What is the spookiest math you know? Pic related

-1/12

1=2

>>8132607

statistics math is very spooky

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>>8132664
Oh shit, if only you knew

>>8132716
/thread

>>8132607
>mfw no mention of spectral theory

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>>8132792
>mfw you don't have a face

0.999...=1

[math]sin\left(\frac{1}{2} arcsin \left(2x-1 \right)-\frac{\pi}{4} \right)^2 = x[/math]

>>8132811
wew

-1/11.999...= infinity

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>>8132607

>>8132944
kek

>>8132607
[eqn]\oint_\gamma f(z)\, dz =
2\pi i \sum_{k=1}^n \,\mathrm{I}(\gamma, a_k)
\,\mathrm{Res}( f, a_k ) [/eqn]

Anything with Calculus ever

>>8132607
[math] \int _{\Omega} d \omega = \int _{\partial \Omega} \omega [/math]
The integral of the exterior derivative of a differential form evaluated on the the whole domain is the same as integrating the differential form over the boundary.

This implies all of the classical results in vector calculus such as the theorems of Stokes, Green, and the divergence thoerem.
The fundamental theorem of calculus is also a trivial corollary.

Approximating functions with orthonormal polynomial bases

>>8132607
1+1=3

>>8133001
nice

Spooky Snakes
[math] \begin{array}{*{20}{c}}
{}&{}&{\ker \left( {A \to A'} \right)}& \to &{\ker \left( {B \to B'} \right)}& \to &{\ker \left( {C \to C'} \right)}&{}&{} \\
{}&{}& \downarrow &{}& \downarrow &{}& \downarrow &{}&{} \\
{}&{}&A& \to &B& \to &C& \to &0 \\
{}&{}& \downarrow &{}& \downarrow &{}& \downarrow &{}&{} \\
0& \to &{A'}& \to &{B'}& \to &{C'}&{}&{} \\
{}&{}& \downarrow &{}& \downarrow &{}& \downarrow &{}&{} \\
{}&{}&{\operatorname{coker} \left( {A \to A'} \right)}& \to &{\operatorname{coker} \left( {B \to B'} \right)}& \to &{\operatorname{coker} \left( {C \to C'} \right)}&{}&{}
\end{array}[/math]

>>8133810
[math]\ker \left( {C \to C'} \right)\xrightarrow{{SpookySnake}}\operatorname{coker} \left( {A \to A'} \right)[/math]

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>>8133810
Keep chasing your diagrams pleb

>>8133822
Not him but that's not spooky at all, non algebraic numbers have plenty of weird representations.

The thing with [math]\pi[/math] is that you always have to remember it's relation with [math]e[/math].

Once you see that, and assuming you know how to arrive at [math]e[/math], your series doesn't seem spooky anymore

>>8132851
Kek

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>>8132607
The Ramanujan Modular formula is spooky, because Ramanujan himself said that a Hindu god of mathematics had appeared to him in a dream, telling him this identity. Even though you can prove it posteriori, I suspect that nobody will ever derive it on their free time without knowledge about it.

discrepancy theory

sometimes i can't get any sleep because thinking about it is so fucking terrifying

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>>8132607

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>mfw I don't understand any of thisshit

>>8134804
Can someone explain?

I guess H is the schrödinger hamiltonian and it has something to do with point particle angular momentum but google isn't giving me anything useful

>>8134804
Can you put this in the form of a frog meme?

>>8132792
Tell me all you know about spectral theory. Why do you consider it spooky?

>>8133389
Holy sh that's really cool. But could I just ask, at the risk of sounding stupid, in what context would you need to define an integrand's boundaries in terms of another function?

>>8133389
>The fundamental theorem of calculus is also a trivial corollary.

But since you need the fundamental theorem of calculus to prove Stoke's theorem (for differential forms) thats kind of circular, isn't it?

>>8134804
If this is real math, this is the spookiest math.

>>8134804
looks like qft to me, fuck qft

>>8135408
Khan Academy has a great series of videos on that

>>8135408
that's phd level triple integral stuff, anon

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>>8135443
It is just QFT

>>8132716
>>8132784
>implying statistics is math.

Liouville's theorem is pretty terrifying.

>>8136645
Fuck off undergrad

>>8135393
>Why do you consider it spooky?
>spectral
> adjective 1. of or pertaining to a spectre; ghostly; phantom.
How is that not the spookiest!?

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hodge theater construction

For some reason whenever people draw `handles' on a space to show how you can change the homology, the pictures of the handles are unsettling to me

https://www.youtube.com/watch?v=kxuU8jYkA1k
this. someone explain this shit to me already.

>>8135408
Basically it's a correlation which allows you to, by evaluatng the easiest one, also evaluates the other one

Spectral Theorem.

