Math's Fundamental 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

Executive Producer: Derek Muller
Writers: Adam Becker, Jonny Hyman, Derek Muller
Animators: Fabio Albertelli, Jakub Misiek, Iván 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










コメント数 46 466
Amecha 年 前
So basically... Can math prove itself? No. But math can prove that math can't prove itself.
Sundaresh Venugopal
Math always proves itself. But neither is one who scores a zero in a math exam truly a poor mathematician, nor one who scores a centum in a math exam truly a good mathematician.
Jesse Hiller
Jesse Hiller 12 日 前
@Fomalhaut the rule of math is that it can prove anything doesn't exist, including itself
See A G
See A G 17 日 前
I bet religious folk can use math to prove math
André Gustavo
André Gustavo 21 日 前
So if math can prove that math can't prove itself then math is not reliable. Since it's not reliable, we should not trust the proof it makes that it cannot prove itself. A whole other paradox comes
Anthony Browning
Anthony Browning 21 日 前
How else would you prove it?
Steve Sether
Steve Sether 2 ヶ月 前
I very strongly wish mathematics was taught in a wider perspective like this video is. We teach mathematics as if it's a world onto itself, disconnected from everything. In reality, it's highly connected to history, philosophy, and nearly everything.
Santino Solis
Santino Solis 3 日 前
Math isn't a specific subject. It's a collective of ideas that apply to all things in life. It might be described as the "code" of life. People, especially in the educational context, struggle to understand this and even more to teach it. It ought to be taught that there are specific forms of mathematics for each subject to be taught. But I suppose it's easier to declare it a specific science, and to alienate the children and adults who struggle to understand this backward concept. I myself was awful at specific mathematics as a child. I still am, in many ways, but I have taught myself to learn each subject-specific form of math as I encounter it. I think of this as further proof that all parents, if they truly give a damn, should homeschool their kids. But, most parents give fewer fucks about their kids than about pets, so oh well. Guess we'll have to keep dealing with generation after generation of traumatized, ignorant morons.
Number 6.
Number 6. 21 日 前
@Marcus Nelson I went to different types some bog standard public US, private, free school,college and at home in both Michigan, England and long Island New York. Before going to university. I find what kind of education you get depends on the parents background and education. The more manual labour the environment the less value will be placed on learning. Observation, logic and the 4 principles of the scientific method will stand you well in navigating people.
Steve Sether
Steve Sether 21 日 前
@Pedro I claim no such thing. I only claim math can be taught in a more holistic way that attaches it to other areas of knowledge.
Marcus Nelson
Marcus Nelson 21 日 前
@Luceat Lux I have also heard that MBTI is nonsense. I do find it useful and largely agree with the result and description that comes along with it, for me. Many of my friends throughout my life have ended up being the same type. I get on best with NTs I think.
Marcus Nelson
Marcus Nelson 21 日 前
@Number 6. which type of school did you go to and in which country?
Linuxdirk 2 ヶ月 前
So Gödel basically said “The next sentence is wrong. The previous sentence is true.” but in a super complex and complicated way.
Alexander Bayramov
@Honourable Doctor Edwin Moriarty superb explanation, to say that liar's paradox is not math and something else is math really simplifies the concept
Look At This
Look At This ヶ月 前
godel was explaining psychohistory aka cliodynamics, the prediction of the future by using the past if we can predict what the past will be we predict the future but we cant predict the future only the past and we can't predict the future in the past only the past in the future... so its highly complex to say the least...the calculations are infinite indexes of historical databases of everything that can ever been catalogued into a tiny little quantum dot and to have our tiny little peon brain wrap itself around that is highly egotistical for our mental comprehensive capacity at our stage in development within the cosmos... we are just the smallest fragments that make up a seed that will one day cover the universe...
Heliogen ヶ月 前
@Keen Observer The problem is that no matter how we define it, it will always have flaws. There’s an excellent comment above in this thread that explains it more thoroughly, but essentially Godel proved that any system strong enough to define basic arithmetic is either incomplete or incorrect.
