Proof of the Jordan Curve Theorem

Q.E.D.

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(Thank you to @Matt56734771, for bringing this to my attention)

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Epidemic Sound - Ebb and Flow - Trailer Worx

Hi, Al. This video is a dub of a Twitter / Reddit meme about the proof of the Jordan curve theorem. Please show it to people who will like it. Thank you.

[gosha]

There's a point in mathematics where it stops being about making things make sense and becomes about making things that already do make sense into utter arcane wizardry.

[WaluigiisthekingASmith]

There are two types of people. Those who look at this theorem and say "oh alright. That makes sense, " and those who have witnessed horrors beyond your comprehension, seen what the mathematicians create when left alone, and simply wish they could go back to the days that the Jordan curve theorem seemed an obvious fact.

We’ve reached a point where Jeaney can recite mathematical theorems and it’s still funny.

[calinacho]

"It's like trying to prove 1+1=2"

It has been done. It took 200 something pages of dense mathemathical nonsense but someone did do it

[sofer]

If anyone's wondering, the Jordan Curve Theorem was *immensely* arduous and difficult to prove. To this day, the shortest mathematical proof is like 3 pages long, and only because it used Brouwer's Fixed Point Theorem as a starting point.

[Sayeedbutmunchesoncurry]

The counterpart to Bend it like Beckham: Curve it like Curry

[shellfire]

Props to Jordan for getting ALL SHAPES named after him

[Vendavalez]

Jordan wanted to name something after himself and thought “this one should be easy!” Without stopping to think why no one had claimed it yet. He did eventually find out why, but he pushed through. Mad respect for Jordan.

[RaonMiru]

Makes you wonder what exactly was Jordan going through when coming up with something so blatantly obvious?

[hasiumcreeper]

If anyone is curious why the Jordan curve theorem is so difficult to prove, it's that mathematicians can come up with some crazy wackadoo curves. For instance, you should google Weierstrass's function, which is a curve which is continuous everywhere but differentiable nowhere. If you take a slice of that and connect the two edges, that is *technically* a Jordan curve, but it's not so obvious that it has an inside and an outside

[alicebrolin]

Took a break from writing my masters thesis about Jordan curves and saw that Jeaney posted this...

[jcnot]

Ah yes, the engineer’s favorite way to prove a theorem aka “proof by shut the hell up.”

[HelloIAmAnExist]

I wish obviousness was an accepted form of proof in mathematics. It sure would make math class way easier

[Ryann]

Imagine someone proved the Riemann hypothesis and the paper is just, "It's pretty obvious" and nothing else.

[grzegorzha.]

Kirchhoff literally got a law named after him because he said 1/2+1/2=1.

[normanstevens]

It's also absolutely obvious that you can't take a solid ball in three dimensions and partition it into a finite number of disjoint subsets which can be put back together to make two copies of the original ball.

[eauna]

Mathematics memes, and especially the Jordan Curve Theorem, give such a world of fun most people don't dare enter because of how badly school math is taught.

Love that you dared give math memes a try!

[daveauburn]

For anyone who is wondering why such obvious "theorems" require proofs: The system of mathematics that we know and love is built on axioms (a set of elementary rules that are considered true which uniquely define a system) and every other "obvious" observation (like 1+1=2) must be consistent within this system (otherwise its not a very good system, is it?). However, an absolute legend by the name of Kurt Godel proved that mathematics is not a complete system, i.e there are things which are true but can't be proven (unless you change the axioms, in which case you are now using a different system where 1+1 may not be 2). What's funny is you can actually prove the incompleteness of mathematics using mathematics itself.

[KSignalEingang]

A fine example of the technique of Proof by Exasperation

[ardnys]

that font gave me freshman flashbacks. aw man i went through all calculus textbooks available in the library and studied every single limit proofs for the calculus midterm, and there wasn't even one question. it was already very painful to wrap my head around those proofs, and then they did that.
that font still haunts me. those math textbook fonts...