Math Has a Fatal Flaw

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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.


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

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

Written by Derek Muller, Adam Becker and Jonny Hyman
Animation by Fabio Albertelli, Jakub Misiek, Iván Tello and Jonny Hyman
Math City Animation by Another Angle 3D Visuals (www.anotherangle.ee)
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music and SFX by Jonny Hyman Additional Music from Epidemic Sound
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett
Associate Producers: Petr Lebedev and Emily Zhang




21 May 2021




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Amecha 7 aylar önce
So basically... Can math prove itself? No. But math can prove that math can't prove itself.
Sunil Gangwani
Sunil Gangwani Gün önce
@FOR Vpbof-20 It proves you have a head. Simple.
Sam 5 gün önce
Nope, it's logic. That is not exclusively math
David '06
David '06 7 gün önce
Veritasium has commited a logical fallacy
Gerrie van Boven
Gerrie van Boven 8 gün önce
@Charlie Christian No, just like any other paradox, it's merely a lack of understanding the question, rather than the answer.
Charlie Christian
Charlie Christian 9 gün önce
Lol so should we ostracized and attempt to do away with all signs ofathematics just because it requires faith to accept the things that it proposes.....
John Johnson
John Johnson Aylar önce
Fun fact: Einstein and Godel were close friends. Einstein once said later in life that he kept going to the Institute for Advanced Study (where they both had a position) just to go on walks with Godel. Godel once found a solution Einstein's field equations that he presented to Einstein as a birthday present. There's also a funny story where Godel applied for US citizenship, but his paranoia led him to conclude that the US constitution is inconsistent and allows for a dictator to take power. He then tried to present his discovery during his citizenship test, but the judge, a friend of Einstein, thankfully cut Godel off.
Attila Seyfullah
Attila Seyfullah 13 saatler önce
@Saaber Shoyeb pulling out is a good thing but it was a rout. Trump was pulling out of many areas in a much more balanced manner. Although as a Muslim, I am glad that Sharia is now law in Afghanistan.
Attila Seyfullah
Attila Seyfullah 13 saatler önce
Democracy as a concept comes with it's optional self-destruct button. If you want to make sure that button is never pressed, you would have to commit undemocratic actions. In Turkey, what I mentioned was somewhat used to justify the 1960 coup that overthrew a democratically elected administration and manufactured a new democratic system. It was accepted as common narrative that a coup can be justified using the argument of the self-destruct button. Now it is believed to be unjustifiable. Which makes more sense. Wether you like the outcome or not, if you truly support democracy, you must allow the system to self-destruct democratically if the people wish to do so.
Angel bass
Angel bass Gün önce
Amazing story!
PegDowncom 3 gün önce
@Anna well said
Birkenwald47 4 gün önce
...just to go on walks with Gödel ??? Sehr unwahrscheinlich!!!
Darduel Aylar önce
I can't get over how good this video is.. I'm 3/4 into my Introduction to set theory course as a math major and I have watched this video before the semester and rewatched it now and it just explains so many advanced concepts (that aren't even in my course) so good it is incredible
Accountability Partners Community
This is a great video because most people who aren't deep into math or studying at university never get these problems under their minds. These problems and issues with artificial intelligence programming in computer science are what initially led me into philosophy.
;ن; Gün önce
But as a 14 yo, I think way too much of this that it s destroying me. It distracts me from my real life because of all the random deep thinking moments. Idk if that's a good thing 😕
Accountability Partners Community
@Jordan Eisenman I'd be interested in more details regarding your areas of interest.
Jordan Eisenman
Jordan Eisenman 4 gün önce
And philosophy led me to math and data science. Weird how they wind together.
jameson44k 7 gün önce
@Kevin Austin No and no, learn mathematics instead of armchair philosophy.
Accountability Partners Community
@Kevin Austin Do you think Mathematics is more like a science, more like a language, or more like a logical system? Do you think Mathematics is one thing or a plurality of things?
Marc Rover
Marc Rover Aylar önce
I have heard about Alan Turing or the "Turing Machine" at least 500 times in my life. And, this was the FIRST TIME anyone EVER mentioned how his life ended. The guy saves countless lives, and because he isn't attracted to females, they destroy him?
Jhenoah 3 gün önce
Yeah, I was pretty neutral on gay rights, but this was a major window of reconsideration. It was a really big tragedy what happened to him.
Guilherme 6 gün önce
Britain in the 50s looks as barbarious as old civilizations.
Karl 9 gün önce
@Art Donovan About him yes, but even I've noticed that untill the last decade and a bit, any story involving him rather than focusing on his life, generally omitted the parts that this video and The Imitation Game handled well, I only really knew as early as I did as I was told by others in the LGBT communit. I've found most documentaries, even British ones from 15 years ago plus and still some TRvidrs now, generally don't mention it unless they're LGBT them selves.
Gabriel Is Ant
Gabriel Is Ant 10 gün önce
@Rehak Mate whats wrong with you
Marc Rover
Marc Rover 13 gün önce
@Art Donovan Yep, never heard of his demise. But, I don't know why that's hard to believe. For, whilst he had a impact on a lot of things, he was pretty consistently a secondary figure. If you do research on WW2, Computers, Free Will, Transistors, or Code Breaking, Turing will definitely be mentioned, but it's not like his LIFE STORY is relevant to those topics. His contribution/education/background is mentioned, and that's basically it. His personal life isn't congruent with those topics.
DoomMantia 8 aylar önce
This is one of the best videos on this channel ever. My brain hurts a little, but I thoroughly enjoyed the experience.
jsalsy 9 gün önce
Definitely more out there to give you headaches if you enjoy them
George Tsitsiani
George Tsitsiani 12 gün önce
Took words right out of my mouth.
Tako Au
Tako Au 12 gün önce
I can’t imagine this 30-minutes video covers one of my major course about finite-state and Turing automatons in college. Natural language, primitive recursive functions and state machines are always my favourite topic!
DoomMantia 14 gün önce
@Peter Codner Way to be needlessly pedantic.
Peter Codner
Peter Codner 15 gün önce
With what organ do you experience the "pain"(hurting) of your brain? Can a mirror reflect itself? It is axiomatic that it cannot.
Ethan Barel
Ethan Barel Aylar önce
This is the best video I have seen in a long time. You litterly blew my head so many times, the video is amazingly made and it is so interesting even for a teen like me who doesn't like school math too much and doesn't know math, school should teach us stuff like this because students will actually have interest in classes
lukkemela 11 saatler önce
This stuff is usually taught in courses like real analysis, discrete math or logic in universities, unfortunately not with all these cool animations :(. The course itself doesn't have so many prerequisites so you could potentially teach it to whoever knows what a limit or an integral is, but it's so difficult to understand certain topics and theorems that if you tried to actually teach these things to every high school student 99% of them would stop paying attention. And you can't explain some concepts non rigorously because it would be a mess to understand correctly what is what. For example you can take the part where he talks about "countable sets". But what does "countable" actually mean? It could look obvious but it's not. If you don't explain it in a formal and rigorous way, you wouldn't understand why Q is countable but R is not. This one was probably the easiest part (since countable is still a concept that you could grasp without formalism), but that's pretty much it. I would recommend to find the beauty in things that you are currently studying. Ask questions to your teacher if you don't understand why something is like that, be curious. You will eventually reach this part of math and it will be great if you will still have this curiosity! Or you can go to TRvid channels like "the bright side of mathematics" (probably the best one that I found so far) and learn those topics right now. If you like the way he explains things and cool animations I highly suggest 3Blue1Brown, another great yt channel!
ahall 8 gün önce
Literally literally literally, you know? Literally, literally! xD
Jayden Lupton
Jayden Lupton 12 gün önce
I literally couldn’t agree more
Vincent Lextrait
Vincent Lextrait Aylar önce
The lineage Cantor->Gödel->Turing has one additional ramification: Rice's Theorem (1951). Wikipedia does not do it justice, failing to give a layman explanation of it. It is a very important theorem which generalizes Turing's answer to the Halting Problem. It predicted why UML would fail, why code verification software is snake oil, why some programming languages, contrary to marketing will remain hopelessly slow... Very useful indeed. Ignoring it has wasted billions.
