Math's Fundamental Flaw

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.
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:
Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. - ve42.co/Dunham2013
Conway, J. (1970). The game of life. Scientific American, 223(4), 4. - ve42.co/Conway1970
Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. - ve42.co/Churchill2019
Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. - ve42.co/Gaifman2006
Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky-in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. - ve42.co/Lnrt2010
Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. - ve42.co/Poincare
Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. - ve42.co/Irvine1995
Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. - ve42.co/Godel1931
Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. - ve42.co/Russel1910
Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. - ve42.co/Godel1986
Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. - ve42.co/Cubitt2015
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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

[@TanyaNirielle]

This comment deserves more likes

[@DebdyutiBiswasdebbisful]

Underrated

[@reverieWithRupam]

Woah...

[@nDenTzMotionZztrujillo]

You nailed this comment

[@moazz5779]

This comment is just too good

[@chorian5424]

mom: why did you get a B in math! me: math has a fatal flaw

[@cohensmith6100]

B is good

[@ALBINO1D]

@@cohensmith6100 and A is excellent.

[@cohensmith6100]

@@ALBINO1D ya but like why get mad abt a b when most mfs fail math

[@ALBINO1D]

@@cohensmith6100 is your benchmark just to be better than worst, or to be the best? Learn a lesson from Ash Ketchum.

[@cohensmith6100]

@@ALBINO1D Hes like over 20 and hangs with 12 yrs old girls ill pass man

[@yhwh9778]

I love how the set theorists answer to self reference was "I changed the definition so that doesnt count."

[@dominicbonogofski]

It's like a kid on a playground saying they weren't playing when someone else tags them.

[@EonsEternity]

​@dominicbonogofski i dont feel like thats a valid analogy, theres nothing wrong with going youre right this is a flaw and trying to adjust the rules to fix it. Maybe its just the problem with analogies is that they can also be unproveable though so its also a contradiction based on perspective 😯

[@dominicbonogofski]

@@EonsEternity I was just implying that it had the same energy behind it.

[@smarchar]

this brings up a question: what if the turing machine's answer to haltability was to simply make a new rule: the turing machine cannot accept itself as an input. that would remove the proof against haltability. so does that mean mathematics could be decidable as long as it doesn't self-reference? or does this prove that set theorists were in denial? if neither, then what makes set theory different from mathematics in that in can exclude self-reference and still be useful, while mathematics/turing machines cannot?

[@randompersson]

​​@@smarchar@dragonsaige I had that thought as well, but then that would eliminate self-reference, which is very useful in answering a lot of questions correctly. At least, that's what my logic led to. I'm just a software engineer with a passion for maths. I could be entirely wrong.

[@vgamedude12]

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

[@mattiamazzanti8418]

Philosopher ask a question,Phisicists Turn questions into math

[@chetsenior7253]

Indeed. Just remember that numbers aren’t real. I mean that in the sense that they are always tied to an object or idea. You can’t go out and find a 7 in nature, you especially can’t find a negative seven.

[@shrekeyes2410]

thats because they are philosophers, They are natural philosophers.

[@mafuchin]

PhD student here. Math is applied philosophy. You cannot have one without the other.

[@alecepting1371]

Exactly, the foundation of mathematical proofs came from the Greek philosophers.

[@mikejohnstonbob935]

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

[@nbjornestol]

He actually refused to eat any food not prepared by his wife. Unfortunately she was hospitalized, and couldn't prepare food for him, causing him to starve to death.

[@lavabeard5939]

@@nbjornestol he couldn't prepare his own food?

[@segmentsAndCurves]

@@lavabeard5939 He was a mathematician (logician) after all.

[@kindlin]

@@segmentsAndCurves Does that excuse a man from being able to provide for... himself?

[@kimochi5009]

@@kindlin It doesn’t excuse, but it explains why he didn’t prepare his own food.

[@lemond1649]

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

[@viacheslav7870]

"You are proof that one can actuality have a value of zero!"

[@sleepybraincells]

@@viacheslav7870 lmao

[@siinxx7656]

@@viacheslav7870 I'd rather listen to the first 10,000 digits of Pi than some irrational numble like you *crowd commotion intensifies*

[@emaanahsansarfraz1940]

Hello! How are you all? If anyone needs someone to listen, someone to talk to, or a friend. I am here to talk, listen, and be a friend. I hope you all are safe and well. Know that you are amazing and have rights as a human. I am very sorry for anything that seems bad that may have happened in your life. I want you to know that you are incredible and are capable of wonders. What matters is your inside, not your exterior. Love yourself and cherish yourself. Words cannot explain how astonishing you are. You deserve care, love, and happiness, don't let anything make you feel otherwise. Please have appropriate action for anything that you know is wrong. Anything that seems bad or wrong in your life right now will get better. Please don't do what is wrong, fighting back and harming others will not solve the problem. Please understand that and do the good thing. It will one day come back to you. The people in the world are so much more than what we know about them, not everyone opens up about the beautiful things and acts they have witnessed, not all those amazing doings are acknowledged. Please understand that and know that. If you feel like no one cares about you, know that I care about you. Keep your head up high and never give up! Together, we can be a better community! Stay safe, healthy, happy, kind, understanding, positive and strong!

[@rashidabegum9206]

"You are more irrational than any number I've ever seen!"

[@charlesfletcher42]

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

[@AndresFirte]

This is the best math joke I’ve heard in a month

[@prabhakarsingh6821]

Oohhhhhhhhhh

[@1stlullaby484]

Give me the reference please 😂

[@charlesfletcher42]

@@1stlullaby484 In Conway's Game of Life, 3 living cells around a dead cell make the dead cell alive again so, the joke is that they could have resurrected Conway by having the people (cells) surround him (the dead cell).

[@Mike_droptv]

Wouldn't work. They'd have to stand there for a whole generation and everyone's bound to use the restroom at some point 😅

[@zedx4749]

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.

[@bladr-the-goat]

Me too brother, me too....

[@anon1963]

Proofs are horrible, man

[@crismamuerta]

😢

[@5001Fergies]

Fr its so awesome seeing everything ive learned over the years recontextualized into a cohesive story of cause and effect, i wish my professors told me about this connection before 😂

[@NVIK5]

Weil fell off not tear

[@michaelh4227]

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

[@moncorp1]

dank meme

[@inthebackwiththerabbish]

lmfao

[@Scipio_Africanuss]

I’m gonna go to my math teacher and be like “math is incomplete and inconsistent,” and she’s gonna say no it is and then I will now more about math than her and I will be so happy

[@inthebackwiththerabbish]

@@Scipio_Africanuss ahahaha bro let me know what she says 😂

[@Rob-cm9jr]

@@getonthecrossanddontlookba5004 I assure you math and time are constructs of man, not God.

[@amecha5368]

So basically... Can math prove itself? No. But math can prove that math can't prove itself.

