Millenium Prize Problems

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Anonymous

Millenium Prize Problems 2016-02-07 09:01:38 Post No. 7840297

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Millenium Prize Problems 2016-02-07 09:01:38 Post No. 7840297

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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. [math] \displaystyle P=NP [/math]

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 [math] \displaystyle P \neq NP [/math]

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. [math] \displaystyle 10^{13} [/math] 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, [math] \displaystyle 10^5 [/math] 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

[math] \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) [/math]

one can easily find at leat one closed-form solution applying the bubble integral. In the equation, [math] \displaystyle L [/math] 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?

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>>7840390

4chan /b/

They love this stuff

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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

Ok, please do it then.

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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 [math]s = 1 + i·10^{12893}[/math]. 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

>this thread again

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.

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