Vincent Lextrait
Vincent Lextrait 4 gün önce
@Sam ahahahah.
Sam 5 gün önce
Code verification is not snake oil, because they do not verify arbitrary powerful languages and programs but specific ones and they check certain properties. I would discuss this with an expert before making such claims. Theory and need in practice are not equivalent.
Vincent Lextrait
Vincent Lextrait 20 gün önce
@Jimin Park, cannot agree more with you. The extreme promises of code verification tools are the issue. The problem is already in the name.
Jimin Park
Jimin Park 21 gün önce
You're ignoring a key point: a program doesn't have to be perfect (complete) to be *useful* . Rust's lifetime analyser is an example; while it can't *always* prove that a Rust code is memory-safe (hence some theoretically safe codes will not compile without using unsafe blocks), it nevertheless can gaurantee, for some but useful cases, that such code don't contain a bug related to memory-safety. Even this incomplete code analysis tool turned out to be very useful and practical for removing a major class of bugs. It's similar for type systems, code verification tools, and description languages. Rice's theorem does tell that a perfect solution doesn't exist, but it doesn't tell at all that a useful solution does not exist.
KINJAMOV 26 gün önce
@Vincent Lextrait I guarantee that Google employees use sequence diagrams. Maybe they're not officially using all of the UML standards, but there's only so many ways to communicate software design. What's your alternative? Do you just draw simpler diagrams and say they're not UML?
Paul M
Paul M Aylar önce
I'm glad I was an engineer. I learnt to use advanced mathematics to build things but I never had to worry about this stuff thank goodness. I think it's kept me sane.
Tamas Elteto
Tamas Elteto Aylar önce
Hi Derek, As a Hungarian mathematician, I feel somewhat sad because of you missing to refer to Janos Bolyai as one founder of the hyperbolical geometry. Though we know Gauss worked on the subject, he did not publish his results unlike Bolyai or Lobachevsky. Therefore,I would not deem him as significant contributor to hyperbolic geometry. By the way, the stoy where and how Bolyai worked on his theory and how he published it - in short, it became an Appendix (we Hungarian mathematicians respect this word) to a math book written by his father, for which he spent one year of his income - and what was the afterlife of the theory, how it reached the French Academy, would deserve a video on its own, I would say. Best regards, Tamas
kisslas 23 saatler önce
I'm not a mathematician, but this is exactly what I was about to say! Thanks for beating me to it (and putting it much better than I could have). Still an amazing video overall, though. :)
Joseph Pruitt
Joseph Pruitt Gün önce
You have been noticed Hungarian mathematician
Peter Jerde
Peter Jerde 8 aylar önce
There was a brief moment while reading Hofstedter's *Gödel, Escher, Bach* where I felt I truly understood the concepts... This video brought me right back to that feeling! Very well written, presented, and produced! BRAVO!
Victorel Petrovich
Victorel Petrovich 2 aylar önce
@Leah C Checkout Babbage, and others, which were develloping computers regardless of Godel and their math plays. Turing was just one of the many who dabbled into computing.
Victorel Petrovich
Victorel Petrovich 2 aylar önce
@sdfsdgsdfsdf23423423 Yep. Glad I'm not alone judging along similar lines.
Victorel Petrovich
Victorel Petrovich 2 aylar önce
@Jonathon Meyer There would have been much more progress in math if Hilbert turned out to be right about all 3 questions. Computers would have been made anyway, don't worry. (read about Babbage and others).
Wassup Rocker
Wassup Rocker 5 aylar önce
same. exept for the card parts i didn't tried to understand because i remember i understood the puzzle already and do not need to do it again lol (heahach))
Leah C
Leah C 7 aylar önce
@sdfsdgsdfsdf23423423 You make some interesting points; can you elaborate further on your last statement about the technology world flowering in spite of Godel? This video made it seem like his studies inspired Turing and the development of computing systems.
jfxl1977 11 gün önce
This was very enjoyable to watch! I wish everyone would find this sort of thinking invaluable and necessary to better understand ourselves and our world. Thank you for fostering critical thought!
Paul Taborsky
Paul Taborsky 22 gün önce
I"d just like to point out that 'there will always be true statements that cannot be proven' (one of the first sentences in the video) is not quite what the incompleteness theorem actually claims. What it says is that in every sufficiently complicated formal system, there exist undecidable arithmetical propositions. That is similar to the difference between saying 'There is somebody, whom nobody knows' and 'For each person, there is somebody whom they don't know'. Undecidability characterizes formal systems, not particular propositions. Also, Godel never claimed that such undecidable propositions are true. They may be true, but we could only know that if we knew that the formal system they belong to is consistent, and we may not know that.
Peter Codner
Peter Codner 14 gün önce
so "there will always be true statements that cannot be proven' ; so or therefore what? Of what syllogism does that form a premise? Is it not axiomatic that a mirror cannot reflect itself?
Craig Gidney
Craig Gidney 16 gün önce
Yes, one of the particularly mind bending things about a Godel sentence is that you can add the axiom that it is *false* to your formal system, and still get a consistent system. Normally people (e.g. Roger Penrose) consider it obvious that these statements are true, but you don't necessarily create problems if you take them to be false. Another way to phrase Godel's theorem would be... "there's always a remaining degree of freedom in your formal system; another statement or its negation that you can add as an axiom without causing inconsistencies".
BUTCH NEWS Aylar önce
That was good. I had the good fortune to live in a communal house with a math student doing his PhD. I decided it helped to be really weird and a bit crazy to be a math type. His PhD, he told me, was to be about mathematical applications to the forest industry, very useful where we live
Samuel Luria
Samuel Luria Aylar önce
Read a book as a kid in the 80's called Gödel, Escher, Bach, and it really opened my eyes.
Samuel De la Cruz
Samuel De la Cruz 3 gün önce
Dr. Hofstadter is a real genius.
DSUM 6 aylar önce
As a working mathematician, the scariest part of incompleteness is that when I can't solve a problem, I don't know if the problem I'm working on is just really hard... or if it's actually impossible.
D. Jensen
D. Jensen 15 saatler önce
As an engineer, numerical methods saved my sanity.
!MUSHU 11 gün önce
You’re a “mathematician” but still can’t figure out the golden rule? Stop it.
neorator 13 gün önce
But don't just all of those unsolvable problems have the same thing in common: they somehow reference themselves. So by being able to prove that all unprovable problems are somehow selfreferencing you would have a prove for everything
Peter Codner
Peter Codner 14 gün önce
A "working mathematician" in the sense that you are paid to do sums? You experience fear when you cannot what you call " solve a problem"? Of exactly what are you afraid?
