The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements.

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Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem.

Lesson by Marcus du Sautoy, directed by BASA.

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[Morningstar_]

A long time ago, the mathmaticians lived together in harmony. But everything changed when Gödel published his incompleteness theorem

guys it's been over a year, PLEASE stop replying

Guys it was funny for the last two years, but you can stop replying to this now.

help

[AKHELUS.]

Mathematicians: trying to prove that all equations can only be true or false

Gödel: hippity hoppity your certainty is my property

[ossapinhosfazemhumah]

"Its Gödels all the way down"

most underrated joke in this entire series.

[thealienontheinternet]

Imagine if he didn’t manage to prove his Incompleteness Theorems because they turned out to be true but unprovable. Complete mindfuck that would have been

[cyberkebab]

"Breaking math" is the most badass thing a person could ever achieve and you can't change my mind

[vanditrikhi]

Isaac Newton dancing for Gödel is now ingrained in my mind.

[bruceli]

Godel almost received his Nobel Prize but his theorem was incomplete.

[cullenmott]

*"...and* *he* *was* *even* *less* *confident* *that* *Mathematics* *was* *the* *right* *tool* *to* *investigate* *this* *problem."*
This is a big lesson on life. Sometimes you have to go outside the system to identify and solve the problems within it. And you have to have the courage to do so, even if doing so leaves you completely alone, and working completely alone for a long time. The moment you get to strongly suspecting there's a major problem in something that matters a lot to you, you should start looking into it and you should consider that the structure of the system in which the problem lies may be contributing to it. The work of Gödel is a textbook example of this: the structure of Mathematics disguises paradoxes within Axiomatic proofs. So Gödel divested a bit from Mathematics and went outside the field to (a part of Philosophy called) Logic to try to identify (and maybe even solve) these problems. And he ended up revolutionizing his field.

Whether the system is mathematics, or the world-economy, or even your own government, if there are problems you're noticing more and more, you may have to go outside the system to truly understand what's going on. The system may be disguising or even contributing to these problems. And you may be the only one who can solve (or begin to solve) them because you may be the only person who is able to see them.

And so the work begins, and in all likelihood it's going to be heavy. And as you work, you may have to endure a lot of push-back and isolation before you can make a big change happen. There's almost always consequences for people trying to fix the problems of the world. You should do it anyway. It's only through honestly representing your truth in the face of the falsehoods of your era that you and the world will know peace.

[pratikshahgreat]

"Jim is his own worst enemy, and enemy of my enemy is a friend. But...." - Dwight Schrute

[RyeedAglan]

LOL, Godel, Noether, and Hilbert are drawn so adorable

[faizanquraishi]

Mathematicians : *represent numbers by alphabets.*
Godel: *turns alphabets back to numbers.*
Math students: "Is this the power of a god?"

[BattyBest]

Dude took "Math is just numbers" to a whole new level

[neizanmendez]

Gödel casually making mathematicians notice that they have wasted 20 years of their lives in an unsolvable problem while being that cute in the video lol

[ordisidro]

Teacher: Why didn't you show your complete solution?!?

Me: well ma'am, according to the Incompleteness Theorem....

I remember when I was in thrid gradr my math books had written in the cover "Maths make sense". And as a kid that hated math, I spent time trying to figure out any mistake in it, something that didnt make sense. I actually did it a few times, buuut it was actually just me making mistakes, not maths. Well, glad to see one guy did my childhood quest

[Xx_Eric_was_Here_xX]

not only do i appreciate the concise synopsis of the theorem, i also appreciate getting to see godel dancing around in glee

[wiandryadiwasistio]

heisenberg's uncertainty principle: *here comes trouble...*
gödel's incompleteness theorem: *...and make it double!*

[itzjustnub]

“The man who broke math”
Me when the calculator says *syntax error*:
*look what he needs to mimic a fraction of my power*

[scottrackley]

A math professor I had said this, "No arbitrary system of rules can explain itself without external input"

[ByTobys]

I love how it’s Hilbert (we must know, we will know) who’s walking down the cliff at 4:09