[@Logan-zf1ft]

hahahahha good one

[@rob_olmstead]

well... you can't prove the rule using a rule because the rule is universal and immutable

[@kathanshah8305]

Yesn’t

[@Pineapple-hx9ty]

"math can't prove itself" to the power of -1

[@MsHellokitty666]

I was asking myself the exact same question

[@LukeRadick]

I love how tightly intertwined mathematics and philosophy are

[@DC-zi6se]

Philosophy is everything. Mathematics is based on logic, a branch of philosophy of "reasoning", which forms the groundwork for the formal science which is in this case mathematics. There are other formal sciences like Computer Science, Statistics etc. Sometimes logic is also included in the list of formal sciences.

[@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.

[@bryantaylor993]

Wow! I’m sincerely happy to see that you’ve found your path! Keep it up! …And don’t worry; no religion makes any sense.. if you found something to believe in, charge on!

[@captainzork6109]

I've been wondering how numbers relate to life. I'm approaching it from the perspective of psychology, where we often use null hypothesis significance testing and the law of big numbers. We take a group of people, do an experiment, and we check the average. But our phenomenon of interest is the (average) individual, which is different from the group average! Group-to-individual generalizability cannot be taken for granted. The difficulty lies with multiple realizability: -2 and +2 are the same as 0+0. Except for the standard deviation of course, I guess. But clearly, taking averages obfuscates things. Why? Because counting things reduces information. When you say a pair of shoes, or even two shoes, you equivocate two non-identical things. And it is the same for people with depression, who may not even have a single symptom in common with each other. One study which checked "depression profiles" of ~3,000 people found that the most commonly occurring profile occurred 1.4% of the time amongst the ~1,000 different depression profiles identified. Yet, if a study is done on depression, imagine how difficult it would be to test a psychotherapy or psychoactive drugs without being able to refer to depression as a single concept The question is whether mathematics applies to the real world. The answer is obviously still: yes, extremely applicable. Numbers allow us to see patterns in the world, which is an utmost necessary condition for intelligence to work. The way the universe and its objects worked in the past is, at the very least, a really great analogy for the future But might it be possible to describe accurate and precise truths about the world with numbers? The capacity to abstract is fundamental for us to make to be capable to think and talk about the world -- to talk about "depression", without having to mention all the specific cases in mind which represent that concept. Yet, if the utmost of specificity is desired, would that be possible? It would be interesting to see if quantification, or counting, is valid in its strictest sense. Is there any phenomenon in the world which is identical with another (as opposed to merely equivalent), and of which we would therefore not lose any information if counted? Or might every single thing, in its strictest sense, be different from one another?

[@alexisparedes1805]

@@captainzork6109 That is why different lifestyles should be normalized because just like in math, everything thing is correct as long as true happiness exists.

[@captainzork6109]

@@alexisparedes1805 I like that this is what you took from my 400 word essay I don't necessarily agree math is correct if it makes you happy. But to "yes-and" on what you said: Yes, and being more knowledgeable about how people live their lives in different ways, would help us to refrain from holding ourselves and others to unrealistic societal standards. And that would indeed reduce suffering and increase happiness

[@matthewyoung6263]

"1+1=2" "The above proposition is occasionally useful."

[@Jayess-c]

What's 3x+1?

[@Jayess-c]

Or y3X+1 it is impossible to get an answer it's like pi

[@kam9910]

@@Jayess-c lol dude they literally made a vid about that, it’s that where you got it from

[@Jayess-c]

@@kam9910 what are you referring to?

[@kam9910]

@@Jayess-c if you were trying to pose it as your own equation you made up, I’m not sure rlly, I’m just 11 lol

[@OddNumber1524]

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

[@Smitology]

And you only need two barbers to break the paradox. They can shave each other; the rules never said that wasn't allowed.

[@jamesflanagan6977]

Engineering student here, my first thought as well

[@jeffirwin7862]

2 barbers 1 town

[@kelpf0rest]

@@jeffirwin7862 IYKYK

[@majiachen101]

@@theknightwhosayn1 only the barber can shave anyone, that was one of the rules

[@axmedazeez]

Truly one of the greatest mathematics-related video out there on KZbin. I often find myself returning back to this video, and thanks to you, I was inspired to major in engineering. I started loving math; it's such a great language!

[@tpbenze5032]

It really is and highlights how amazing math is and how useful it is despite its limitations. I think most people would be surprised that our whole modern system of science is built on these grounds, but it works amazingly

[@TheAlmightyFather]

Not to disway you, but if you love math, go to math! Not engineering. As much as math is involved in engineering in a lot of ways, in practice it does not.

[@P-39_Airacobra]

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

[@krissisk4163]

"There will always be true statements that cannot be proven." Oh yeah? Prove it. ....He proved it.

[@poorvisingh232]

Brains!

[@levibyler1132]

Plp are to smart

[@charlesballiet7074]

you mean like Epstein not killing himself

[@jenidu9642]

Proving something is impossible is also a proof

[@HerrCookienator]

Dis gave my brain a new wrinkle

[@DanielG03]

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

[@tejasdeepsingh456]

Lmfao

[@SoumilSahu]

tbh the conjecture itself is pretty elementary to understand.

[@wildanimus2559]

@@tejasdeepsingh456 ditto

[@angryyoungman4389]

@@wildanimus2559 Charizard

[@crystalgiddens7276]

@@SoumilSahu what is gobbledygook? - In particle physics, a lepton is an elementary particle of half-integer spin (spin 1⁄2) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutral leptons (better known as neutrinos). (fûr′mē-ŏn′, fĕr′-) Any of a class of particles having a spin that is half an odd integer and obeying the exclusion principle, by which no more than one identical particle may occupy the same quantum state.

[@xintongbian]

I've known these topics for years and also watched many videos, I have to say this one is so beautifully done, all those thoughtful illustrations

[@daimaryjohn]

I love you

[@alexisparedes1805]

you are a cocky one huh? lower your standards because you know nothing haha

[@daniela.fagundes1448]

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

[@cipherxen2]

Mathematicians: we must prove this equation Engineers: Eh, it's good enough, we'll just use it

[@mattstokes3881]

bridge collapses

[@cipherxen2]

@@mattstokes3881 and they learn from their mistakes, and makes better bridges

[@MarkAvo]

I feel seen

[@aloysiusvo318]

@@cipherxen2 No no no as a civil engineer student u have to prove some math equations to make sure the measurements are right. So idk what tf are u talking about

[@deusexaethera]

Mathematicians: "We must prove this equation is true in all possible scenarios across all possible universes." Engineers: "Bro, do you even constraints? I only need the equation to be true _on Earth for the next 50 years."_

[@benjaminparker5044]

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

[@chronicles1192]

that feeling

[@Smo1k]

Read Douglas Hoffstadter and comprehend even less. In an entertaining way ;)

[@SoloPilot6]

If we had had videos like this in high school, I wouldn't have come out of math class convinced that 2 + 2 = CAT . . .

[@yash5879]

It is a proof which proves that not everything that is true can be proven after all ¯\_(ツ)_/¯

[@akhilaryappatt7209]

it's zone out time

[@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.

[@ogieomorose3628]

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

[@Mackinstyle]

If you're a mathematician and you are labelled a "corrupter of the youth", you are doing something very right.

