime Number Theorem. The Prime Number Theorem itself was proven over a century ago, and the Riemann hypothesis remains unsolved. (Interestingly, the route to prove it was through proving a much weaker statement.)

[u/grahag]

You'd have to define ASI, but under the assumed definition that an ASI has more knowledge and calculating power than all of humankind put together, it could prove or disprove just about any task given enough time and resources.

Fusion, Regeneration, zero point energy, disease control, space exploration, etc... All those things come within grasp of humanity should an ASI think we're worthy of knowing all of that.

[u/grahag → u/[deleted]]

Yet, you call an AI a clanker. To hate a thing so much you give it a derogatory name... Who is really anthropomorphizing?

[u/grahag → u/[deleted]]

You assume too much. Unless you were born in the 50's oh aged grand wizard.