/sci/ - Science & Math

>>9396299
Noether's theorem.

>>9396305
Yeah this one is nice too

Absolute value lemma blew my mind and load.

Like wow. |x| < y <=> -y < x < y. That's just beautiful. I always shed a tear.

>>9396310
All right but this is obvious to anyone with a brain

It says that you have two lines X and Y. X is shorter than Y.

>>9396317

No shit, it's a meme """lemma""" to teach brainlets how to prove triangle ineq in baby analysis. It's just the definition of AV written in such a way that even brainlets can see the connection.

>>9396299
[math]\exists y\forall x, p(y)\implies p(x)[/math]
it was formally proven in a logic class,
kinda like that there is a formal proof that we can prove something for an arbitrary y and then infer that it holds for all x.

that one about conditionally convergent series

>>9396299
[math] \int _{\partial \Omega} \omega = \int _{\Omega} d\omega[/math]

>>9396352
meanignless unless you defined what the fuck those 4 symbols mean

just like
abcd = fg

>>9396356
Yeah but everyone here knows what it means.

>>9396360
Explain to a chemistry brainlet?

>>9396299
I am a mathematician myself but nothing I've learnt has come close to the Noether theorem. It is so simple but when you start reading QFT you realise just how important symmetry is. I think it should be at least mentioned in schools.

I also remember being excited by the Gleason theorem (on density operators) and the Frobenius theorem (on R/C/H algebras) in uni. More recently, I can finally appreciate the beauty of the Atiyah–Singer theorem on analytical/topological indices.

>Noether's theorem
>Noether
>No ether

Fucking anti-ether fags still trying. Ether will prevail.

>>9396364
It's stoke's theorem, look it up. lots of applications

>Gödel's completeness theorem
Huh, thats really interesting I guess
>Gödel's incomplentess theorem
OVER THE LINE

>>9396299
>the inverse function theorem and the chain rule
hands down, those are the two theorems making any theory involving differentiable manifolds possible

1+2+3+4+5+.... = -1/12

>>9396299
The well-ordering theorem. This transfinite stuff still looks a bit mathemagic to me.

cantor's diagonal

>>9396428
>inverse function theorem
>not Implicit function theorem which has the inverse function theorem as a corollary

The pigeon hole theorem.

If you have N holes... And N+1 pigeons...

...you cannot give own hole to each pigeon...

MIND = BLOWN

OP posts bait thread.
But nobody falls for it.
I'm sorry OP.

>>9396562
fuck i thought i had seven syllables. wtf!

>>9396562
>>9396565
oh wait I did nobody is 3

Gij, j=0

>>9396450
they are completely equivalent. you can prove implicit f.t. from inverse f.t. easily

>>9396299
>Dold-Kan Correspondence
>Brown's representability theorem
Literally jaw dropping

>>9396356
>doesn't understand standard notation
>"muh meaningless!"

Cauchy's residue theorem is pretty neat, I guess.

>>9396299
Cij= (-1)^i+j * Mij

1+1/2+1/4+1/8+.... =/= infinity

>>9396429
that's wrong though

>>9396299
Nullstellensatz for obvious reasons

Also these >>9396619 , or moreover the Stable Dold-Kan which essentially includes both

>>9396727

>residues

Complex analysis was a mistake

Not a theorem, but a principle from Linear Algebra. Shakes me to my core every time.

Every invertible linear transformation is just a change of basis matrix.

>>9397239
if you're studying math or physics, wait till you get to differential geometry, principal bundles stuff. shit's gonna blow your mind.

von neumann ergodic theorem

>>9397266
Doubtful. Those both read as weak. The linear thing really changed how I see physics and the universe. Principal bundles are... just things. Nothing follows, it's a definition.

>>9397272
There are interesting theorems for principle bundles.

For instance G-bundles w/ flat connection (over a space X) are in bijection with homomorphisms from the fundamental group of X to G.

I'm sure you can pick some physical significance out of that, considering gauge fields are connections on principle bundles.

>>9397346
>I'm sure you can pick some physical significance out of that
>I'm sure

meaning you haven't yet
meaning its a little bit less meaningful

>>9397359
I'm not a physicist, I know that what a physicist calls a gauge field is a connection on a principle bundle. But I don't know anything about the physics of gauge fields.

>>9397228
You can use them to calculate crazy integrals that you normally can't

>>9397372
That shit is beautiful. I came in the back of some chicks head in class when we went over it.

>>9397363
That's my point. You don't need to know anything about physics to understand the meaning of what I said. Knowing and understanding the math is the important part. Any linear transformation, ANY LINEAR TRANSFORMATION is just a change of basis matrix. Think about it. Push a car across a road? It never even moved. We just changed some perspective.

>>9397381
you're a dumbass. you don't realize the person you're speaking to knows and understands much more about all this than you'll ever do. you're saying meaningless shit.

>>9396299
Nullstellensatz

Kodaira Embedding

GAGA

>>9397391
t. highschool brainlet who browses this board thinking it makes him look smart

>>9397381
>Any linear transformation, ANY LINEAR TRANSFORMATION is just a change of basis matrix. Think about it. Push a car across a road? It never even moved. We just changed some perspective.
this logic is kind of misleading

>>9397499
brought me back to the old futurama episode where the ship moves the universe

>>9397381
>>9397506
DUDE, I bet you watch Rick and Morty, am I right?

>>9397506
a transformation and a change of coordinates are two very different things. just because they coincide in the very special case of R^n, it doesn't mean that they can be considered the same concept.

Ito's lemma
spectral theorem
Feynman-Kac formula

>>9397542
No, they aren't. So long as it's linear, and so long as it's invertible. Which I'll grant is pretty limiting, but hey. It's what OP was asking for.

>only having read one approach

Yoneda Lemma
Donaldson's Theorem

>>9397440
>>9396619
Patricians

>>9396356
Look at me I don't know what a manifold is, this is meaningless

>>9396386
kek

>>9397206
thats not wrong. just dont put that in your math or calculus test.

>>9396352
HNNNNNNNNG

One of my favourites is Weierstrass Factorization Theorem for Entire Functions.

My man Euler just assumed it's true cause it is too natural not to be.

>>9396459
Actually has some really cool applications if you take the time to read a combinatorics book

>>9396299
Euclid's Division Lemma

>>9396299
Godel's proof restored my faith in math

>>9396299
Brainlet

>>9396541
>the CLiT theorem

>>9396374
I like this painting. Who's the artist?

Rao-Cramer bound, Stein's paradox.

>>9396356
same can be said of any theorem