Several prominent tech figures have been claiming the Hodge Conjecture (another Millennium problem) has been solved. How big is this?
hodge was suppose to be one of the easier ones
>>17051773Depends on what the solution is.Proof the Hodge Conjecture is true? Very significant in algebraic geometry.A counterexample? Not particularly surprising, probably just indicates the statement of the Hodge conjecture needs to be restricted more.
>>17051807If it's true no way AI proved it.
Fuck no... not the hodge twins conjecture wtf brossss
>>17051773When they solving PNP
>>17051903You looking to make some career in math mayne?Dat's good, dats real goood
>>17051924they did, and they're pretty cheap these days
>>17051929>cheap> $1 for high frequency high power
Announce it, dammit!
>>17051773
I wish it was the Riemann Hypothesis instead so that mathematicians would really lose their minds because they've been hyping up this problem as the hardest thing ever.
>>17052025>Riemann HypothesisIt is by far the most useful conjecture. But the hardest one is collatz conjecture.Mathfags did everything to prove it with zero progress.
>>17051773Not very. All those math problems are useless.
>>17052036>most useful conjectureno it is not. Yang Mill's is way more important and has deep implications for particle physics and if P=NP is true it would have the biggest implications. Riemman hypothesis would open new research avenues in number theory but number theory is mostly worthless
what are the actual real world benefits of proving them?
>>17052040>no it is not.The whole cryptography literally depends on it being true dumbass.
>>17052040>if P=NP is truedon't we all sort of "know" it's not true, and we're just waiting for someone to actually prove it? I doubt there's many people who actually understand what both versions mean and imply, and really think P=NP lollike, if you were to bet on it...
>>17052040>Yang Mill's is way more important and has deep implications for particle physicsnta but no it's not. Physicists just consider it to be true already. They're not waiting for any proof. Ultimately, none of these problems are useful except to mathematics itself.
>>17052040>and if P=NP is true it would have the biggest implications.There is a zero percent chance that P equals NPliterally nothing suggests that, not even a little.
>>17052042funny that cryptography also depends on p=np not being true, and not just that, but any other way of coming up with cryptography besides prime numbers which the riemann hypothesis seems overspecialized for
>>17052040I find it so funny how this board underestimate P=NP implication. It's the end to all. And I mean to everyone be stemcel or humanitycel or neetcuck.
>>17052053care to explain for someone with brain damage? :(
>>17052048>>17052053P != NP, so no need to dream about things that doesn't exist.
>>17052054If P=NP computers can basically do magic. They do many magical things but this is like solving all problems we have at once.
>>17052053>>17052054It's not the end to anything. Even if every NP can be solved in polynomial time, that says nothing about how efficiently it can be done.
>>17052054It's when machines conquer luck
>>17052057>galactic algorithm copelmao everytime
>>17051792>basic arithmetic>high school math>Math Olympiad problems>toy open problems (Erdos, etc)>"simple" Millenium Prize problemsYou are here>rest of the Millenium Prize problems>Collatz>Hard problem of consciousness (solved by removing any potentially conscious beings from the universe)
>>17052056I read a bit tell me if I got itthe difficulty of testing a solution implies the difficulty of finding the solution?so if P = NP easy testing = easy finding? (somehow)but if not then they are not relatedIt's like trying to find a general algorithm for the ontology of the word problem itself
>>17052053>I find it so funny how this board underestimate P=NP implicationIf there were a way to solve 3SAT in polynomial time, we probably would have found it already, if not humans, then AI, especially given how strong it has become at competitive programming(a year ago). You can brute-force the shit out of it.The fact that nothing has been found suggests two things: either 3SAT is solvable in polynomial time, but the algorithm is stupidly complicated and probably has some ridiculous complexity like O(n^10) or worse, making it practically useless anyway, or 3SAT simply isn’t in P.
>>17052059It's the next most likely thing after P != NP.
If Hodge is solved, doesn't that mean we can solve for the shape of the universe?
>>17052073Stop trying to ragebait me. It's working.
>>17051773I'm 100% sure that it wasn't solved.
>>17052040Funny when you learn Gödel was a P=NP believer.
>>17052061>Hard problem of consciousnessneurofag here. this isnt real. its some philosophy bunk.
>>17052040>>17052045The Yang-Mills problem is not just the mass gap question itself. The problem requires the actual construction of a mathematically rigorous non-perturbative quantum Yang-Mills theory.The kind of construction would definitely impact physics.
>>17052165so tired of the philosocuck slop. they repeat a bunch of old nonsense, and in reality almost all of them are zealots trying to pass as intellectuals
>>17052042it doesn't you redditard brainleteer
>>17052168Making quantum field theories rigorous is irrelevant for the same reason getting a singularity from Navier-Stokes is irrelevant. Both are approximations to something deeper; it's just that in particle physics nobody knows what the deeper theory is yet.
>>17052201Having a proper formulation of a non-perturbative quantum Yang-Mills theory is definitely not irrelevant.
>>17051792kek, i love how we're now at the point where people are dismissing it as the "easy millennium problems"
>>17051773this guy isn't prominent in math or tech he just posts AI alarmist engagement bait on twitter all day long.
>>17052183reddit derangement syndrome
>>17052038
>>17052183
>>17052315i was also sure the previous leaks about n-s were baitnow i'm not so sure
p=np is factually irrelevant."oh yes, p=np and the lowest p is O(N^tree(3))"vs"p isn't np"vs"Taylor's theorem states that p=np for finite values, we only care about asymptotics if the asymptote is reached this millennium"
>>17052168physics is not just engineering
>>17052337they started work in response to the fake rumors about it being solved
