Math's Fundamental Flaw

Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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References:

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Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Executive Producer: Derek Muller
Writers: Adam Becker, Jonny Hyman, Derek Muller
Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman
SFX & Music: Jonny Hyman
Camerapeople: Derek Muller, Raquel Nuno
Editors: Derek Muller
Producers: Petr Lebedev, Emily Zhang
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett

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[rochestephan]

Ironic that Godel's death was the result of a self-referential paradox: he died in order to not die

[lemond]

I don't know why but I love the idea of mathematicians gathered in a room yelling and hurling insults at one another

[notdannydevito]

Why didn't they just have three people stand beside John Conway after he died?

[vgamedude]

Everytime people get into the weeds with math like this i feel like im just listening to philosophy with a different label.

[benjaminparker]

Ah yes, the iconic half way point of the video where I stop comprehending a single thing said

[michaelh]

Teacher: Your math is flawed.
Student: No, math itself is flawed.

[LukeRadick]

I love how tightly intertwined mathematics and philosophy are

[dougieh]

It's disgraceful what they did to Turing. 😢

[anthead]

Gödel was also first to ask P vs NP question and he asked it in the letter to John von Neuman.
Those dudes had some world changing conversations.

[mikejohnstonbob]

Godel's friends: "No one's trying to kill you Godel"
Godel: "You can't prove that!"

[zedx]

So this is how these things are connected to each other. In my CS degree we had to study about almost every one of these topics (at least a very little of every topic) and they seemed very disconnected and apart of each other. Discrete mathematics, Automata, Set theory, proofs... etc. This video connects dots. An actual tear fell from my eye at the end of video. Thanks for making these amazing videos.

[P-_Airacobra]

This is actually the MOST interesting video I have EVER seen. Every minute was amazingly clear and intriguing.

[DanielG]

Me: *failing my math class*
Veritasium: “they could be something like the twin prime conjecture”
Me: go on...

[J_Stronsky]

7:49 - 'corrupter of the youth' haha
"Hey kids come here, you want to learn about some illicit infinities"

[FeichengLuo]

I learn about the Veritasium by watching this video about 2 years ago, and it turned out to be the most valuable 30 minutes that I spent on the internet. Maths became almost religious to me after watching it, for it is capable of proving its own limitations within its limited system, although my father kinda disagrees with me on the religious part as a professional in maths. But there's a reason for me. It actually reminds me of the philosophical question of "what we are" and "what we are made for" since they are also related to the self-reference paradox.
I have been suffering from depression and anxiety at the time when I first saw this video. I was about to graduate but had no idea of what I am going to do nor what is the meaning of my life. But this video somehow saved me. For no reason, I suddenly feel relaxed after learning about Godel number and the answer and proof to the three questions. I realized that, just like maths, life is not about meaningful or desidablility either, but we may find what we have done meaningful years later. And this is a proven truth. Just like one of the most famous Chinese poems said, "everyone was made with some talent that must be useful".
Anyway. I finally found my own belief after watching this video. And now, after 2 years, I am back to the college for postgraduate degree and for working out my own value of life. Many thanks to Veritasium for the great work. Wish everyone a great life.

[daniela.fagundes]

I truly believe that this was the most spectular video I've ever seen on this channel! Congratulations to you and your team, Derek!

[OddNumber]

"How about you just hire another barber?" Said the engineer

[kyriakosmousias]

As a mathematician I haven't seen a more elegent presentation of these concepts, especially Godel's theorem. Amazing job thank you.

[blackdwarfrecords]

Oh, well done sir. Your closing line here very nearly sent a chill up my spine. Thank you for another well-spent half hour.

[ogieomorose]

This channel teaches the basics so easily. When explaining something such as complex numbers, they go into the most basic foundations, akin to explaining an organism from the level of quarks and gluons as opposed to the conventional educational system which just tells properties outright. Brilliant chose an awesome channel to sponsor