Give me your most powerful mathematical theorem. The first time you read it you were bedazzled; it can't be true! The statement was just too grand! But no it was true.
I think overwhelming majority of mathematical theorems are idiotic, too simple, pointless, uneconomic, nonproductive, obvious, discuss some meaningless concept like philosophy or infinity.
But here are few I actually find very useful: 1. Pythagorean theorem 2. General rule of derivation 3. Four color theorem 4. Taylor's theorem 5. Binomial theorem 6. Fourier series 7. Dirac delta function 8. Brouwer fixed point theorem 9. Arrows impossibility theorem
Connor Walker
Noether's theorem.
Angel Rodriguez
Yeah this one is nice too
Austin Brooks
Absolute value lemma blew my mind and load.
Like wow. |x| < y -y < x < y. That's just beautiful. I always shed a tear.
Adam Torres
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.
Brody Long
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.
Adrian Wood
[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.
meanignless unless you defined what the fuck those 4 symbols mean
just like abcd = fg
Michael Reyes
Yeah but everyone here knows what it means.
Matthew Smith
Explain to a chemistry brainlet?
Grayson Kelly
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.
John Long
>Noether's theorem >Noether >No ether
Fucking anti-ether fags still trying. Ether will prevail.
Grayson Peterson
It's stoke's theorem, look it up. lots of applications
Logan Walker
>Gödel's completeness theorem Huh, thats really interesting I guess >Gödel's incomplentess theorem OVER THE LINE
Liam Stewart
>the inverse function theorem and the chain rule hands down, those are the two theorems making any theory involving differentiable manifolds possible
Benjamin Thompson
1+2+3+4+5+.... = -1/12
Ryder Phillips
The well-ordering theorem. This transfinite stuff still looks a bit mathemagic to me.
Hudson Ramirez
cantor's diagonal
Robert Hall
>inverse function theorem >not Implicit function theorem which has the inverse function theorem as a corollary
Henry Lewis
The pigeon hole theorem.
If you have N holes... And N+1 pigeons...
...you cannot give own hole to each pigeon...
MIND = BLOWN
Dominic Price
...
Nicholas Nguyen
OP posts bait thread. But nobody falls for it. I'm sorry OP.
Cameron Baker
Gij, j=0
Justin Adams
they are completely equivalent. you can prove implicit f.t. from inverse f.t. easily
>doesn't understand standard notation >"muh meaningless!"
Aaron Price
Cauchy's residue theorem is pretty neat, I guess.
Wyatt Smith
Cij= (-1)^i+j * Mij
Nolan James
1+1/2+1/4+1/8+.... =/= infinity
Jacob Ramirez
that's wrong though
Carson Williams
>residues
Complex analysis was a mistake
Nathan Jones
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.
Jaxon Carter
if you're studying math or physics, wait till you get to differential geometry, principal bundles stuff. shit's gonna blow your mind.
Justin Stewart
von neumann ergodic theorem
Thomas Lee
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.
Jack Collins
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.
Colton Long
>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
Kayden Myers
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.
Charles Anderson
You can use them to calculate crazy integrals that you normally can't
Asher Miller
That shit is beautiful. I came in the back of some chicks head in class when we went over it.
Isaiah James
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.
Adam Collins
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.
Nicholas Walker
Nullstellensatz
Kodaira Embedding
GAGA
Ayden Price
t. highschool brainlet who browses this board thinking it makes him look smart
Sebastian Mitchell
>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
Brandon Gomez
brought me back to the old futurama episode where the ship moves the universe
Dylan Parker
DUDE, I bet you watch Rick and Morty, am I right?
Justin Ross
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.
Logan Price
Ito's lemma spectral theorem Feynman-Kac formula
Ryder Diaz
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.
Austin Harris
>only having read one approach
Chase Nguyen
Yoneda Lemma Donaldson's Theorem
Patricians
Cooper Brown
Look at me I don't know what a manifold is, this is meaningless
Thomas Hughes
kek
Alexander Cooper
thats not wrong. just dont put that in your math or calculus test.
Asher Torres
HNNNNNNNNG
Dylan White
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.
Joseph Nguyen
Actually has some really cool applications if you take the time to read a combinatorics book