[@TheOOOOOOOOOOOOOOO]

nerd burns

[@Aereto]

@Linus Fu Yet neither can prove nor unprove logical paradoxes. The same way no one figured out why we can pin point an electron's vector and position separately at the expense of the other, and never both.

[@deepankurnayantara]

I watched this video when its title was still "There's a Hole at the Bottom of Math".

[@tannerwitt3030]

@@Aereto wait whaaaaaat

[@theycallmealex454]

Exactly. If one proposes a theory or statement that pushes all of our minds to think hard enough, regardless if it's wrong or not, overall it's something right.

[@ArthurBCamara]

I'm a PhD in computer science. This is a full-on Discrete Mathematics intro course. This is amazing.

[@Kirmeins]

I never saw much of this in DiMa... most of this I picked up somewhere along the line and often in the actual CS introductory courses or while trying to understand more basic concepts using YT. Only to be distracted by that one video on the side called "The halting problem" or some such and getting curious. :D

[@ltu42]

Right on! A semester of DM in one video.

[@camrouxbg]

@@Kirmeins Yeah, thing is that DM is so vast that it is really easy to set up a course that doesn't touch on any of this material. The DM course I took was like this... introduction to game theory, a little combinatorics and cryptography, coin weighing problems, stuff like that. But I think the important thing is the ability to get students interested in the material, and then they go looking for other courses that cover it.

[@sanjarcode]

I agree, this is also the key for appreciating the role of AI/ML theory. And randomised algorithms.

[@iamtheusualguy2611]

I had this in my theoretical CS module more than the discrete maths one and while I hated the exams and the assignments, I thoroughly enjoyed getting my mind blown by such a profound topic. I've never thought that we actually would go into deeply philosophical questions about the fundamentals of logical systems, truths and math itself while studying computer science. And how it all connects to computers in the end. Brilliant video, it creates this amazing feeling of profound enlightenment I had when I first encountered this topic and I hope it reaches as many people and blow people's minds just like it had mine.

[@lexslort1437]

I honestly and wholeheartedly believe this is the best video this platform had ever seen. I share it often with my students. Derek, Amazing work and Thanks.

[@ZZ-sn7li]

This is the only KZbin subscription channel you need... Can't get enough. Thank you so much.

[@anthead7405]

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.

[@batfan1939]

Was waiting for P = NP after The Halting Problem. Maybe next time.

[@enemdisk6628]

Nice

[@DavidLiMusic]

Veritasium needs a video on P vs NP! Would be amazing.

[@pvic6959]

meanwhile me to my friend: Do you think dogs know theyre adorable?

[@codycast]

@@DavidLiMusic yeah because there isn’t enough n/np out there

[@baronblair5811]

To me this is one of the most influential videos I've ever seen on KZbin. I think this video should be a prerequisite for children to watch in education. Why does this discovery not disturb more people?!

[@mit5oner]

This is top 10 videos of all time. Literally the best explanation ever of one of the most interesting scientific (and existential) concepts.

[@elchingon12346]

“1+1=2 The above proposition is occasionally useful “ I need this on a poster for my classroom 😂😂😂

[@PiotrKaszuba8403]

😂

[@sdgathman]

“1+1=2 The above proposition is occasionally useful “ It's also racist. smh

[@LIGHTISBURNING]

So trueee

[@ccgarciab]

@@sdgathman "I proudly and loudly misunderstand things"

[@DevinDTV]

@@ccgarciab sounds like you weren't aware that math and logic are constructs of whiteness which inherently oppress people of color

[@kyriakosmousias9009]

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

[@WritersMoment]

I just don't understand where equation g came from. Why would it have been a contradiction to prove g, just because it said "this can't be proven"? If one had proven it anyways, Gödel's statement would have been wrong, yes,but what of it? Why did he write "this can't be proven"? Purposefully trying to MAKE a paradox by setting contradicting rules and then saying "See? Major problem, math incomplete." doesn't make any sense to me. If things naturally contradict, isn't it the axiom's fault? Shouldn't we just rethink the basics?

[@abhinavgaming2110]

@@WritersMoment well if he didnt do that contradiction then we wouldnt know the completeness of math

[@henningbreede6428]

@@WritersMoment I didn't watch the video, so I don't know how they explained it, quite possibly very incorrect. However the point of the 2nd Gödel incompleteness theorem is if your axioms fulfill a bunch of desirable attributes (such as being able to prove all true statements about the natural numbers), then you can encode its own consistency. Those are known as Gödel sentences. As the axiom system can not prove that, it's therefore not complete if it's consistent. It's possible for an axiom system to not have arithmetic, but be complete and consistent, have arithmetic, be complete but not consistent or be consistent, have arithmetic but not be complete. So it's not possible to rethink the basics to get all desirable quantities. Math is not flawed tho, since having arithmetics and a consistent axiom system is possible and absolutely sufficient for everything that mathematicians do.

[@WritersMoment]

@@henningbreede6428 Wait, do you always comment in comment sections of videos you haven't actually seen?

[@henningbreede6428]

@@WritersMoment No, this is the sole exception. I clicked on the youtube video because it was recommended and after reading the comments I'm not very motivated to watch it either. It doesn't seem to do a good job at addressing common misconceptions.

[@MidNightStudiosFilms]

Wow, this is great content, Veritasium! Sometimes your videos just transcend the brilliant educational films they always are, and become pure art.

[@chrisc9769]

What happened to Turing was a tragedy, then and now. While i am an American i love Military History, specifically WWII. So i am familiar with Turing and the work he did during the War. (Not so much his other work which is fascinating) It has always bothered me how he specifically was treated after the war and it was good to see him get his Roaly Pardon in 2013.

[@tuomasronnberg5244]

"Later generations will regard set theory a disease", "No one shall expel us from the paradise that Cantor has created" Those dudes felt *really* strong about abstract maths back then.

[@Kabup2]

It did remember 'God don't play dices' from Einstein.

[@JonathanHuertayMunive]

you might want to read mathematicians debates nowadays... nothing has changed

[@abhisheksoni2980]

Later generations are just making tiktok videos.

[@DevinDTV]

it's not at all surprising that they had strong feelings. they were literally debating how reality works. not just physical reality, but abstract reality too.

[@RandomFilmmaker]

Pythagoras beat them at their game though

[@emilyrln]

"19th century mathematicians HATE this one weird trick!"

[@gmarais1986]

Haha when will those ads stop being a thing? Gödel would have known

[@splifstar85]

Funny thing is Henry Pointcare seems to be a formalist at heart, as he claimed “later generations would have recovered from the disease” - meaning maths is Complete, Consistent and Decidable.. since he was sure that there would be a system that could with certainty disprove Canter 😏🤷‍♂️

[@billrich9722]

Oh, look. A meme.

[@FlyoviaUSA]

You won't believe what Kurt Gödel looks like at age 115!

[@Jnglfvr]

Comment of the year.

[@thamersuliman4112]

Bro, I swear I sleep hearing your videos like hundreds of times. Your voice is so calm and one-pitched it helps me sleep every time.