John Doe
John Doe ヶ月 前
@Keen Observer Well, tell me when you've found a proper answer because as far as I see we're making things way too complex, more than it has to be. The point we struggle understand might just be that because it just is. Take existence for example, people always say that time is infinite but doesn't realize that while infinity doesn't have an end, it might just not have a start. The idea is that paradoxes are repeatable answers. They might be our "neither", we're trying to make something of it but what if it just is? Advanced mathematics won't get you very far from where you are now. You are free to take my word for it or go mess around and find out, that'd be a time waste. A time wasted on only defining infinity which'll be a small contribution to giving our existence a reason. Be warned though, you may just end in a downwards spiral, and once you realize and acknowledge it, it may just be too late for you.
Keen Observer
Keen Observer ヶ月 前
@John Doe And to go back to your idea of right and wrong, I believe "neither" might be a viable answer as there are some things are are neither right nor wrong. For example, if I ask the 2 questions: do we live in a simulation? Do we live in the real material world? What if the answer to both is "yes and no"? i.e We cannot live without simultaneously being in a simulation and in real space, and one cannot exist without the other, hence the answer "yes and no". I may be completely wrong or illogical but I am sensing that we may be lacking this sort of perspective in maths.
EdgyShooter 2 ヶ月 前
Meanwhile in physics: "Can you prove this statement is true?" "I'm just going to assume it is and continue from there"
Luis Herrera
Luis Herrera 17 日 前
Imagine the cow is a sphere
Kian 20 日 前
@Dale Johnson actually learned a lot from that thanks
Number 6.
Number 6. 20 日 前
@Michael Asta as long as you go to the trouble of proving or disproving your assumptions in an independent system the method is not flawed.
Uranus 20 日 前
Don’t forget to ignore air resistance and friction.
Michael Asta
Michael Asta 22 日 前
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.
seniorgir 2 ヶ月 前
The more I learn about Turing the more amazing I realise his brain truly was. Ever since I watched The Imitation Game I've been fascinated with Turing, and honestly the fact that he was driven to suicide makes me feel disgusted at the waste of a revolutionary once in a generation brain. Imagine how far science could have come if he lived longer.
Negary 27 日 前
@Ben Botts ,may I recommend you ,,Man’s search for meaning “ by Viktor Frankl? I think you will like the philosophy he teaches. Now about the topic at hand, let me just say that rejecting your own sexuality is no easy feat. I do believe that the analogy @Outback Catgirl made is not entirely appropriate though. Breathing is the most basic need of (almost) all living beings on earth while sexual orientation might be only present in humans. While it may be caused by a difference in the behavior of the limbic system as many studies have proven, this does not imply that it is unchangeable. The behavior of every individual plays a big role in the development of the brain. And I think that here is where the real ,,choice” could in theory apply. And make no mistake, this choice is more akin to ,,I choose to live my whole life as a monk” then ,,I choose cereal for breakfast” And even then, one might never be able to radically change their likes and dislikes, just controlling the amount of control said ,,likes and dislikes” exert on their behavior. Thanks for reading my ramblings -An aspiring neurologist
Ben Botts
Ben Botts 28 日 前
@Riya Choosing one's truth in life comes with good/bad outcomes from those you consider family, friends, et al. I believe this is a choice. Being gay, straight, or non-associative (whatever the correct term is for that 3rd option) ... I believe those are all choices. If we cannot claim agency of our own lives and what defines us then we are subject to simply being rolled some cosmic dice in a game of universally bound craps where we have no ownership of ourselves. As before I have stated I believe this is a choice and not something we are inherently born with/into ... others do not agree with me & that is okay. I'm not vying for anyone to agree with me nor am I hoping for someone to shift my perspective or change my mind. I appreciate the feedback, even if I respectfully decline your belief; I am thankful to read others' thoughts/input on the topic. Some folks want to railroad me or paint me to be some ignorant clown. Which is awkward, to say the least. Have a good night.
