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Millenium Prize Problems
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You are currently reading a thread in /sci/ - Science & Math

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ITT I will try to solve (and in fact solve) all the Millennium Prize Problems one by one. I will do so by a new proof technique that has been proved to be quite powerful. It combined homothopy theory with algebraic geometry. Having said that, the proof technique itself is elementary though. So, let's go ahead.

1. $\displaystyle P=NP$

By definition, polynomila algorithms admit decomposition in chains of smaller polynomial algorithms. Consequently, polynomial time algorithms do not solve problems where blocks, whoose order is the same as the underlying problem, require simultaneous resolution. Thus, in fact $\displaystyle P \neq NP$

2. Hodge conjecture

Assuming that if a compact Kähler mainfold is complex-analytically rigid, the area-minimizing subvarieties approach complex analytic subvarieties. The set of singularities of an area-minimizng flux is zero in measure. The rest it left to the reader as an easy routine excersize.

3. Riemann hypothesis

This is a simple experimental fact. $\displaystyle 10^{13}$ roots of the Riemann hypothesis have been already tested and it suffices for all practical applications. In fact, one state a suitable statistical hypothesis and check it on the sample of, say, $\displaystyle 10^5$ roots.

4. Yang–Mills existence and mass gap

Well, discrete infinite bosonic energy-mass spectrum of gauge bosons under Gelfand nuclear triples admits non-perturbative quantization of Yang-Mills fields whence the gauge-invariant quantum spectrum is bounded below. A particular consequence is the existence of the mass gap.

5. Navier–Stokes existence and smoothness

(To be continued)
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>>7840297
(Cont.)

I haven't worked this one in such detail, but observing that

$\displaystyle \| L (u, v) \| ^ 2 = \sum_{n \ge 25} u ^ 2_ {2n} v ^ 2_ {2n +1} / n ^ 2 \le C\|(u_n/\sqrt n)\|_4^2 \|(v_n/\sqrt n)\|_4^2 \le C\|(u_n/\sqrt n)\|_2^2 \|(v_n/\sqrt n)\|_2^2 = C \left (\sum u ^ 2_ {n} / n \right) \left (\sum v ^ 2_ {n} / n \right)$

one can easily find at leat one closed-form solution applying the bubble integral. In the equation, $\displaystyle L$ is a bilinear operator.

6. Birch and Swinnerton-Dyer conjecture

The problem with former attempts has been in the way elliptic curves have been dealt with. But this really admits a proof with a computer by checking the (finitely many) categories of curves.

I also have a simpler than Perelman's proof of the Poincare conjecture, but it's not worth the prize anymore
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Where should I best publish it?
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>>7840390
>Where should I best publish it?
Reddit
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>>7840390
4chan /b/

They love this stuff
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>>7840399
>>7840404
Seems like you don't take it seriously enough.
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>>7840451
no seriously, go publish it.

Good luck getting totally wrecked in peer review.
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>>7840466
Peer review is a joke
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>>7840297
just by reading the text on the riemann hypothesis: you're not a mathematician and don't have any idea of what you're talking about.

We don't care about practical applications. We don't care if it's been proved for a large count of numbers. We care if its true or not, because if it's just "more or less" true we won't be able to build more knowledge on it and we would need to check if new theorems are true, somewhat true or false.

And, just so you know, it can be false for any number. See some examples of conjetures disproved by large numbers: http://math.stackexchange.com/questions/514/conjectures-that-have-been-disproved-with-extremely-large-counterexamples It can happen again.
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>>7840467
this

I simply go though this. I got connections.
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>>7840476
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>>7840470
> What is hypothesis testing
> Hurr durr it's not math
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>>7840480
A counter example disproves the conjeture. An example does not prove it.
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>>7840482
Such a counterexample would be meaningless for any sane application.
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>>7840484
sane application such as?
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>>7840488
Any theorem that assumes Riemann hypothesis.
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>>7840490

You are not a mathematician and don't know math. We are not physicists. We do no not want things that are "true enough". It's either true or false.

