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)
(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
notice me senpai
Amazing. Truly amazing.
What if N=1? Then P=NP
Checkmate losers
>tfw i'll never be able to understand this post
This is pasta
>>8483074
Prooves
>>8482964
You better be millionaire by now, where is the tv report with your exploits?
I don't understand a thing, but with this we are supposed to make cooler things like proper a.i girlfriends and more lethal drones, correct?
Proving Riemann hypothesis by proposing a statistical test and saying that 10^13 roots suffices.
Truly Gauss is reincarnated