Riya ヶ月 前
@Ben Botts but why? it is not a choice, you wouldn't choose to be gay if it could lead to your family disowning you, being ostrasiced by the whole society around you, loosing everyone you love and literally being killed in some countries. you don't willingly choose that. it isn't a thing to agree/disagree on
Nate M
Nate M ヶ月 前
@Ben Botts Odd way to answer the question, but I feel like the logic is more like: There is a group of people outside your door. One person knocks at a time, and as this happens a couple times each person is asking the same question. If you were to give the group an answer then the group of people will leave, including the countless ones who haven't gone up to knock yet. That saves you time and keeps you from having to keep going to the door and give the same strange response! Most people asking aren't angry, just more confused as we don't understand what you're implying. If you are implying something than we are trying to educate you on the contrary. There is nothing wrong with learning more.
DSUM 11 ヶ月 前
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.
Арт Гуффович
just keep working on it. If its impossible, thats life, but society gets quantum computers or other super advanced future stuff in the process
Usopper ヶ月 前
@Scott It implies both ways, we don't know if it is solvable or not. No point pondering if it could be solved in the future with far superior intelligence and better mathematical tools because WE DON'T KNOW. We simply cannot see the future so it is a waste of time to be thinking about it. The only way to know a problem is solvable is after solving it, but there is no way of knowing if a problem is solvable without solving it. Even chess, even though it is a "solvable" game, is extraordinarily complex. Even the most powerful engines and AI currently are not even close to solving chess, the number of possibilities being only one factor.
Usopper ヶ月 前
@Scott Chess being solved by brute force is one of the most ridiculous things I have heard, especially when you mention it would be solved in the next decade or so (even if you give a problem an infinite amount of time to be solved by brute force, it won't always be, depending on the problem). I don't think you comprehend the number of possibilities involved in chess.
Meow Mix
Meow Mix ヶ月 前
Sounds like my dilemma with creating financial market algos lol
Pablo Sampaio
Pablo Sampaio 2 ヶ月 前
Para mim, como professor de Matemática Discreta e Teoria da Computação em cursos superiores de Computação, este vídeo é simplesmente apaixonante! Pela quantidade de assuntos profundos dessas disciplinas que ele apresenta de forma tão intuitiva e pelas informações históricas que eu mesmo não conhecia em tantos detalhes (e que Derek apresenta de forma legal, como um tipo de romance histórico). Vídeo obrigatório para quem é da área de Computação!
Anderson Marinho
Anderson Marinho ヶ月 前
Professor o problema que nenhum professor fela da pota leva isso pra sala de aula. Brasil eu te amo! Um dia seremos mais
BradyPostma 2 ヶ月 前
I rewatched this again. This is one of the best educational videos ever. Not just on this channel, not just on this site. One of the best in this world. Profound but conversational,it makes connections between a dozen aspects of our society and describes the fabric of logic itself,the setting in which our thinking occurs. What an accomplishment!
BradyPostma ヶ月 前
@Hjertrud Fiddlecock If you go away knowing that there will always be true facts that cannot be proven, then you carry with you one of the greatest realizations in human history. That's not moronic. That's brilliant!
Hjertrud Fiddlecock
@BradyPostma cool. I've watched it twice now and i think I'm just gonna accept that I'm a moron and move on to greener pastures
BradyPostma ヶ月 前
@Hjertrud Fiddlecock I think I understood by the second watch-through. It's complicated, but it doesn't make you prove it. It just tells you the premise that was proved.
Hjertrud Fiddlecock
@BradyPostma sooo... are you less or more confused after 10 times than after your first watch?
BradyPostma ヶ月 前
@David Klausa My words indicated that I watched it at least three times. The unspoken reality is that it's more like 10 times.
eleana ヶ月 前
I literally teared up at the very end. Thank you Derek for inspiring millions of people to pursue math, science and engineering!