[@johaanvinaysingh7898]

I admire the fact that you take concepts and bring it to life. Taking us on an adventurous journey making it more fun. You really brought my intrust in science back I had took a break but coming back here after a year feels great. Great work! Nice explanation on how math is incomplete and inconsistent and how a turing machine program with binary code makes it different.

[@J_Stronsky]

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

[@igorswies5913]

wanna learn how to divide by zero?

[@tilakmehrotra]

Noooooooo

[@mischief9499]

lmaoo

[@bujfvjg7222]

illicit infinities are creations of the universe, just like ourselves.

[@TheJanitorIsIn]

Socrates back from the dead

[@steelfirebladez1081]

Mathematicians: “I used the math to destroy the math”

[@hisxmark]

Math is not destroyed. It is a science. It improves itself.

[@caber1487]

@@hisxmark i do fear the day human is no longer able to wrap our brain around maths, that we might hit a "wall", if we have not already had.

[@sajeucettefoistunevaspasme]

@@caber1487 that is not how it works

[@larrycarter1192]

0 is like infinity and infinity and is like 0?

[@goodgoyim9459]

@@hisxmark race and IQ proves many things regardless of what you want to believe lots of anti science ppl here. odd.

[@voidentity4295]

This is so beautiful! Thanks for being one of the people that helped me truly discover mathematics. I grew up hating math, but thanks to mathematicians, physicist, computer scientists and programmers here on youtube i have grown to really love and appreciate the subject.

[@jasonevans4970]

When you put it like incompleteness it sounds negative, but I think that the fact that mathematics is essentially endless is incredibly hopeful, when viewed as a human activity.

[@Zenovarse]

I mean when you view it that way then a theorem can absolutely be complete and consistent and decidable. A system that assigns true to every statement in inherently complete and consistent and decidable. Even a system that assigns the value to be an oracle that is possibly obtained tomorrow is consistent and complete and decidable - all undecidable problems are simply deferred.

[@Zenovarse]

All Gödel proves is the symbols not, and, or, sets and whatever logic used to manipulate those are incomplete.

[@MindForgedManacle]

@@Zenovarse Well, not quite. Basic logical systems of propositions are complete. But once it's got the machinery to encode number theory then yeah.

[@Zenovarse]

@@MindForgedManacle WDYM? If you write your logical system as propositions in your logical system, Gödel shows either it will not be complete or not consistent?

[@Zenovarse]

@@MindForgedManacle a kind of a trivial system that works is a system that has 1 statement, corresponding to the system validity is true. But in a non trivial system like the ones we use it is not the case?

[@TylerJaneBronson]

Seeing the game of life running inside the game of life gave me goosebumps. Had to pause for a minute to digest that. Just beautiful!

[@sherlockmaverick]

Where?

[@RAMBO14001]

Just like the human dimension...

[@Touay.]

@@RAMBO14001 It's simulations all the way down ....

[@Alex_Hetherington]

So wait... if the camera kept zooming out on the game, it would continuously be simulating itself?

[@GaganpreetSinghKapula]

Same feeling 🤩

[@tlewis84able]

I can’t decide if I’m smarter or dumber after watching this.

[@cjc722]

The smarter you are, the less you know

[@YavNe]

@@cjc722 The smarter you are, the more you know. But the smarter you are, you know that you know less.

[@janmango4692]

@@YavNe This is at the core of the Dunning-Krugereffect.

[@joaogabriellucas1865]

You are both, that's the lesson 😉

[@Ou8y2k2]

Both; it's a paradox.

[@gregorypaul3677]

I’m going to act like I understand this video

[@jannelukaswessendorf4672]

great work. definetly have to rewatch this more than once to understand, but it's a great video.

[@kaushu42]

The moment he showed the game of life running inside the game of life, I was totally blown away. Such a mind bending topic to contemplate.

[@frazzled5791]

I felt like i was going to start crying!

[@pushparahi5681]

What game? Can you mention time

[@Mackak_]

@@pushparahi5681 around 30:00

[@albanana683]

I wrote an implementation of Game of Life as an A level project on a Commodore PET. I had to use machine code as BASIC was too slow. I got a bad grade compared to others in the class who wrote simple stock entry systems, as the teacher didn't understand what I was trying to do.

[@kaushu42]

@@albanana683 That sounds great! If only this video was available back then, then the teacher would have definitely given you the best grade. The game of life is awesome.

[@LordofReason-cd8ug]

This is one of those videos where I know what he's talking about... But I also dont know what he's talking about.

[@lordgod7269]

Its unprovable lol

[@alberteinstein3612]

Ahhh yes quite the contradiction Now prove it

[@whitewolf3014]

I know what you are saying... but I don't know what you are saying!

[@Excalibursin]

+Cheesy Boi Basically there are several mathematical proofs that mathematicians made. The bulk of these mathematical proofs is setting up an entirely new, imaginary system of math, or numbers or letters etc. In the end, it turns out that none of these systems can ever resolve the following statement: This statement is false. Because of this, any system of mathematics or language that we know how to create will always have unsolvable problems.

[@alrightyru]

@ 23:42 he says about the Turing Machine "...although this sounds simple..." ..um, No 😬

[@tetraphobie]

This is a fantastic video and the best explanation of Godel's incompleteness theorem. 👍 👍 for showing how it relates to the halting problem, too. I wish I had access to your videos back when I was in college trying to study engineering. I find them truly inspirational.

[@rafaelubal]

Amazing video. I'm very impressed about the quality of this content; through and deep, yet approachable. Congratulations.

[@shubashuba3978]

Godel really woke up and said "i'm gonna ruin this man's whole career".

[@Kirmeins]

He failed... I mean... I've heard Hilbert's name propably a thousand times but this video felt like the first time I heard about Gödel. And I'm from Germany... :D

[@guifdcanalli]

@@Kirmeins its a joke my dude

[@bibi1338]

That's probably because you're from Germany and Hillbert was german. I'm from Austria and I heared about Gödel way earlier and lot more than Hillbert.

[@DonVigaDeFierro]

Gödel could have nuked the basis of formal logic, for all I understand.

[@camrouxbg]

@@Kirmeins even if you're only studying mathematics, you won't really hear Gödel's name until final year of undergraduate study at the earliest, unless you do an awful lot of advanced reading. Hilbert, on the other hand, has his name scattered throughout undergraduate and graduate topics in mathematics and physics. Gödel's work is considered fairly esoteric and difficult, while Hilbert is more spread out. So it's not surprising that you wouldn't have heard of Gödel if you haven't touched on foundations of maths.

[@wordedjewel5629]

Engineers be like: "Does is work tho?" "Well yes, but if you look closel..." "Then yes"

[@andres91cr]

Word

[@amanawolf9166]

Two principles I follow. KISS and IIWIAS KISS = Keep It Simple Stupid IIWIAS = If it works it ain't stupid

[@fftere]

@@amanawolf9166 that's enough for me, let's leave the puzzles for those who can bother

[@thephantommarauder7748]

Mathematicians: Start crying uncontrollably*

[@jdotoz]

@@thephantommarauder7748 Don’t look at the way we do trig.