Peter Codner
Peter Codner 14 gün önce
@Ern de Che Proven to whom and to what standard?
Alexandra Gouveia
Alexandra Gouveia 24 gün önce
This is brilliantly explained! These problems are what got me interested in set thwory and the axiom of choice! I was lucky enough to run into these when I studied The Banach-Tarski paradox (an interesting topic for a video, if you have not covered it already)! This both shows the brilliance and power of humankind as well as its darkness and self-destruction. Two brilliant minds lost early from something preventable. Turing's case is particularly frustrating and ridiculous. The man literaly saved hia fellow countrymen lives as well as other countless lives. He shoukd be considered a hero, at least for Britain. But no, they drove him to kill himself over the most stupid thing ever, being gay. I don't care it was another time, shiw me where is the logic and humanity in that. How in the world is him being gay in his personal life the government's problem. It is not like he was indoctrinating children or somethin (even then he did not deserve it). Truth is we did not deserve Alan Turing. Britain certainly did not deserve him. And so many others have not had their stories told or their potencial shown. In his very short life he changed the world forever...imagine what he cluld have done if he had not died at the government's hands. And what Goedel could have further acomplished with proper mental health treatment. Deeply saddening.
Conrad Roberts
Conrad Roberts Gün önce
Thanks for reminding me of both the dumbest and nerdiest joke I know: Q: What's an anagram of "Banach-Tarski"? A: Banach-Tarski Banach-Tarski
kc 12 gün önce
@Lil Yeet theory?...sorry?.... spelling error w next to e...thorry...🙃
Dooplon 22 gün önce
@Lil Yeet What?
Lil Yeet
Lil Yeet 23 gün önce
Noname Aylar önce
I cant stop watching this. I actually wanted to sleep. Never ever would i read anything about mathematics, but damn Veri makes it so interesting and easy to understand that it makes me feel good to be able to understand University level of Mathematics.
dkeithtag Aylar önce
The beauty of it is that math prefectly represents its imperfections.
dkeithtag 13 gün önce
The definition of ‘perfection’ is the colloquial one in this discussion. A problem without a tangible solution is perfect in that one’s understanding of the same agrees with the fact;; ergo, a good man knows his limitations.
Peter Codner
Peter Codner 15 gün önce
You plainly have no idea what "perfect" means; it means finished or accomplished, not without flaw- whatever you take to be a flaw. First define your terms.
Peter Codner
Peter Codner 15 gün önce
It may be that what the authors are struggling to convey can be boiled down to: A mirror cannot reflect itself-which is indeed axiomatic.
Adrian Simper
Adrian Simper Aylar önce
An absolutely superb video, as always, but I have to take exception to the title. To describe something as flawed means you must start with a preconception of what something should be, and then find that it falls short against that preconception. To describe the flaw as fatal you must be assuming that the thing has a ‘purpose’ which its flaws prevent it carrying out. Surely we have learnt from Hilbert (and we learnt sooo much from Hilbert), and the experience you describe so well, that mathematics is just what it is. We can discover things about it, but if we have created preconceptions of what it should be like then that’s our problem - it doesn’t detract from the beauty. And if we have intentions of utility then that’s our problem as well (thank you, Hardy). Mathematics can never be flawed. But our preconceptions of what mathematics ‘should’ be often are.
Peter Codner
Peter Codner 15 gün önce
The term for which you may be struggling - and are spot on about preconceptions is "hidden premise." It is a preconception or assumption that borders on religion, which can be defined as any set of related unquestioned assumptions presumptions, preconceptions or norms.
E Fun
E Fun 26 gün önce
The title is click bait, Veritasium jas a video on click bait you might wsnt to watch lol
Brandon M
Brandon M 27 gün önce
Can you elaborate on who this Hardy is and what his contribution to the conversation was that you referenced here? I would be very curious to learn more.
Xavier Bergeron
Xavier Bergeron 8 aylar önce
Seeing the game of life being carried out in the game of life was a really impactful moment in this video
Mateus Ferreira
Mateus Ferreira 3 aylar önce
mohamed amine khadhraoui
It was a really impactful moment of my life in general. Due to the music probably.
Richard Bloemenkamp
Richard Bloemenkamp 8 aylar önce
It is a bit a shame that everything in this video was already quite widely available on TRvid by other people, including Life-in-life. Veritasium adds a great presentation with extraordinary video and visuals. He could add a few more references to the people that made Life-in-life and other modern accomplishments and recognize a bit more that he is presenting other peoples work, but for the rest he is doing a great job.
funkadunkle 8 aylar önce
@Da'Vion Archie this man's on to something....
Da'Vion Archie
Da'Vion Archie 8 aylar önce
It’s possible to make computers in minecraft. So we can assume it’s possible to run minecraft within minecraft
IGN Aletheia
IGN Aletheia Aylar önce
I remembered my Symbolic logic (Russellian logic to fuzzy logic and so on) course from college to my graduate degree. Damn I didn't know the philosophy of logic and philosophy of mathematics behind such course. It makes me want to tackle this areas even if I am not good at it. (Coming from someone who practice continental philosophy). Thank you for sharing this.
IGN Aletheia
IGN Aletheia Aylar önce
Can you do please the Gettier problem, the problem of Criterion, the problem of moral luck, the problem of evil, the omnigod problem, the mind and body problem, the problem that we cannot know the external world but we only know our experience (Immanuel Kant's Noumenon and Phenomenon problem), determinism and freewill (although this has been solved by soft determinism but it still begs the questions that leads to the problem of criterion) these are the topics that are unanswerable in philosophy right now. I am not sure if some of them has been answered but when I taught these problems to my students they were always left hanging hahaha.
Rab McNair
Rab McNair 23 gün önce
This has become my favourite channel on TRvid, so thank you very much for uploading this great content. The fact it has 15M view at time of writing gives me hope for humankind.
Maddox Aylar önce
Maths is just amazing, unlike what we learn in school/college as it’s not taught in a interesting way :|
Anthony Moses
Anthony Moses 23 gün önce
My only regret is that I can't like this video separately for each and every time I watch it. This is my 5th or 6th time watching it in its entirety and I'm sad I only get to like it once. Thank you so much for giving us such great content in an easy to understand format.
Mackinstyle 7 aylar önce
If you're a mathematician and you are labelled a "corrupter of the youth", you are doing something very right.
SOHAM _PAUL 6 gün önce
@Linus Fu H Hhhh ⭕ ⭕ নমস্কার
Peter Codner
Peter Codner 15 gün önce
"Right" meaning likeable or desirable? Maybe but for whose purposes?
TheHortoman Aylar önce
tell that to my uncle the pedo mathematician
Shadow Knight
Shadow Knight Aylar önce
Hahah ya
Quetzalcoatl Aylar önce
@Umar Ahmed Still doesn't make sense to me. Infinity for me is an abstract concept. If something is countable it is not infinite by nature. Infinity is that unreachable number to which no addition, multiplication by a number greater than 1 and subtraction can be performed unto. Or when it is the denominator, the result is a perfect 0. It's just an abstract mathematical limit. Once you reach it, everything is "frozen" or "locked" mathematically. Cantor proof is nonsense. And no Hilbert thought experiment doesn't work because you can't perform a subtraction to the last room once it's occupied. Infinity - 1 doesn't exist because infinity is disconnected from the countable series. So you can't reach it through infinite addition. Such a set {0,1,2,3.....infinity} cannot exist.
timyzfr6 Aylar önce
That just blew my mind! 🤯 literally speechless! You sir are a very gifted teacher and a brilliant mind
Peter Codner
Peter Codner 15 gün önce
It certainly provokes a number of rather mindless clichés of the sort beloved of those that struggle with language.
aegiswings 28 gün önce
This was awesome! The hardest class I took as an undergrad at Harvard was a philosophy class (yes, philosophy) that basically covered all of this.