Renegade Vile
Renegade Vile ヶ月 前
To show how important Turing is to compute science, I have never heard of someone studying a degree in Computer Science and not seeing the concepts of Turing Completeness in their math classes. Unless you work in specific fields, it's unlikely you will actively use any of that knowledge, but it's still very important to know.
Azerty ヶ月 前
not sure if thats a good metric, i agree but id say that example just doesnt really say much thats like saying "to show how important Grug was, his basic teachings of one rock + one rock = two rock to bash other creature over puny head with is still taught in schools today" Turing completeness is just an inherit feature of computers, they wouldn't be possible without that definition and you would not be able to understand computers fully without already knowing that
Mackinstyle 年 前
If you're a mathematician and you are labelled a "corrupter of the youth", you are doing something very right.
august pettersson
@brien maybe you becoq
No Name
No Name ヶ月 前
Socrates agrees with this statement
Ethan Newland
Ethan Newland 2 ヶ月 前
@Brien831 Just want to say your explanation of Cantor's proof is really solid. Especially compared to other people in this comment section that have never studied in a related area and as such when they hear about his proof dont fully grasp it.
Victor Rabinovich
Victor Rabinovich 2 ヶ月 前
I suck at math and this is awesome!
Tea Formula
Tea Formula 2 ヶ月 前
Not always
Mr Gïdds
Mr Gïdds ヶ月 前
Mathematics is amazing because it transcends numbers. The reasoning we find in math can be transferred to any logical problem outside math, and the building blocks of the technology that powers our world is made possible by math. So, my hope is that in the near future we can teach math in a broad perspective like this so that people won't grow to hate it, rather they will grow to appreciate it and use it daily. Math is connected to everything, so it's about time we started treating it that way.
thepassenger 19 時間 前
I second this
hey ho
hey ho 2 ヶ月 前
Amazing Video... there was a time when i understood this better... now I'm still not sure I get it =) To me this is very roughly a formalized and airtight version of the paradox: "If there was a machine that could answer everything, you could ask it to phrase a question it can not answer. If it just tells you "that doesn't exists" it didn't really answer. If it phrased that question it wouldn't be a machine that can answer everything anymore. So in a way there can not be a machine that can answer everything." Any logical system, complete enough to ask a hole into it's own completness, can't be complete. Yet, it needs that capability to be complete. I think their fight boils down to a weird human mentality, where some people are intereseted in math because they consider it to a path to "perfect order and truth" while others, like me, are fascinated by it, because of its riddles and the way it lets you glimpse into the paradoxical and chaotic. I like questions more than answers =)
Rad Dead II
Rad Dead II 2 ヶ月 前
I had this moment of epiphany when the game of life simulated itself… I legit felt like I just travelled through dimensions at that moment with this sense of enlightenment and clarity… I just regained my motivation to pursue aerospace and astrophysics again
Burned Pizza Crust
@pyropulse how is that obvious? can u explain?
pyropulse 2 ヶ月 前
This really isn't that amazing..... it is an obvious consequence of the rules that govern it What is amazing is that someone actually pulled it off by actually doing it; but the fact it could be done was obvious from pure logic
sophia ouchari
sophia ouchari 2 ヶ月 前
that’s nice to hear :)) hope you pursue your dream and achieve great things man
Pavol Hradsky
Pavol Hradsky ヶ月 前
Hello. I just wanted to tell you that this is my top 1 video on JPvid. During that year I have seen it like 6 times and every time I find something new and fascinating. Just wanted to thank you for your work.
DoomMantia 年 前
This is one of the best videos on this channel ever. My brain hurts a little, but I thoroughly enjoyed the experience.
George Tsitsiani
George Tsitsiani 6 ヶ月 前
Took words right out of my mouth.
Tako Au
Tako Au 6 ヶ月 前
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 6 ヶ月 前
@Peter Codner Way to be needlessly pedantic.
Peter Codner
Peter Codner 6 ヶ月 前
With what organ do you experience the "pain"(hurting) of your brain? Can a mirror reflect itself? It is axiomatic that it cannot.