[@wojciechlawniczak645]

The quality of this documentary is astonishing. I wish I had access to such materials as a kid, actually I felt like a kid again for over 30 minutes

[@andynguyen6668]

I watched this in high school in 2020, and I did not understand a thing and thought it was really uninteresting. Now im watching this again in college, and while Im taking my first discrete Math class(Berkeley's CS70), I now understand and find everything interesting!

[@nerd2544]

same here a single CS semester course of discrete math + another foundational course on proofs, logic, sets in my math minor and boom everything in this video is familiar and understandable

[@ethang.9116]

Veritasium: “Math has a fatal flaw” Me: So that’s why I failed my math test

[@enveloreal]

your math test failed you

[@Starstruck8970]

Bruh

[@heyeso]

@@enveloreal True, It denied the possible that your answer is concrete and relevant

[@iamshane4960]

@@enveloreal You are not taking a math test, but rather the math test is taking you

[@sharonolsen6579]

"Math has a fatal flaw" I believe this was my repeated assertion for the entirety of my school years... ; D

[@EdgyShooter]

Meanwhile in physics: "Can you prove this statement is true?" "I'm just going to assume it is and continue from there"

[@bugdracula1662]

I mean that is how the halting problem works

[@TheOriginalFaxon]

A lot of why we do what we do in modern quantum theory (physics, mechanics, gravity, etc...) is entirely based on knowing these principles as well. Once you establish that there are some things you may never be able to prove, you can assume that if your model is in fact flawed, you will be able to prove that it is flawed eventually with enough evidence and research or computational power, or the correct real world simulation that answers the question, just as everything in this video was more or less shown conclusively (except for the things which conclusively couldn't be, because yay uncertainty principle). If your assumptions are in fact correct, it should actually be easy to prove they are, even if you don't know WHY they are. There are actually numerous technologies which we know work, but have no idea why, and the same goes for systems within the human body and specifically the nervous system in particular. Some of the imagery you'll see or otherwise experience mentally, while on psychedelic drugs like mushrooms, LSD, DMT, and even dissociatives like ketamine and phencyclidine, match up with the kind of fractal geometry you'll see when you feed certain known mathematical patterns into a computer visualization system. On some level our own brains may in fact be Turing Complete computing systems. I suspect as we go further and further with the research into neural networks, and simultaneously try to properly understand the method of functioning behind the biological computer we all use to think, which simultaneously gives us our sense of self, and the ability for meta-consciousness, the ability to be conscious of one's own consciousness. You can dive off the deep end into theory all night on that one and at the end you'll be even more confused than you were when you dived in to begin with, what with everything you learned, but someday somebody is going to figure it out, and completely revolutionize the world yet again. After the ascension of quantum computing, that will most likely be the next major computer revolution, assuming they don't happen simultaneously in some ultimate singularity event.

[@joseromero99]

@@TheOriginalFaxon a00

[@Number6_]

This is why physics has become more of a religion than a science. This is why these branches of physics haven't seen any progress in the last 70 years.

[@ChristAliveForevermore]

Physicists rarely question whether or not they *should* assume such and such to be true in the first place. Einstein at least had an axiomatic criteria (least number of assumptions in the simplest possible form which frames the most general kinds of problems). Even then, his long talks with Gödel likely helped him to come to terms with the fact that axiomatic (assumptions-based) mathematics which has prevailed for 3000 years is fundamentally flawed.

[@samvegsharma2675]

i literally clapped in a room I was alone..For the great men on whose shoulders we have build the modern scientific and technological world... Kudos to those scientific minds mentioned in this video...

[@Cpt_John_Price]

Man you are overreacting.

[@DJGaming-co4il]

You clapped, but while you were alone?... Does that mean you just clapped ursel-

[@aarushi129]

mathematics is so beautiful. i loved the way you were trying to explain the godel's number. having never heard of it before, i found it even more exciting.i am planning to persue a career in mathematics. would surely come back to this video once i have actually studied about it.

[@camtono]

My brain initially melted with the infinite hotel rooms and now it's leaking from both of my ears

[@Neal_Schier]

I hear you...

[@alex0589]

I failed maths at 14 years old and never got any other education. My brain sublimated in a cloud of pink fog that came out my nose

[@CronosTsHastaroth]

@@alex0589 You should try again. The key for leaning is not give up. It's hard and tedious, but the feeling of understanding something is indescribable.

[@FatedHandJonathon]

@@alex0589 You didn't fail maths, maths failed you. It's an epidemic in curriculum worldwide; math is perhaps the most consistently mis-taught subject. Like Neto Fransisco above, I encourage you to give it another go. If you're willing, I can recommend the KZbin channels ViHart and 3Blue1Brown, along with the book _Burn Math Class (And Reinvent Mathematics for Yourself)_ by Jason Wilkes. Understanding math is not nearly as hard as school has led you to believe. With the right teachers, it's the single most intuitive subject you can learn.

[@masternobody1896]

trying upgrade your brain to infinite brain it will be easy to understand

[@temiolu3049]

OVER HALF AN HOUR OF CONTENT, youtube> TV any day

[@Medan1993]

and here I am, watching this on TV ;)

[@AxxLAfriku]

WOAH WOAH WOAH!!! Let me get this perfectly straight: You comment something that is completely unrelated to the fact that I have two HAZARDOUSLY HOT girlfriends? Considering that I am the unprettiest KZbinr worldwide, it is really incredible. Yet you did not mention it at all. I am VERY disappointed, dear te

[@LeventK]

@@AxxLAfriku Are you OK?

[@nothuman5335]

@@AxxLAfriku what

[@halfblood7]

@AxxL Some types of madness are beyond the limit of infinity

[@JinHansson]

I read a book that introduced Gödel's theorem and didn't quite understand how mathematical statements were supposed to be expressed as numbers, but this video worked wonderfully on that.

[@mathematicalpoetry4066]

What a conceptualy beautiful video illuminating a wonderful part in the aesthetics of thinking.

[@alexander1989x]

When he showed "It's the Game of Life... running on the Game of Life" it literally blew my mind.

[@ritwikism]

Can someone explain that better? It was cool but I think I don't fully comprehend what is happening

[@amineabdz]

@@ritwikism he put an input in the game of life that it's output, instead of random patterns, was the game of life itself.

[@guack1453]

@@ritwikism they basically built a computer on the game of life that runs the game of life

[@cookiecan10]

@@ritwikism Since the Game of Life is Turing complete, that means you can essentially program anything with the Game of Life. At 29:50 they zoomed out to show how someone had programmed the Game of Life inside of the Game of Life. The idea is somewhat similar to simulating a computer on a computer, like a macbook running a virtual machine of that same type of macbook.

[@ProfezorFirdaus]

@@cookiecan10 hence going back to Derek's first answer: Life. If life is turing complete (which it must be), there must be a way to fully simulate itself

[@scp_researcher953]

thats byt far the best way anyone can ever conclude a study session. Like you professor

[@empty-o29]

This has to be one of the best videos on the internet.

[@Linuxdirk]

So Gödel basically said “The next sentence is wrong. The previous sentence is true.” but in a super complex and complicated way.

