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)
>>8116742
(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
right?
>>8116744
>one can easily
why does math fag has to say that all the time. its a weird cultural thing you should stop doing. it gives no other meaning to the sentence other than some subtle bragging? wtf
>>8116742
>This is a simple experimental fact. 10^13 roots of the Riemann hypothesis have been already tested and it suffices for all practical applications.
The Riemann hypothesis has no counterexample, therefore it is true. Quod erat demonstrandum. Where's my million?
YOU ARE POSTING THIS SHIT EVERY 2 WEEKS, STOP BEING A FAGGOT
>>8117522
It's something that pseudo-intellectuals picked up from misunderstanding actual intellectuals. This type of language is often used tongue-in-cheek in papers. Unfortunately, it has spread to become a way of implying superiority.
Don'T need to solve these. These problems are bullshit because they require an infinite amount of work
>>8117542
I love this pasta
You solved these baby tier problems, good on you.
Now when will you try and solve the real grown men problems ?
>>8117542
They only failed in the past because people used fucking magnets but magnetic fields cannot do work, ergo the time to complete the proofing task equalized at exactly -1/12.
>>8117522
What "one can easily" or "it can easily be shown that" really means is
>This is a simple step I'm going to skip. Take a minute and think until you realize why it's so simple.
Of course there are faggots that say "it is trivial to show that" and you have to fill in three fucking pages. No defense for that.
>>8116742
All numbers are whole numbers, I've shown it for an infinite number of numbers.
Just show that PA is inconsistent and prove them all by contradiction.