>>8135328

As far as I know, that looks like QFT applied to condensed matter systems. The first term in the hamiltonian is the typical energy per particle and the second term is the interaction between two particles. So this can be the Hamiltonian for a two electron system.

>>8132607
A bunch of formulas by Ramanujan are pretty spooky
[math] \frac{1}{1+\frac{e^{-2\pi}}{1+\frac{e^{-4\pi}}{1+\frac{e^{-6\pi}}{1+\cdots}}%
}}=\left( \sqrt{\frac{5+\sqrt{5}}{2}}-\frac{\sqrt{5}+1}{2}\right)
\sqrt[5]{e^{2\pi}}[/math]

[math]e=mc^{2}[/math]
how is that not spooky?

>>8137246
No-one understood continued fractions better than Ramanujan.

Once, a roommate of his, P. C. Mahalanobis, posed the following problem: "Imagine that you are on a street with houses marked [math]1[/math] through [math]n[/math]. There is a house in between, [math]x[/math], such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. If [math]n[/math] is between 50 and 500, what are [math]n[/math] and [math]x[/math]?" This is a bivariate problem with multiple solutions. Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction. The unusual part was that it was the solution to the whole class of problems. Mahalanobis was astounded and asked how he did it. "It is simple. The minute I heard the problem, I knew that the answer was a continued fraction. Which continued fraction, I asked myself. Then the answer came to my mind", Ramanujan replied.

Why is everyone on this board so afraid of math?

>>8137275
>not using the nondimensionalized form using planck units

The formula is [math]E = m[/math].

https://en.wikipedia.org/wiki/Planck_units#List_of_physical_equations

>>8137280
When the universe was 1 planck time old, it had a diameter of 1 planck length and a temperature of 1 planck temperature. A substance of 1 planck temperature radiates light that has a wavelength of 1 planck length (and light has a planck speed of 1).

>>8135534
Funny thing is, these ballon-lines look just like the curve for the mandelbrot when you plot |z(n)| = |z(0)|

>>8137283
idk about that, where did you read it

>>8137323
From a few wiki pages on planck units.
A sentence from https://en.wikipedia.org/wiki/Planck_units#Derived_units, a sentence from https://en.wikipedia.org/wiki/Planck_temperature#Significance, a calculation of what should be the planck speed together with an online confirmation.

Nondimensionalization using planck units makes things so elegant.

>>8137276
I solved the first part quickly:
we have
[eqn]1, 2, ..., x, ..., n = n \times (n+1)/2[/eqn]
since the sum from 1 to x is equal to the sum from x to n, then
[eqn]2 \times x = n \times (n+1) / 2
\implies x = n \times (n+1) / 4
[/eqn]
now, I have no clue how to continue from here. guess I lost my math skills.

>>8137352
The point is that he had such an intuitive understanding of continued fractions that he somehow solved it not your way at all, but by giving a continued fraction (who the hell thinks like that?) that was furthermore the solution to the whole class of problems. His mind was of a different realm.

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This counts as math right? For those who don't know what's going on:
This calculates inverse square root without use of division or multiplication. It does so using that hex number. Some serious crazy black magic shit.

>>8137666
it does use multiplication.

>>8137689
It does, but that's not what really calculates the inverse square root. It's the bit shifting that's important; which is done without any division or multiplication.

>>8136856
WHAT THE FUCK

Is this what mochizuki does all day!?!?!?!1

>>8137359
yeah, I understand that, and, indeed, that's the thing that I'm lacking. I need to find a way to generalize the solution...

>>8132811
1-x bro

>>8133389
I agree wholeheartedly. I don't think it's spooky, but it certainly is the most beautiful.

>>8137279
it's fucking impossible to do yet it appears to be the key to everything.

we fear it like some sort of god.

>>8133001
i remember using this a whole lot when first introduced to it, and it almost feels like cheating due to how easy some integrals become. Recently i had a problem where i though "ha, just integrate over an infinite halfcircle, there is one pole inside that i need the residium of..."
but how the fuck do you calculate the residuum? wiki says its the (-1)st coefficient of the laurent series, but it seems tedious to compute

how do i quickly figure out the residues of a function? lets say the poles of 1/(1+x^n)

>>8136645
Nice meme :^)

>>8132607
1/0

Also infinity is pretty spooky.

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>>8138799
le Cauchy

>>8138179
>it's fucking impossible to do yet it appears to be the key to everything.

Once someone quoted something in that very sense, but I can't remember who said it.

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>>8137739

What the actual fuck

>>8134804
This kind of solid state physics is the best. It is just beautiful. I wish I could do something like this and not fuck around with goddamn DFT...