If the conjeture is false, you can't trust any theorem based on it. False statements allow to derive complete and utter crap that can't be trusted.
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>>7840493
Hypothesis testing is rigorous math.
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>>7840496
this
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>>7840496
Say that the Riemann conjeture is true except for $s = 1 + i·10^{12893}$. You assumed it was true, but it isn't. So I can say that as s is a zero of the zeta function, its real part is 1/2. However, the real part of s is 1. Thus, 1 = 1/2. This is obviously false.

This is what I'm saying. Assuming false statements destroys math. Hypothesis testing is for statistical inference, not for proofs. In this case, statistically it is an insignificant zero, but it's still not enough.
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>>7840503
Except that you won't find such an example.
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>>7840512
Except that you may
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>>7840512
prove it
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>>7840516
I bet you can't. And it won't be possible within our lifetime. And the lifetime of many next generations until the mankind ends. So there is no harm to make the said assumption. But yet again, hypothesis testing has already done the job.
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>>7840519
Except that you may
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>>7840525
Prove it.
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>>7840527
Burden of proof
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>>7840516
Except that there's no way you could compute numbers of such magnitude. Never in this known Universe.
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>>7840529
I provided a proof. Good luck arguing that hypothesis testing isn't rigorous.
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>>7840530
Prove it
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>>7840537
The numbers that have been checked are already far away from the total amount of particles in the Observable Universe.
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>>7840533
Hypothesis =/= proof

Hypothesis is the thing that has to be proved
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>>7840539
And if the universe is infinite?
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>>7840542
Observable Universe is not. The rest doesn't matter.
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>>7840546
But the observable is always growing.
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>>7840547
Wow, dude. Now, you really stepped into a shitpile. The cosmic event horizon has a finite asymptotic limit in proper units, you dumbass.
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>>7840470
nigga you dumb as fuck, yo readin comprehension is a fuckin joke , yo
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>36 replies
>8 posters
OP has been pretending to troll himself hasn't he
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>>7840580
> Ignoring proofs, you don't comprehend, by pointing at virtual trolls
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>>7840298
Which categories are you talking abt? Because last time I checked there were infinitely many non-isomorphic number fields.
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>>ITT : b8 so hard
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>>7840616
I don't get it. What it the actual bait in this story?
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>>7840496
No, it's actually not. I'm not the retarded op, but hypothesis testing is the exact opposite of rigorous math. Rigorous math is built off of proofs. Hypothesis testing is just used to see if it's worth the effort of attempting a formal proof.
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>>7840297
report
sage
hide
ignore
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>>7840915
What's the problem, butthurt kid?
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>>7840902
Not OP, but hypthesis testing is based on well-founded probability theory.
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Suddenly, sci went into philosophy.
Difference between math and science:

Science use induction:
Hypothesis: If I snap my hand the light's turn off, and if i snap my hand again it will turn on again. THus the snapping of my hand has a direct impact on the status of the light (on/off).
The hypothesis is the implication.

If the hypothesis is tested 10^29 times and for every test the prediction was true we, scientist say that the implication is true.

The mathematician does not use induction.
The mathematician has created a system and inside the system there are axioms that with logical reasoning shows that an implication is true. Meaning that every proof can be tracaebacked to the axioms. In order to use ab = 0 => a or b is zero in a proof you have to prove it first, every proof is built through logical reasoning successively which also makes the system consisten. That is why hypothesis testing is fragile.
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>>7840519
how fucking autistic are you
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P=NP
P/P=NP/P provided P!=0
N=1

Or
P=0 and N can be any number
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>>7842431
Wrong.

if N = 1 or P = 0, then P = NP
if N != 1 and P != 0, then P != NP
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>>7842449
But you're going to share credit, right?
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>>7841261
It doesn't work if you want to prove mathematical statements.