Kiwi Connoisseur
Kiwi Connoisseur 21 gün önce
I went to Harvard and took that class and it was easy af
E Fun
E Fun 26 gün önce
Yeah you went to Harvard, good for you
Andrè L Immelman
Andrè L Immelman Aylar önce
Wow! Understood very little, but nevertheless appreciated the brilliance of the presentation! It seems to me that mathematics is all about finding patterns within numbers… if I’m correct, then I’m intrigued… what are some of the patterns hidden within the recesses of math? And are there any impressive examples?
Charles Trudel
Charles Trudel Aylar önce
@SaiLens yup, you found it, and yup, stuff in nature obey this sequence. its not just random xD
SaiLens Aylar önce
@Charles Trudel It's A Rough Guess, But Is It 13 Followed By 21?
Andrè L Immelman
Andrè L Immelman Aylar önce
​@Charles Trudel Brilliant! Thank you!
Charles Trudel
Charles Trudel Aylar önce
Fibunacci is one such example: 0+1+1+2+3+5+8+? I let you find what follow 8 here... thats one of the weirdest sequence of number ever.
robert cruz
robert cruz 4 gün önce
In retrospect, I just love how the loop was closed, or rather elevated in a loop synthesis. Math is a derivative of Philosophy via humanity's curiosity and inquisitive propensity, whose main aim is for the betterment of mankind and society. Then the imperfection of the derived evolved to achieve the aim of the source, furthered by the same inquisitive propensity by its recipients.
Anthead 8 aylar önce
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.
Travis Collier
Travis Collier 4 aylar önce
@Anthead The course title was Introduction to the theory of computation, or something like that. I was an engineering major, not maths or computer science. I really only took pretty basic CS for fun. It did turn out to be amazingly useful though (I mostly do bioinformatics these days).
Anthead 4 aylar önce
@Travis Collier which course, if I may ask
Travis Collier
Travis Collier 8 aylar önce
@Mr Fl0v Depends on how precise you want that description to be. A box of electrical stuff with blinking lights is pretty accurate ;) Seriously, as I've said already, modem computers are based on von Neumann architecture. That basic architecture has been extended and tweaked significantly of course. That "are" stored program electronic computers. It has been quite a while since I took intro theory of computation though. If you want to learn more, great! Do a web search and maybe even look into taking a course. It is cool stuff.
Mr Fl0v
Mr Fl0v 8 aylar önce
@Travis Collier If computers aren't precisely and exactly Turing machines, then what are they intrinsically? Oh, and please don't just tell me they're an alternative version of "Turing machine", that'd be the idler's way out.
Travis Collier
Travis Collier 8 aylar önce
@Andy Polasek Read/skim the Wikipedia pages on von Neumann architecture and Turing machine. Seriously, it is a bit of a pedantic point, but this is really basic stuff. Back in my day (I'm old) it was literally computer science 101 (CS1 at my school) stuff. It's also interesting, at least IMO.
Paolo Castiglione
Paolo Castiglione 19 gün önce
This video is truly a masterpiece. Great job!
Evil Beanz13
Evil Beanz13 28 gün önce
I nearly failed Grade 11 cause I got obsessed with a exponential list of number . That i just couldn't solve an equation for and thats what i worked on every day through every class after school . it consumed me . 🤣 i filled up a pile of note books trying to solve it . Eventually my physics teacher asked to see it and told me to give up cause its impossible to solve and predict.
Scott 23 gün önce
Thank you so much. This is a brilliant video. I studied Theology, philosophy and I am now reading for my MSc in psychology. I always struggled with maths until the past two years when I realized it is a language like any other we use. Wittgenstein's work on language games open my eyes to this block I had. Once you see maths as a language you realize how beautiful it is and see the world around you in "number" form. For example, trees, leaves even objects like rocks are not constant. They are "alive" in some sense as they are aging, composed of elements that are continually moving and aging. This can lead to the question do rocks etc have a form of consciousness? Are we all connected through different levels of consciousness with each other and the world around us? Your video on electricity shows there are energy fields all around us. Buddhist philosophy on the sea of consciousness. Mystic theologians who move beyond "language" to commune with God and mathematicians are all expressing the same idea. We have systems of languages, maths, our alphabet that try to express truth within that system or game. Using those systems leads us to new ideas, inventions, and as history moves onward in its beautiful and ugly dialectic. However, those systems themselves contain paradoxes, contradictions that keep the eternal dialectic alive. The "truth" that there is no truth, that language systems and games are useful but ultimately limited is a very freeing and beautiful realization. You can use it to "answer" the questions with those systems but at the end of the day can step away and leave the game. Some are unable to do this and that is where madness can arise. Thank you, keep making them they are excellent programs. They should be shown in all schools, then you may not get the question from children, what the point of learning maths, ill never use it. lol
Scott 14 gün önce
@Peter Codner You've missed the point. Re-read a few more times, and you may get there.
Peter Codner
Peter Codner 14 gün önce
What a pity it is that you can probably count the number of fluent maths speakers on the fingers of one hand.Maths is a language is like saying that fish are expert in riding bicycles.
Peter Codner
Peter Codner 15 gün önce
A language of sorts perhaps; certainly a language with very few speakers thereof.
jonathan real
jonathan real Aylar önce
I come to this channel for answers and most of the time I leave with more questions and these questions get stuck in my head all day. They are the type of questions I could have never came across in my life and everything would have gone smoothly and I wouldn’t be having this headache yet I here I am.
Peter Codner
Peter Codner 14 gün önce
Lucky you. Blessed are those that find themselves with more questions than answers although another put it as "Blessed are those that hunger and thirst after righteousness."
Matthew Ao
Matthew Ao 8 aylar önce
Can we just appreciate how well animated and produced this video is? God, so much effort.
Ward Fadel
Ward Fadel 14 gün önce
@Peter Codner just to tell her that incompleteness theory is agreed everywhere and it is a breakthrough and no way to compare it with the electricity video of this channel which oversimplified some aspects of the experiment although it was a nice one.
Peter Codner
Peter Codner 14 gün önce
@Ward Fadel So, or therefore, what?
Peter Codner
Peter Codner 15 gün önce
Far simpler clearer and quicker to advance the axiom that a mirror cannot reflect itself.
John Wicked
John Wicked 16 gün önce
@Fred Esch nice 👍
xodz 19 gün önce
The chart scene looks lile Flash MX discontinued
John Shooter
John Shooter Aylar önce
Literally Mindblowing. I wonder if there might be some kind of interface problem between math (as an maybe "language of the universe") and "spoken language" which may lead to some kind of unsatisfactory results. Seems to me that at some point you always have to switch from math to "spoken" language and vice versa.