>>8136856
>Vortex mathematics
turned it off immediately

the solutions for 2(x)^2 = x always fucked with me

>>8139028
Can you put the parentheses better?

>>8137666
that's some spoopy C alright
I don't understand jack shit.
Like that
i = * (long *) &y;
da fuq? what ever does interpreting floating point representation as integer do?
i = 0xdeadbeef - (i >> 1);
looks like a really arbitrary number wtf is this
when will it stop

>>8136856
Literal autism.

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>>8134804
qft theory indeed, H is the hamiltonian written in the second quantization scheme, the first part (with the h_{ij}) is a one body operator, the second one is a two body operator, it's basically a way to rewrite any quantum operator using creation and annihilation operators. If you are interested in that stuff a nice introductory book is pic related, currently reading it because i have some homework to do, describing Meissner effect using this shit.

>>8138799
If it's a singular and non-essential pole (so a pole of the nth order) you can use this formula for computing residues (z = a is the pole):
Limit(z -> a, 1/(n-1)!*D(f(z), n$z)). You can easily prove this with Cauchy's formula.

>>8140131
Don't forget Paschen's correction to this:
1/lambda_nm = R(1/m^2-1/n^2)

>>8137698
Bit shifting IS multiplication/division
Left shifting is multiplying by 2^n while right shifting is dividing.

>>8132697
-1/24-1/24 = infinity

>>8134841
This, how do you guys understand this shit?

As someone with what I thought was a 'good' level of math. (Graduate Engineering), how do you guys familiarise yourself with all of this notation, and more importantly why.

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>>8140272

practice, little by little you start to associate those symbols with abstract objets in your brain, the same way your brain inmediately sums, multiplies, factorizes polynomials. It helps being "smart" but hard work is waaay more important. I look back at highschool or undergraduate level maths and wonder why i found it difficult at the time, and the answer is that i ain't smarter just that i have accumulated 8 years studying this kind of stuff.

And why? Because is the way to describe certain physical phenomena, as simple as that.

Hi everybody

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>>8138949
>>8137739

quite interesting stuff indeed

>>8138976

you know judging before experiencing is a trait of the naive?

>>8140272
https://en.wikipedia.org/wiki/List_of_mathematical_symbols

>>8132811
how fucked would i be on a math test if i wrote this for a final answer instead of x =

>>8137739
>>8138949
>>8137739
>>8140908
Samefag

>>8132811
wow, that's...sinful!
>badumtssss

concept of zero is the darkest spookiest satanic answer.

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>>8134804
>he amputated his diagrams

>>8132607
The sphere theorem.

https://en.m.wikipedia.org/wiki/Sphere_theorem

>>8141431
I can do better.

f = zero to the power of f

>>8137739
I'm fairly convinced that he is constantly on methamphetamine all fucking day
Mochizuki is on a different level.

>>8137666
>using the shit version

0x5f375a86 is more accurate than that one in every case

>>8136856
>>8140908
This looks extremely similar to some whiteboard video I saw years ago on youtube of a dude rambling about pic related. I had forgotten the name and wanted to look it up again, so thanks for that. I had discarded it as complete shit until he presented the signed toroidal grid with signs which got me a tiny bit interested in it for the pure math aspect. Though I'm still extremely skeptical and, for example, the appearance phi appears to be a completely different topic only vaguely related by the geometry involved in this one.

Googling brings up a lot of links to creation bullshit, which does not help. It's unfortunate the prominent people involved appear to be nutjobs. Are there any pure mathematicians studying this without trying to fill it with supernatural meaning? There is no quicker way to lose my interest than attributing mystical importance on account of curiosities. Yet, I still find myself drawn to curiosities. So I'd be interested if there is anything that isn't shit.

>>8136856

Really interesting food for thought. I think I almost partially get it

I will try to explain.

I remember one time I was playing around with a program and I noticed this relationship: imagine a box grid 100x100. You are moving about the grid. Everytime you hit the edge of the grid you are put to the opposite side of the side you intersect with.

Now we are no longer really dealing with a square. topologically, It's more like a torus if you think about it.

He is noticing the relationship between the length and width of the square with these properties and somehow relating it to the way a gear works. I don't get what the sequence he came up with had to do with this.

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>>8137666
>>8139202

I don't know C++ syntax very well nor do I understand pointer arithmetic fully but I'll try to explain:

> da fuq? what ever does interpreting floating point representation as integer do?

Really what they are doing is taking advantage of the fact that floats are stored in memory in a form of scientific notation. They use information already available to better generate the guess that they plug into the derivative of 1/n^0.5

> looks like a really arbitrary number wtf is this

accessing them requires pointers. The magical constant comes from the fact that (picture related) requires a guess. I think the magical constant could be a ballpark estimate of one of the numbers in the scientific notation.