[@digama0]

The hard part is defining "the next sentence" and "is wrong" using + and * on natural numbers. From a modern perspective, Goedel numbering is pretty obvious (you can encode any string of characters as ones and zeros since this is literally what computers normally do to store text), but all of these ideas were appearing around the same time. (The trick with using prime factorization encoding is stupendously inefficient and also somewhat complex to express, but it is easy enough to motivate if all you have are natural numbers and + and *. This proof has since been considerably streamlined, but the ideas remain the same.) Also, it's not "this statement is false" (which is the liar paradox which leads to an outright contradiction) but rather a slightly weaker statement "this statement is not provable". If the system was complete, then "provable" and "true" would be the same so the liar paradox would result, hence it ends up being an argument for incompleteness instead of a paradox.

[@honourabledoctoredwinmoria3126]

The Liar's Paradox was already known for thousands of years, but it itself wasn't a proof of incompleteness any more than Russell's Paradox, as you could just say such a thing isn't math. Anything immediately nonsensical like the Liar's Paradox, you just don't care about. But math is still able to prove every true statement you want to prove from basic axioms. But what Gödel showed is that saying a statement ends up as the liar's paradox is something that you could and necessarily need to construct. It is a statement that results from using only things that are indisputably math, the natural numbers and arithmetic operations. There's no way to get around paradoxes by saying you can't express "This statement is not provable" in math. You can't even define "This statement is not provable" as not true or undefined without having an incomplete system.

[@digama0]

@pyropulse Goedel's incompleteness theorem is pretty general but has some asterisks on it. FOL is complete and consistent, but it on its own is not expressive enough for the natural numbers and + and *. You have to add axioms, and with those axioms (e.g. peano arithmetic) the system stops being complete. Another asterisk in the theorem is that the axioms have to be recursively enumerable; otherwise "true arithmetic" = "add axioms for every true statement" is also complete and consistent, but you can't enumerate axioms so Goedel's proof doesn't work.

[@celestrius9197]

I'm pretty sure I've seen this video twice already and godels paradox still seems like gibberish to me tbh.. I admit I'm not well versed in advanced math but i understand logical applications. I only ask this cause obviously people have recently responded to this comment who seem to understand it. Am I crazy for the fact that godels paradox just comes off as trying to apply something that doesn't seem to apply to make a point? Like the hotel paradox of infinity makes sense but godels paradox comes off as an ass pull to me I don't see where the math logically made his point

[@celestrius9197]

I'd like to add to why it confuses me.. I get completeness and consistency but what I don't understand is how choosing specific things to represent others (not yet proven math) and then proving it eventually failed... proves "proven" math wrong.

[@pixelseeker]

Seeing that "game of life" running inside "game of life" gave me goosebumps .... inception seems like child's play infront of it. The dislikes to this video are from people who are watching it sitting/standing upside down.

[@MolecularMachine]

Agreed. It's like watching videos comparing the scale of astronomical objects.

[@EGRJ]

It's like watching videos of Minecraft made inside Minecraft. Which several people have done, apparently.

[@alvydasjokubauskas2587]

And I thought, well if Windows exists inside Windows due to virtualization, and you could even run deeper layers, than it doesn't surprise me, that math's followed the same logic... A paradox that is working, by self referencing itself...Which gave birth to computers...

[@howard8438]

I didn't get that bit, I thought the game of life was essentially a set of rules, so what does that mean to see those rules running on those rules?

[@StraveTube]

I physically exclaimed "OH DEAR GOD" and my wife heard me from the other room and yelled "oh no, what's wrong??" It's okay, she knew what I was watching and I just shouted back "MORE MATH" and she knew what was up.

[@DavidHarrisActor]

Excellent ancillary to Hofstadter’s “Gödel, Escher, Bach” Thank you!

[@astro_penguin_]

I thought so too!

[@jaianeguimaraes129]

Bro, the flames you are lighting in my heart with these videos... Thank you so much

[@jherbranson]

I have to admit, seeing 'the game of life' running 'the game of life' was impressive. That's mind blowing.

[@AleksandrStrizhevskiy]

Yeah, out of the whole video that part blew my mind more than anything else.

[@uttie3408]

Wait. If the game of life can run its self, then the game of life will run its self that will run itself that will run its self... (edit) ...and so on.

[@jherbranson]

@@uttie3408 I actually think it would be worth the effort to build one more iteration on top of the two. Perhaps I'm being unreasonable.

[@HassanAhmed-rf9xr]

@@uttie3408 I dont get it is the game of life something that can run itself infinitely. It's just confusing tbh.

[@danielb270]

@@HassanAhmed-rf9xr you can write a computer program that simulates every computer component (that is what is called emulation), and you can make this emulated computer run windows with the same program running in it. this is the same thing: every next level of emulation requires large amount of setup, and takes a very long time to execute. but a turning complete system is not difficult to simulate: all you truly need is a way to do if-then and store a state, everything else (operating systems, games, hardware drivers, is just built on top of having a set of instructions in the memory modifying the memory and choosing between 2 option based on the memory)

[@nickfosterxx]

I suspect that for many people, making this video might be considered a lifetime achievement. But for Derek, just one more brick in his incredible, historic castle of outstanding teaching.

[@Avisha_Jain]

Yeah fr

[@garmind4868]

look closer at the bricks composing the castle what are the bricks composed of.

[@Zeru64_]

Derek: "... But for me, it was Thursday..."

[@barneyronnie]

I suspect that you are one of his groupies.

[@leowalan5463]

If only he is my math teacher or history teachers

[@priyanshuvettori5179]

I am really happy and shocked at the same time. How does a topic like this have 25 million views, because mostly these kinds of videos are never promoted by KZbin.

[@johnrobinson1916]

It is important to note that in the "incompleteness theorem" that even though it is possible to create a "well formed" statement within the context of a specific axiom system, that may not be provable within that axiom system, it does not preclude proving or disproving the statement in a "larger" axiom system . Some problems formulated in the context of geometry may not be provable with axioms of geometry, but may be provable in the context of algebraic geometry.

[@judypetree2589]

I'm 75, female; I am grateful that I have had enough education to have at least heard of the people you reference. Awed that you explained it all so well that I could not stop listening. Lastly, so proud to have lived this era from beginning to undecidable end.

[@carealoo744]

I get my education from youtune videos:)

[@kebekbutcher]

@@carealoo744 Self education is better than forced education! Have a good day!

[@palashrajput428]

@@kebekbutcher well said

[@scoogsy]

So awesome to have people of all ages getting so much from these videos. I’m 38 and make, and have watched Ve videos for what feels like a decade.

[@oreoicecream1829]

I hope you live long and healthy 🙏❤️👍

[@matthewao]

Can we just appreciate how well animated and produced this video is? God, so much effort.

[@unripetomato4312]

everyother youtuber: animates their ideas to make it easier for the viewer vertasium: climes mountain with no context for a nice backround, spends hours making 3 words with a line through them and custom prints an entire set of cards just to express an idea, just to name a few.