PeterSansGaming 29 gün önce
Yes we actually have to switch quite often. For example when you want to define the logical AND symbol, you need to use the english (or any other language) word for "and". It is not possible to define the logical AND without informal spoken language. This also goes for the logical OR or the existence quantifier or the universal quantifier.
MLMI :: Michael Lucas Monterey Innovatainment
Wow! Impressive! You just verified the existence of the ordinary intellectual & logical competence appreciated by Ludwig Wittgenstein, among other truly great pioneers of real ontology. Thanks, etc.
John Ross
John Ross 13 gün önce
Extremely well done and an excellent explanation of difficult material Poor Frege and Wittgenstein - lately they have been getting left out.
chaincat33 Aylar önce
A question about Conway's Game of Life being undecideable, is that a general statement or do exceptions exist? That also necessarily questions what "stable" means. After all, a single glider will go forever since nothing can stop it, but it's also not really meaningfully changing, so is it stable? And then there are systems that just tile a plane forever. Sure, the entire game of life may be undecideable, but could certain configurations be decideable? Or is this some fundamental problem with the language of math? We can plainly see a glider will go forever and not stop if it's not interrupted, and nothing will interrupt it, but you can't articulate that mathematically?
Julian Asamer
Julian Asamer Aylar önce
It‘s a general statement. There are very many starting conditions for the game of life that are decidable - a trivial example is starting the game with a single alive cell. It‘ll halt after one generation, and it’s easy to write an algorithm that will tell you that. Undecidability means that there is no possible algorithm that’ll tell us whether the game of life halts for an arbitrary starting condition. It might be able to tell us for a lot of starting conditions, but it cannot do so for all oft them.
firstname lastname
firstname lastname 3 gün önce
Just coming back to this, it's the best video on youtube. Will probably watch a 3rd time in a few months. Legitimately a masterpiece of a video and very inspiring
Judy Petree
Judy Petree 8 aylar önce
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.
Peter Codner
Peter Codner 14 gün önce
@capratchet*Why* is "The world is a better place for each person looking to learn."? Is that some sort of belief or religious doctrine? Suppose they want to learn how to decimate Jews, or kick babies and bite the heads off puppies and kittens? There are only two ways to learn in this vale of tears and there is no easy way.
Peter Codner
Peter Codner 14 gün önce
"Education" is a rather vague portmanteau word into which any number of sins and evils can be crammed, just as useless information is rammed down the throats of small beings who would rather play or do some useful work, but No, they must be "educated" whatever educated means, but let us just call it bullied.
Peter Codner
Peter Codner 15 gün önce
"Reference" is a noun in pure English, not a verb; one can no more reference than one can parent or debut- except in that dialect of pure English that is American. If the salt has lost its savour, wherewithal shall it be salted?
Van Schofield
Van Schofield 4 aylar önce
@capratchet this is honestly might be the most beautiful way I've seen the edutube community described and encouraged yet. cant wait to share a classroom with everyone else too.
capratchet 8 aylar önce
The world is a better place for each person looking to learn. I'm glad to share this classroom with you. I look forward to seeing a life time of humanity learning.
Dice Doomkid
Dice Doomkid 23 gün önce
I love the concept and discussion of infinity.
steve ascension
steve ascension Aylar önce
I just learned why I hated maths so much at school, my teachers were so uninterested in maths. This guy is a brilliant maths teacher!
Skylark25 25 gün önce
May I ask, what software do you use for creating infographics like this?
Steven Homan
Steven Homan 25 gün önce
This very thing was what killed mathematics for me in primary school. That, and the problem of measurements. As each measurement can be theoretically, virtually infinite in any measurement; in and of it self. I would ask my teachers my questions about this, and they would become enraged and accused me of being an impudent and stupid boy. Then I was very often extremely sick for long periods, thereby missing large portions of the curricula. When it came to algebra, I thought the full stops or dots were decimal points and reacted appropriately. My answers were howlers. So wrong they weren't even false. I did seek clarification on each occasion, saying I had missed a lot of instruction. Each would in turn claim they would tell me later, treating me as a bufoon. Later of course, independent of a school system I became an autodidact. Discovering that the dots were multiplication signs, as not to confuse the X from the • , algebra is extraordinarily simple I find. Though no longer applicable to my life. I did work as a Senior executive manager in the computer problem solving area for over 28 years. Not to bad for a high school drop out? Had they roused my passionate thirst for knowledge, who knows where that may have led? You see I was being challenged by set theory as a 3 year old, though my father didn't know it. I argued the point that 3 oranges are not the same as 3 Apple's. They are quite distinctly different altogether.
Bruno Ribeiro
Bruno Ribeiro 8 aylar önce
This feels like the start of a new era for Veritasium. The production value is off the charts! And the topic is just beautiful. Congrats Derek and team S2
Fractal 8 aylar önce
@Jeremy Raymond the idea of "purpose" is weird to invoke here..it would be better off to state you rather just dont enjoy it much. it is as useless as much of the things he says in his other videos depending on how restrictive you wanna be. there coild definitely be a better spending of time.
Misha Finadorin
Misha Finadorin 8 aylar önce
@Jeremy Raymond A statement about the entire system that you use to describe 'the useful stuff' is pretty useful itself.
Ben Thorpe
Ben Thorpe 8 aylar önce
@klobe9 I don't understand why he didn't reshoot that segment lol, was like 10 seconds long
RationallySkeptical 8 aylar önce
No, he's been at this level for quite a while now.
Jeremy Raymond
Jeremy Raymond 8 aylar önce
See I don't like it. Theoretical mathematical truths that aren't provable and/or practical are just neat to hear and that's it. It doesn't have a purpose. That's what I don't like. You can make up a story about a hotel with infinite rooms or tell me that there's an infinite number of twin prime numbers but do something with it. Show me an example on why it's worth knowing. This is what I'm talking about at 20:59. It's a paradox. Those can be neat. What did you do with the information though? What *can* you do with that information? I would MUCH rather Veritasium cover content like where he went into public and asked people things like, "Why does the earth rotate?" or "Why do two objects fall at the same speed?" but that's just my personal preference. I'm happy so many people like where his channel is going. I wish I was one of those people.
Alek Yaw
Alek Yaw 19 gün önce
I wish I had you as a teacher in high school. Would’ve actually paid attention.
Trippy Elite
Trippy Elite 22 saatler önce
Would this mean that we cannot be in a simulation since this basically proves that math isn't what our reality is based on? If we were in a simulation, then the answer to these 3 questions would have to be YES. No?
Manos Kapritsos
Manos Kapritsos Aylar önce
For a deeper dive into the Foundational Quest of Mathematics, you can read the graphic novel "Logicomix". It tells the story from the perspective of Bertrand Russell and is very well written.
Anonymus 321
Anonymus 321 Aylar önce
This is such high quality content keep it up
Arthur Barbosa Câmara
I'm a PhD in computer science. This is a full-on Discrete Mathematics intro course. This is amazing.
Joe L
Joe L 8 gün önce
What does you having a PhD in computer science have anything to do with this being an intro course to discrete maths? Also congratulations on completing your PhD
Lil Yeet
Lil Yeet 23 gün önce
You 'are' a PhD are you? I doubt it, you 'have' a PhD in lying
Bryan-Amber Lemieux
Bryan-Amber Lemieux 23 gün önce
Intro course? Lol more like PhD level
J M Aylar önce
how do you know when someone has a PhD? they'll tell you.
hari ganguli
hari ganguli Aylar önce
I had a question if barber can't shave himself than why doesn't give his blade to the 2nd barber in that way they can shave eachother's beard without shaving their own beard by themselves. Explain me please.