When a disagreement arises between an infinite number of mathematicians there is a non-zero probability that approximately 3.14 of them will form a circle and start throwing pi at each other.
Bug Dracula
Bug Dracula ヶ月 前
@alcatel😊😊😊😀☺ ah, understood
@Bug Dracula When a whole person drops out of all their math courses after the first semester they are .14 of a mathematician. The other .84 of them becomes a psychology major working at Starbucks.
SuperGamer5 2 ヶ月 前
4 is a much better approximation.
LOG!C 2 ヶ月 前
@Bug Dracula uhh 1/7.14 if a person duh
John Daniels
John Daniels 2 ヶ月 前
infinite number * non-zero probability = it has happened, it is happening, it will happen again
Alison ヶ月 前
My incredibly-intelligent 11yo son introduced me to this channel. Your content consistently teaches me new things. Love your work.
Ishaan Pandey
Ishaan Pandey ヶ月 前
This is one of the most beautiful things I've ever seen in my life and it's hard to digest the fact that we may never know the ending to that "life game" and similar conjectures which keeps on going on... Thank you Derek for providing us such wonderful content every time 😇
Tom Oakhill
Tom Oakhill ヶ月 前
It is absolutely true the Alan Turing is considered the most important thinker about what computers are capable of. BUT... His designs had nothing at all to do with modern computer circuits. His computers, their circuit designs, were kept a tightly held State Secret by the United Kingdom until the mid-1960's. The UK only declassified them because computers of much greater power had been widely commercially available for years. These computers were based on the work of John Mauchly and J. Presper Eckert who designed, and built, a fully programmable digital computer with internal storage of data and intermediate results from 1943-46. It could decide what sequence of instructions to perform next based on the intermediate results. They then designed a _second_ computer which stored it instructions in the same memory as the data. NO OTHER computer did this: not any by Turing, which had knobs on the front that you turned to program the machine. Every computer to this day names the internal circuit blocks the same way that Mauchly and Eckert named them. In fact Mauchly and Eckert gave these machines the name "computer": ENIAC was Electronic Numerical Integrator and _Computer_ and EDVAC was Electronic Discrete Variable Automatic _Computer_ As Varitasium says, "computer was a job title for women" and EDVAC was an "automatic computer" which automatically did the job of these women. Turning's was called "an electromechanical machine" and was named "Bombe".
Peter Jerde 🌈
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!
daniel gautreau
daniel gautreau ヶ月 前
@Rob Inson I agree. If you didn't already understand Godel's work, Hofstader's book would just confuse you.
Victorel Petrovich
Victorel Petrovich 7 ヶ月 前
@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 7 ヶ月 前
@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).
Andrew 2 ヶ月 前
I work in theoretical computer science and love this video because it so closely relates mathematics and computability! The first time I learned about the theory of computation was an eye-opening moment for me and a small introduction to incompleteness. Whenever someone asks me what I do and what my field is, I tell them that the most famous guy, the guy who really started the field I'm in is Alan Turing. A nice way of explaining modern day computers is that they are equivalent to TM's. Great video!!
Andrew 2 ヶ月 前
@Haytham Hammud Well I'm planning on going into academia, but there are some jobs in industry where theory is very important, mostly in research. It really depends on the niche you are in! A quick example: a friend of mine works for a subsidiary of a big company that produces chips and he does research on optimizing the building and manufacturing processes of these chips. But it is true that there are less jobs in theory than in most other parts of CS! I would definitely describe myself as a computer scientist/mathematician.
Haytham Hammud
Haytham Hammud 2 ヶ月 前
What jobs are there in theoretical computer science ? Basically I’m from the same field but under the headline of math
GrandMaster Pritt
I learned about some of this stuff in my CS class Data Structures and Algorithms, but you actually made it interesting! This was cool to look back on after taking that class, it helped me gain some appreciation. So, thank you for that
peter mitchell
peter mitchell 2 ヶ月 前
Thank you Derek for this amazing video. This is why maths and engineering are so intriguing to me. Simply brilliant.
tophercruzio ヶ月 前
This is one of the best videos on youtube that I've seen. It's an all-encompassing summary of the nature of mathematics and logic
Tyler Jane Bronson
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!
stickplayer2 ヶ月 前
In the 70s I developed an ehanced version of this, with rules that allowed a "live" unit to have unique characteristics (just like real life) -- that is, some could be more predatory, or need more resources, etc. It's really just infinitely variable to represent whatever sort of competative system.