[@sunnyjim1355]

Yeah, but that's irrelevant really - I read all this in a book already. It's the information that matters, not how nice it's presented.

[@donegal79]

@@unripetomato4312 He has a big team around him. Its not a one man show.

[@user-feifei03]

hey I recognize you from ut eng

[@fredesch3158]

@@sunnyjim1355 Uhhh... no, actually no. You, me, and a lot of other people may find it easy to understand written, objective, and scientific language, but many others don't. Some people understand artistic, subjective language easier, some others understand abstract languages easier (like the way sounds and colors relate, and "talk" to each other, like people who know how to use colors to tell a story, or people who write melodies, etc.). So probably a lot of people have a hard time with the math and stuff, and to help them have as fun as we have in this beautiful world of math, people (like veritasium) adapt the math to a more visual, artistic language. Your lack of empathy for people's different necessities helps no one, showing off you read books helps no one, belittling other people hard work helps no one. When you understand that reading books is just one of the many valid ways of acquiring information, and it doesn't make you "cooler" or "smarter", you'll definitely cringe looking back. :)

[@FelipeVRigo]

Blowing our minds. I love to watch your videos, because I always have something to learn.

[@germanic4316]

Excellent video/audio presentation and explanation.

[@Djaytaur10]

Hilbert: I proved everything Goudel: I am about to end this man's whole career

[@msew]

lolololololololol

[@GabrielLima-gh2we]

Actually no, Hilbert didn't proved everything, he created a system of proofs, a formal way to prove everything in mathematics and every other field. On the other way, Gödel didn't want to disproof all mathematics, he proved that not ALL mathematical statement can be proven, that is, there will be always some true statement that we will not be able to prove, but still there will be mathematical statements that CAN be proven, till this day we prove new and old mathematical laws, the problem is we can't know which statement can be proved or not, we might not find the answer right now and say that it is unprovable and 500 years later someone prove it, it is just undecidable, that's the point of Gödel's study.

[@utkarshsaini5650]

@@GabrielLima-gh2we ikr

[@edwardhuang5885]

Godel: Can you prove yourself tho?

[@gabriellarosa7159]

@@edwardhuang5885 Descartes: Yes

[@SuperStingray]

Gödel: *Thanos Voice* "I used the math to destroy the math."

[@DarshanGowda]

You deserve more likes!

[@advocatesagainstabuse3556]

My absolute favorite mathematics professor, whom interestingly was 'merely' teaching precalculus at a 2yr community college began his course with various proofs which illuminated apparent flaws in mathematics. I

[@ryaaa__05]

😂😂😂

[@voicelikemanywaters1017]

except the destruction didn't destroy it.

[@pandakekok7319]

@@voicelikemanywaters1017 Bruh, did you just started another paradox

[@austinhixson625]

The game of life creating and destroying as it keeps iterating is one of the most incredible examples of the beauty of mathematics shown visually. Seeing all of the different patterns it creates is so cool

[@anonymous5405]

We are blessed to have extraordinary people like this carrying the rest of us into the future.

[@danesorensen1775]

"Poets do not go mad, but mathematicians do." G.K. Chesterton.

[@dara_1989]

poets accept flaws 👍

[@zeitlichkeit5094]

Very true. Ultimately it seems life is more like poetry and less like mathematical or logical certainty.

[@alexvidzup9076]

@@zeitlichkeit5094 language is poetry and language is human made. Anything human made assumes that we know something to be true so even talking about maths leads to proving it wrong. That’s me negotiating a price reduction

[@alexeyvlasenko6622]

Plath, Villon, Wyatt, Wilmot, Byron, Crowley, Shelley, Pushkin, Lermontov, Swinburne, Chesterton, Baudelaire, D'Annunzio...

[@jbolanowski1]

@@zeitlichkeit5094 not sure if it's true, but as a romantic by nature i have to give you like :)

[@Moersfreak]

For me, the biggest takeaway of the whole thing is this: how amazingly smart must Gödel have been to come up with that proof? Obviously, every other Mathematician mentioned here is also incredibly, incomprehensibly smart, but with the other mentioned proofs, I can kind of reconstruct how one might have arrived there. But with the incompleteness theorem, I just cannot fathom how one might come up with it. The guy must have been able to just straight see the matrix.

[@linkinlinkinlinkin654]

He was only 25

[@tomwanders6022]

@Markman Dave Thanks a lot bud I have been in an argument with my brother and we clearly defend different ideas, I should probably do the research on it my self. Though it’s not completely about math only partly. Where arguing about videogame strategy, where when it comes to math we usually agree, but if it comes down to different strategies were clearly on different start ups we are clearly on different opinions.

[@ValMartinIreland]

It's cods wallop. Has anyone commenting here ever studied probability? In all scientific claims you must provide the figures to back your claim. That is not done here.

[@david-776B]

@@ValMartinIreland Are you referring to the video? Or the comment? Or someone’s reply to the comment?

[@kaia1962]

@Markman Dave While it's true that groups limit one's freedom, they also expand it. If there are no other people one would be one's own input and output. This would mean we'd never get other information besides the ones already existing in one's individual system. Thus we'd be systems of stagnation. On the contrary, the more people we listen to, the more information we can get. Especially if the others have a different point of view. Thus we have a lot of contradictory Information we can work with. Or in other words: "We have an abstract horizon". With this we not only have the chance to solve the contradiction, but also a synthesis. Whether a group is beneficial or obstructing for an individual, is based on the structure of the group and the level of self-confidence of the individual. Being self-confident means to stand your ground, but also being able to reflect on the critique. Only then you can find the most differentiated solution for your time. 0nly then you can build up on the horizon of your critics and convince them.

[@yellow_tone]

Wonderful! You should definitely do something about math and music. Pythagorean comma and string theory. This is also touching on the subject of infinity and our human perception of finite things hence we had to come up with the tempered tuning equal temperament on a piano which is really a compromise to make our western music harmonics work

[@A.C.C.]

Fantastic, one of the best video I have never seen. Well done.

[@tux1468]

"I'm right" "Okay, prove it." "I can't"

[@monkestronk1227]

Prove that you can't

[@richaellr]

Trust me

[@joundii3100]

@@monkestronk1227 Prove that you can prove that you can't prove

[@jamesmonroe3043]

Is that you Al Gore????

[@jaystarr6571]

Said every YT comment ever.

[@deepg7084]

I have never felt so dumb and fascinated at the same time.

[@OnideusMadHatter]

I'm high and I got to 1:05 and got bored. I'm assuming he's going to start yammering on about the "curse of dimensionality" or the mathematical equivalent of Bible codes... look, we get it, the more of something you have, the more combinations that are possible, until eventually nearly EVERY combination is possible... which is how PASSWORDS work... really not that complicated or exciting.