Joanna Hammond
Joanna Hammond Aylar önce
I remember going through all this at Uni studying Computer Science.
Steven Homan
Steven Homan 25 gün önce
Fascinating, I wrote poetry as a youngster, and eventually arrived at a similar solution to exactitude. The symbols I developed differed of course, but were extremely accurate in their logic and detail. A much older young man loved my poetry, and discouraged me as much as he could, as he could no longer read them. It was just another avenue of expression to me. Kids can be unbounded by formalism. I was.
James M
James M Aylar önce
One of the best TRvid videos ever. Wish I could have seen the extended cut!
notfiveo Aylar önce
I’m relived. I now know why my math problems in school were seldom correct, they were unknowable….. (at least to me)🤣
jonasba276 8 aylar önce
As someone who majors in mathematics while minoring in computer science, this video is absolutely awesome. I've learned about a lot of these things in isolation, but this really connects them all.
Peter Codner
Peter Codner 14 gün önce
@jonasba276 Nice etymology: Middle English (in the sense ‘stupid’): from Old French, from Latin nescius ‘ignorant’, from nescire ‘not know’. Other early senses included ‘coy, reserved’, giving rise to ‘fastidious, scrupulous’: this led both to the sense ‘fine, subtle’ (regarded by some as the ‘correct’ sense), and to the main current senses.
jonasba276 14 gün önce
​@Peter Codner Damn you sound like a nice guy
Peter Codner
Peter Codner 14 gün önce
Apparently you decided to skip English , in the pure form of which there are no verbs to major or to minor and thus no gerunds thereof since they are adjectives. Of course there is nothing to prevent you from inventing your own exclusive-to-you language save perhaps that you will be its only speaker.
Joseph Shinn
Joseph Shinn 8 aylar önce
You like conflating. Well that sums up this whole video. Have fun!
Dad Can Too
Dad Can Too 8 aylar önce
I learned about this from the book, "Godel, Escher, Bach" by Douglas Hofstadter, back when I was doing my Joint Honours Math and Computer Science degree.
t4ngen7 Aylar önce
I’m impressed, surprised and hopeful for humanity all at the same time, by the fact that a video like this can pull this many millions of views in a matter of months.
Jack 14 gün önce
"Alan Turing" was a great man but his death was unfair. He should have left the country because it did not deserve him. Imagine all the things he could have discovered, all the lives he could saved, all the things he could have done but he had to die of humiliation. All because some people thought that they had the right to meddle in other people's sexual preferences. I don't care what other people say about this opinion because any arguments that you give will mean you are undeserving of any device that came from his discovery and innovation.
NineSix Khosly
NineSix Khosly 10 gün önce
Hi Derek, I have a question for you. What numbers do naturally appears in nature? I mean, do we find 1 through infinity or are there numbers that can’t be found in nature like “2” or perhaps 18. To think that nature has a mind of its own is ludicrous but we can easily see the inner workings of nature most likely has its rules, like the hexagons on a honey comb or the pattern in an acorn. I have yet to see a perfect circle made by nature therefore a perfect circle should never exist. I am a true believer than nature invented math. If we were to understand and comprehend nature’s math and formulae I think we will truly leap our science 2,000 years.
Brian H.
Brian H. 5 gün önce
This was an amazingly interesting topic and that says something because I am terrible at mathematical concepts.
Tyler Jane Bronson
Tyler Jane Bronson 8 aylar önce
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!
Damian Szajnowski
And it's all running inside a game of life!
Prince David Bentabal
Prince David Bentabal 13 gün önce
@asdfasdfasdf1 check fundy's minecraft video about that, that is possible now
Di Nam
Di Nam 16 gün önce
Wait until you see the game of life running inside the game of life running inside the game of life.
Tom Wwabo
Tom Wwabo 18 gün önce
Thats Recursion and Turing completeness
10th House Tek
10th House Tek 21 gün önce
That's the reality of reality in a nutshell 😂
Tyler Aylar önce
What happens if you take an infinity that runs clock-wise and then put it up against another infinity running counter clock-wise. Then run more infinities clock-wise and counter clock-wise (every other one) until you get a perfect sphere of them?
Andrew Thompson
Andrew Thompson Gün önce
As a layman, why is dimension/direction irrelevant in Cantor’s diagonalisation proof? Seem like it's is trying to correspond a one-dimensional set (Natural numbers, their direction only up and down in size) with a two-dimensional set (Real numbers, their direction up and down but also "within" and "without" - there are an infinite number of Reals between any two Reals).
Liv ._.
Liv ._. Aylar önce
If this was how school is taught, I would enjoy it so much more
Anushka Jayalath
Anushka Jayalath Aylar önce
I wish I had all this knowledge on youtube available to me when I was a kid.... might have influenced me on a different path... who knows now
Kyriakos Mousias
Kyriakos Mousias 3 aylar önce
As a mathematician I haven't seen a more elegent presentation of these concepts,especially Godel's theorem. Amazing job thank you.
Aisha Aylar önce
Any tips on becoming good at math as a high schooler?☹️
william mabon
william mabon 2 aylar önce
@Dayton Robar What's naturally good? Opinions are endless.
Dayton Robar
Dayton Robar 2 aylar önce
Presentation is everything for people that are not naturally good at math.
Michael Salisbury
Michael Salisbury 2 aylar önce
This is the perfect medium for this stuff.
william mabon
william mabon 2 aylar önce
Godel like Cantor did not see that change is a subset of Infinity. Change allows for a contradiction to operate as a constant in a stream of logic that changes an identity within a mathematical extremity. This fact do not make math incomplete. It simply allow for the growth of change which is actually an expansion of a set's identity given that any contradiction must contain elements of identity to the set in question. Any contradiction is based on finding a counter or opposite identity with like elements thereby making the contradiction a mirror set or a set turned in the opposite direction. Example: the elements of the negative number set do not contain any positive numbers within it but positive numbers do exist. Both sets have like elements within a larger set of change. Each of these sets have an equal number of elements that oppose the direction of the other yet both sets share the identity of likeness of size and division of spatial order. Here we have an order creating a disorder of self. A contradiction or simply an expansion of its spatial self.
Yogi McCaw
Yogi McCaw Aylar önce
Well, let's say that science endeavors to explain everything (the "theory of everything", the "one-inch equation" etc). This video suggests that you'll never get there, and not only that , you'll never know for sure whether or not you'll ever get there. BUT, you learn all kinds of things that transform your understanding of the existence, and therefore the Endeavor is totally worthwhile. Like that old adage, life is not about the destination (the destination, of course, is death), but about the journey (everything you experience along the way).
Zach Cushing-murray
Zach Cushing-murray 13 gün önce
As someone who has studied both math and propositional logic at a high level (as well as some computer science), this video is truly a treat.
wilson3851 Aylar önce
Bravo. A terrific presentation reminiscent of another ground breaking, terrific presentation of how we got to be where we are… James Burke’s “Connections.” Your analysis went micro and short time span… another proof of the “infinite in-between.”
Peter Codner
Peter Codner 14 gün önce
Is there a "we"? Who experiences it? If it cannot be directly immediately personally experienced, I put it to you that is -by definition, imaginary. Is it not axiomatic that all universals can only possibly be imaginary?
Jason McFall
Jason McFall Aylar önce
I have always loved science but despised math. I took to math fine, understand it easily, but find more annoyance from it than anything unless I am using it directly as a tool in my scientific works and learning. I also find myself to be philosophical in thought. Which is another reason I do not find pleasure in math. For I hate the idea of definate. That takes away the beauty of imagination. Which is the biggest angst I hold against math. It, in how I have been taught so far, is definite. Now, I started watching this video with an expectation of pain from the examples of maths claimed definity. But was amazed at what was shown. And of course thankful to learn of this. I never once expected math hating self to say this, but... that math was interesting, thought provoking, pleasurable. How very interesting. Wonderful.
Rubik 8 aylar önce
This video is a masterpiece. The content, the animations. Everything is out of this world
👺samurai boi
👺samurai boi 8 aylar önce
This is a dream for every math teacher
Mac K
Mac K 8 aylar önce
Cardboards were very much from this world ;)
Quinnipi 8 aylar önce
The use of mathematical symbols as buildings is *chefs kiss*
William McBrine
William McBrine 24 gün önce
This kept coming up in my suggestions, and at first I didn't watch it because I already read Godel, Escher, Bach 40 years ago. But anyway, every time I saw "Math has a fatal flaw", it made me think, "Space has a terible power".
Mr TC Gill
Mr TC Gill 20 gün önce
My mind is blown. I am experiencing a paradox of confusion and awe of beauty at the same time. Just wonderful.
Tudor Aylar önce
Amazing. They should give prizes for this caliber of videos.
Lucas Cardoso
Lucas Cardoso 23 gün önce
Dude, you're a freaking inspiration
Magnus Kramnik
Magnus Kramnik 8 aylar önce
Mathematicians: we must prove this equation Engineers: Eh, it's good enough, we'll just use it
Magnus Kramnik
Magnus Kramnik Aylar önce
@NeoFrontier Technologies you're going on philosophical tangent
NeoFrontier Technologies
You can not prove something which must be comprehended. You can not force comprehension. The individual must choose to comprehend. Life is choices - personality choices which effects intelligence and perception of reality.
Syko Soldier
Syko Soldier Aylar önce
@Magnus Kramnik engineer learned from mistake, made a better bridge, and by doing so, found the better math equation that mathematician was trying to "validate", and now math guy wasted a whole bunch of time trying to prove something that you can just experimentally demonstrate is wrong? woah wait what? And now mathematician has new job... "validate" this new equation the engineer found, which, already works demonstrably well in practice. Yeah, well he decided to study math! I mean, we cant let him just.... like, just give him something to do man... feel sorry for him now.
MLMI :: Michael Lucas Monterey Innovatainment
LOL!!! Reminds me of the history of Legacy schlockware AKA bloatware which made Gates & colleagues hyper-rich while addicting the rest of us to ever-more patches, upgrades, hacks, attacks, ransomware, botnets, cyber-war, etc.
sharpfang Aylar önce
@AloysiusVo Of course you do. Unlike in mathematics, though, the proof consists of proper references to the handbook, the standard, and relevant legal documents.
Stiryu Alaghani
Stiryu Alaghani 3 gün önce
May I ask something? If the g card is true without proof, isn't that means that it is an axiom? Futhermore, wouldn't any axioms be enough evidence that Mathematics is incomplete?
Hyrum Leishman
Hyrum Leishman Aylar önce
I simple solution that stuck out to me from set theory on, would be to simply eliminate self reference. Instead of saying that there are no sets of sets, just say a set can't contain itself. (I am not an expert in this field, so please explain why if I am wrong)
Hyrum Leishman
Hyrum Leishman Aylar önce
@Noel Lundström So my idea does exist! Thank you very much for explaining that to me.
Noel Lundström
Noel Lundström Aylar önce
@Hyrum Leishman your idea is called the well foundedness axiom and it is an axiom of the modern formulation of set theory (Zermelo-Fraenkel axioms). It just wouldn't make a difference if you added it to naive set theory (the set theory where the set of all sets exists) since adding another axiom to an already broken theory wouldn't really change anything. A contradiction exists here already so adding another axiom won't really change anything.
Hyrum Leishman
Hyrum Leishman Aylar önce
@Noel Lundström But does the set of all sets contain itself? Also, please explain why this doesn't solve the paradox, because I would really like to know if my idea wouldn't work.
Noel Lundström
Noel Lundström Aylar önce
That doesn't eliminate the paradox, in naive set theory the set of all sets has to exist.
Greg Hodges
Greg Hodges Aylar önce
Videos like this make me fall in love with math again... thanks 😊
BG Games
BG Games 24 gün önce
I was really studying Sets in my coaching and now realise everything taught to everyone is wrong, reality is not taught..
Gromek999 8 aylar önce
Masterpiece of a video
RottenFruit 2 aylar önce
You really do be popping up in strange places.
Arihant Bhattacharjee
Arihant Bhattacharjee 6 aylar önce
@Dr. Michael J. Stefano jeez calm down with the caps
Arihant Bhattacharjee
Arihant Bhattacharjee 6 aylar önce
@P. Chakraborty he is just expressing what he thinks about a video, no need to be so critical
Arihant Bhattacharjee
Arihant Bhattacharjee 6 aylar önce
@THINK PATH Please Stop promoting your own channel in the comments
Air 7 aylar önce
Hey its the robocraft man
C M Aylar önce
This has huge implications for A. I. and the concept of infallibility of science, technology
checkwegg 28 gün önce
great video. i think i have to watch this a few more times to understand as much as im able to.
Master-G Big
Master-G Big 27 gün önce
It takes two different components to create a continuum, one physical, the other electrical. This way they work together in order to complete the one continuum.
westganton 16 gün önce
The Game of Life bit in this blew my mind open to the idea that every biological system is just a system of systems of systems, all the way down. Society is our attempt at organizing the next tier of life, and if we intend to be successful, we need to seek answers within our own microbiology. If cells are like individuals and tissues are like industries, what does that make DNA?
stephan Roche
stephan Roche 8 aylar önce
Ironic that Godel's death was the result of a self-referential paradox: he died in order to not die
Aayush Srivastava
Aayush Srivastava 3 aylar önce
Niranjan 3 aylar önce
@Matthew N AMEN!
Shayer S. Utsho
Shayer S. Utsho 3 aylar önce
@TheUnspeakableHorror Yes. He used self-reference for the benefit of research, while the same self-reference brought about his demise - it's the starkest contrast there can be. It's an irony.
Zaraspe, Bong Jr. G
Zaraspe, Bong Jr. G 4 aylar önce
Alan Sharpe
Alan Sharpe 5 aylar önce
Great, now I have to clean my brains off the ceiling.
AMIT RANJAN Aylar önce
This was brain hurting, I had to go back and forth multiple time to understand things, but i am glad this exists.
Peter Codner
Peter Codner 14 gün önce
Far simple quicker and clearer to pose the question: Can a mirror reflect itself? It is quite simply down that that all those convolutions boil. Nothing more.
Justin Lowery
Justin Lowery 16 gün önce
This video makes my brain hurt, and I am literally the closes thing you can get to proving that human brains are computers in and of themselves.