[@burakahmettr8193]

@@OnideusMadHatter you ill never now if you dont watch

[@OnideusMadHatter]

@@burakahmettr8193 - Okay, I'll watch it. *watches it* ...tha'heck was that?! That's not how you do it! WHAT IS WRONG WITH YOUR SPECIES?! *sigh* Let's start from scratch, or at least what I can vaguely remember from some other reality's remedial education system... You can think of mathematics as being like states of matter, like solid, liquid and gas. The more accurate a mathematical framework is, that is, the more complex its rules are, the less chance you run into conditions of mathematical discrepancies or flaws (paradoxes), but at the same time, the more complex you make it, the less useful that mathematical framework becomes because, although highly accurate, it's dependent on very exacting environmental conditions and as such can't be easily used or applied to other environments or systems. Some mathematical frameworks are more liquid and free form, sometimes decreasing the complexity of the framework and in turn increasing the complexity of outcomes. With forms like quantum physics being the gaseous form of math, where there isn't enough known information to make a solid or even liquid framework and in turn when applied to the environment, the data obtained is spurious at worst and imprecise at best. The POINT is that Math can be treated as a kind of living tool that you can "evolve" into an unknown from the proverbial gaseous state to a more solid state. Math sometimes uses VARIABLES, but a variable is NOT the same as an UNKNOWN. That is, in any mathematical framework, there will be unknown factors that arise simply as a result of perceptive restrictions or working restrictions. That is, either the variable recording isn't accurate enough, or the modeling is too slow to be useful without making the mathematical framework more simplified or fuzzy. To put this in simpler terms, in algebra you can't use an unknown as a variable because it might not be a static variable... it could change temporally, which in turn would create multiple, conflicting outcomes from the same system over time... mathematical discrepancy if you like. Or the use of "variable variables". Math can never be complete because there are an unknown number of unknown set conditions. Or an "unknown unknown". ...okay, tired now. Maybe tomorrow I'll talk about "manipulative math"... there's no degree for it in your schools... they'd be too terrified to teach it to you. But I will!

[@Lor00D]

facts

[@OnideusMadHatter]

@@AvntXardE - Okay, but what about infinities? Like, you have static infinities and then you have incremental infinities or temporal infinities. Do you have a branch of math where THOSE are used as variables?

[@dragomirdespard974]

Only thing I regret right now is not having watched this video sooner. I kept putting it off for a while, often for the fear of not understanding Godel's stuff. Thankfully, Veritasium has done such an amazing job of explaining. This is probably the best video I have watched in my entire life so far.

[@ChiefKeefSA]

Tone is sick dude - keep it up 👍🏻

[@briandermody89]

Godel: Want to play a card game? Me: Um, I'm good.

[@babaranwar5462]

Or are you? *Moon Men by Jake Chudnow (the Vsauce theme song)*

[@goose5462]

Me: nope, your weak ass logic just makes you look pathetic. Anyone with basic intelligence can create logical paradoxes.

[@securityresearcher3336]

Your reply was great. Prefer going to Who Wants To Be a Millionaire!!!

[@NerdWithLaptop]

Me: sure! (Like an excellent card shark, slips out card “g”

[@pirojfmifhghek566]

My first instinct would be to assume that the battle between Intuitionists and Formalists couldn't have been that dramatic. But then I remembered that there was an actual riot featuring thrown chairs and fistfights on opening night of Stravinsky's Rite of Spring over the timbre of the bassoonist. Man, nerds back in the day were hardcore.

[@HebbY_]

They still are. It's just harder to hide a murder

[@fftere]

Reading this really depresses me, how far we've fallen as a civilization. Look what we used to fight for, the greek requirements and essays about Virgilio just to enter universities, the academic debates in the common tongue, intelligence as something more than an industrialized misconception of public education ("nerds"), our music sensibility, etc. The idiots took over (I know, I'm one of them), the grandchildren of the Revolution, the City of Men, Rome.

[@mothra3477]

The fighting on the opening night of Rite of Spring was about much more. It is a very visceral work. It features a very unconventional choreography, with violent and sexually suggestive movements (far from a more traditional ballet, like the Swan Lake). The music itself is rather dissonant, and uncommon for the time. And, on top, it's about the ritual sacrifice of a virgin. Groundbreaking and controversial art always generate strong reactions; against and in favor. I would totally fist fight someone over the rite of spring. It's so riot worthy. And I think it's great if people are passionate about things and are willing to take stuff like music or math this seriously.

[@666Kaca]

@@fftere The hell does rome have to do with anything? Also you think we've fallen as a civilization? Elaborate.

[@thetrickster9885]

@@fftere wtf Drink some vodka dost

[@JohnKooz]

Agreeing with other praising commenters, I agree this video introduces and explores some of the uncertainties in math and computer science, but it concluded with an optimistic light. Thanks! Another great one from Veritasium!

[@ANSHULVERMAResScholarPhysicsII]

This has to be the best mathematics video on YT, watching this 5th time in one year

[@MrEmayhew]

“We must know - We will know” And we do know. We know that we cannot know. And that is still knowing.

[@jakubdaraz4138]

Socrates :D

[@JasonJason210]

Isn't that a contradiction 😜

[@nias2631]

@@JasonJason210 its kind of like knowing the empty set.

[@j.dragon651]

I think, therefore I am, I think?

[@KasumiRINA]

@@j.dragon651 you've got another think coming!

[@seanboyize]

One thing I take away from mathematics and the objective direction of absolute truth we use it as a guiding tool is the philosophical creativity pushing it forward as well. The evolution of mathematics alongside our development in civilization and technological dubs is something I didn’t really appreciate or enjoy until after I finished my undergraduate degree. I was very averse from mathematics for many reasons but now I really appreciate the precision mathematics provides for us as a species and the similarities in linguistics when you begin to really wrap your mind around our understanding of physics

[@tonylikesphysics2534]

This video was amazing. I wanted to comment specifically, but learning Alan Turing killed himself and the circumstances surrounding that just destroyed me inside. I hope he rests in peace 😢

[@XavierBergeron]

Seeing the game of life being carried out in the game of life was a really impactful moment in this video

[@funkerdoo]

FACTS, i don't know how to explain it but that was mind blowing

[@a2rhombus2]

I actually cried. I'm not sure what came over me.

[@dumnor]

You can actually find files with game of life running on game of life that is in turn ran in the program. So its game of life all the way down.

[@soulhacker63]

I was reading about it 2-3 months ago so I my self made some patterns.... But then it because headache..... And not after watching this video I got to know why it was a headache....

[@remivreuls6034]

So the game of life can run the game of life but that game of life can run another game of life but is the original game of life running on another game of life?

[@Alex-nx5wi]

This feels a bit like a philosopher taking an engineers job

[@megamanx466]

Or when an engineer becomes a philosopher. 🤔

[@gdpvk]

It's actually mathematician proving a math job.....even though its not a math expected in Ur bank balance

[@specialknees6798]

Math pretty much is philosophy

[@TheJanitorIsIn]

I'm not certain which came first, but certain branches of analytic philosophy use the same forms of notation and logic, and a lot of it really has this same feel, in reverse.

[@inyobill]

@@specialknees6798 I was thinking much along the same lines (Maths = Philosophy). Any difference in my thought is inconsequenttial and adds nothing to what you said.

[@tamirlanger9479]

Thanks Derek, I *LOVE* your videos, and this one was no different!