Zoomjah Aylar önce
At the end of this video I was struck by the mention that Turing is behind the device I'm watching on. In fact in my case I know this to be true... but I was thinking couldn't there be some people watching it at some point from a device that is not of digital origin, like the old TVs? I did a google search that said the TV was invented in 1927 and that Turning invented the computer in 1936. So if that's true, then maybe someone listened to you saying that they are watching this on a device that came about as a result of Turing's invention... but in fact just maybe in "their case" it didn't. (-:
Ahmed Gaafar
Ahmed Gaafar 3 gün önce
great video indeed, and amazing subjects in all the videos.
Lemon D
Lemon D 8 aylar önce
I don't know why but I love the idea of mathematicians gathered in a room yelling and hurling insults at one another
MrKotBonifacy Aylar önce
@Umar Ahmed Sigh... Yes, SOME of them, SOMETIMES, "once in a blue moon" might have crossed that treshold Also, a duel, although a very confontational act, is not "physical" one (at least not a duel conducted using firearms). "Risky", "harmful" and "deadly" - yes, by all means - but not "physical". Matter of "honour", "dignity" - but NOT a physical confrontation like in a drunken pub brawl. Anyway, the first post in this topic was about "mathematicians yelling and hurling insults at each other" (thus "getting emotional", but not "physical"). Others expressed their... doubt's, let's say - "why, scientists are the better breed - educated, cultural and all" - to which I replied "well, they're people too - they have emotions, they can turn nasty, or even spiteful" - and in fact they often do, as it is evident for anyone following "scientists' polemics". There's even that wonderful piece of a fiction story "How the World was Saved" - a "robots' fairy tale" from "The Cyberiad", a book by Polish writer S. Lem: _One day Trurl the constructor put together a machine that could create anything starting with n. When it was ready, he tried it out, ordering it to make needles, then nankeens and negligees, which it did, then nail the lot to narghiles filled with nepenthe (...). Only then did Trurl invite over his friend Klapaucius the constructor, and introduced him to the machine, praising its extraordinary skill at such length, that Klapaucius grew annoyed and inquired whether he too might not test the machine. "Be my guest," said Trurl. "But it has to start with n." "N?" said Klapaucius. "All right, let it make Nature." The machine whined, and in a trice Trurl's front yard was packed with naturalists. They argued, each publishing heavy volumes, which the others tore to pieces; in the distance one could see flaming pyres, on which martyrs to Nature were sizzling; there was thunder, and strange mushroom-shaped columns of smoke rose up; everyone talked at once, no one listened, and there were all sorts of memoranda, appeals, subpoenas and other documents, while off to the side sat a few old men, feverishly scribbling on scraps of paper. "Not bad, eh?" said Trurl with pride. "Nature to a T, admit it!" But Klapaucius wasn't satisfied. "What, that mob? Surely you're not going to tell me that's Nature?" Then give the machine something else," snapped Trurl. "Whatever you like." For a moment Klapaucius was at a loss for what to ask_ Unfortunately, that piece is a tad on a "lost in translation" side - you see, the original text was in Polish, and Polish term tor "natural science" is "nauka" (which could mean both "learning", "teaching" and "knowledge". Which had to be replaced, unfortunatelly, by that rather silly"natural" in translation - but that's not the biggest flaw here. In the original text after "Surely you're not going to tell me that's Nature?" came a line, from Klapaucius, "But the Science (= "Nature") is something completely different!" To which Trurls' reply was something like: "So, you have any better idea? [on what a science is]. Then tell that to the Machine, and it'll make/ create it gladly in no time flat". (Slavic languages are "pro-drop" and "null-subject" languages, as bot the pronoun and the subject of the sentence can be easilly deducted/ infered from the grammar of the sentence.) To which question/ challenge Klapaucius was lost. (= He didn't know what to say/ answer/ had no better idea whatsoever what "science" is supposed to be.) So anyway, because of the "plasticity" of Polish language (and other Slavic languages too), AND a highly "inventive" vocabulary of Lem his works are often next to impossible to translate info languages lacking a "proper grammar" - like, for instance, English). But I digress here... Cheers!
Umar Ahmed
Umar Ahmed Aylar önce
@MrKotBonifacy minus getting physical?! Galois died in a duel at 21. And wasn't Pythagoras rumored to have killed someone for proving that there are irrational numbers?
Luka 4 aylar önce
“Corrupter of youth” 😂
Grevoron 4 aylar önce
the mic drops could've been the hottest known to mankind
J K 4 aylar önce
Oh Reginald.... I DISAGREE
Martin Marchev
Martin Marchev Aylar önce
There is another really weird infinity numbers property. That always blow me away - Galileo's paradox
Andy Melendez
Andy Melendez Aylar önce
So interesting. Makes me wonder about probability/ determinism and reconciliation of opposites. Crazy huh?
persona Aylar önce
basically how one man rocked the entire foundation of thousands of years of work
Ken Ken
Ken Ken 26 gün önce
Your explanation to Halting problem is on point. The visualisation is great.
Niklas 8 aylar önce
This is basically my whole computer science studies in 34 minutes.
Zoran Matijević
Zoran Matijević 7 aylar önce
@Brandon puntin One of the first things general science methodology and logic professor explained to us.
kotzpenner 7 aylar önce
@Al Sharairi set theory and all that is what I struggle with the most
Al Sharairi
Al Sharairi 7 aylar önce
@kotzpenner what math are you in rn? Just got my CS degree so maybe I can give some insight
kotzpenner 7 aylar önce
Well, I'm studying CS and the math is hard af to the point of considering dropping out. (And it's only 2 courses out of 3 years) Like the whole video allover I was thinking "what's the point" like 80% of the time lol. And I studied that stuff for months and have another exam in 2 months again because I botched it the first time.
Subjekt 7 aylar önce
Ditto for my math degree
James Smith
James Smith 18 saatler önce
At 20:01, the number g must be represented by g successor operations, which when encoded must give a number much larger than g. Ergo, the card he has created can't exist: the Godel number generated by the proof can't be part of the proof.
Jamie. K
Jamie. K 8 gün önce
This video is fantastic. As an unscholarly non-mathematician, it took rewinding to properly understand some of the logic. When I did, I felt I understood how people could dedicate their lives to something so cold. But math isn't cold. It's attempting to solve everything. It's wrong in its conclusions, or the assumed logic it works with is unproveable or false; but it is proof closer than we as humans can. Even if it takes hundreds of pages to solve one plus one, it is the only true proof of what we hold in our hands. Mathematicians stubbornly refuse to believe that everything doesn't exist, and dedicate their lives to proving it, miniscule by miniscule. Thank you, Veritasium, for providing mind-boggling amounts of human research in a digestible size for my mortal mind to (hopefully!) comprehend.
Allister Blossfeld
Allister Blossfeld Aylar önce
Damn you make math seem interesting. Why couldn't you be my math teacher growing up?
The Way
The Way 26 gün önce
Well done! I just want to notice that human mind is a special representation of reality that has no self-reference link to itself. The last question is a human mind is product of some supercounsessness system or it's finite product of reality?
The Way
The Way 15 gün önce
@Peter Codner No pain, no game, bro! Thanks!👍⚡⚡⚡
Peter Codner
Peter Codner 15 gün önce
Whose reality? If you experience any sort of pain that is undoubtedly real, or cannot-be-different, for you, but no-one else, so *whose* reality?
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