Ken Fryer
Ken Fryer ヶ月 前
@Alex Hetherington no... the game of life used as a computer is very inefficient. Your saw how slow it was to run the game of life on just a few pixels. It would grind to a halt after just a few factors. But theoretically it could, but practically not
julio ヶ月 前
Me too
sam ヶ月 前
@Alex Hetherington If we had a big enough board, could we simulate a human brain? After all, your brain is just a bunch of dead things coming together to make an alive thing, could we do that here?
Elliot Janzen
Elliot Janzen ヶ月 前
Game numbers moment
Mary Hart
Mary Hart ヶ月 前
Thank you for this video. You have given me a new appreciation for mathematics. Math has always frustrated me but I love how this makes it almost alive.
Soyuno Forinfo
Soyuno Forinfo ヶ月 前
A truly brilliant video. The most fundamental theorems of meta-mathematics and computability, described clearly and beautifully in half an hour. Absolutely outstanding.
Tom Oakhill
Tom Oakhill ヶ月 前
At 20:40 he states the Gödel Incompleteness Theorem the way I was taught it 35 years ago: Any system of axioms sufficient to describe arithmetic will either be able to prove false statements or will not be able to prove true statements, where "prove" means "to decide they are true." There is a corollary in computer engineering: all electric digital logic circuits, complex enough to do arithmetic, will have unused states they can arrive at from which they cannot return. In other words, every computer will need to be shut down now and then.
Burned Pizza Crust
what if i never shut my computer?
Shein Phyo
Shein Phyo 2 ヶ月 前
I don't mind long video, @Veritasium. The videos here are the one I can watch in one sit without knowing how long the time has passed. Keep up the great work!
Matthew Ao
Matthew Ao 年 前
Can we just appreciate how well animated and produced this video is? God, so much effort.
Ward Fadel
Ward Fadel 6 ヶ月 前
@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 6 ヶ月 前
@Ward Fadel So, or therefore, what?
Peter Codner
Peter Codner 6 ヶ月 前
Far simpler clearer and quicker to advance the axiom that a mirror cannot reflect itself.
John Wicked
John Wicked 6 ヶ月 前
@Fred Esch nice 👍
xodz 6 ヶ月 前
The chart scene looks lile Flash MX discontinued
qwertyuiop 1tiop
qwertyuiop 1tiop ヶ月 前
Hello, I want you to know that you are a saviour to my final year undergraduate maths history grade. Our lecturer didn't write notes, gave us a ridiculous reading list of 20 very dense maths books, each over 1000 pages, and didn't record the lectures, all for an exam that is 50% of 1/8th of the final year that is weighted at 60% (so in total 3.75% of my degree). We are expected to understand the full history of maths from prehistory to know and also understand all the different areas of maths philosophy. This video gave me a fundamental understanding and allowed me to exit the anti-philosophy-learning stance I had taken.
Deepti Bala
Deepti Bala ヶ月 前
Thanks to content creators like you who make the time spent here absolutely worthwhile!
Dakotah Rivers
Dakotah Rivers 2 ヶ月 前
The history of mathematics is absolutely fascinating.
Hsenag Rahdeers
Hsenag Rahdeers ヶ月 前
I've watched this video thrice already, pretty sure I'll have to do it again to prevent myself from feeling dumb! Brilliantly made, without a doubt!
Magnus Kramnik
Mathematicians: we must prove this equation Engineers: Eh, it's good enough, we'll just use it
tmc che
tmc che 29 日 前
Engineer, knowing does not require proof, when experience is sufficient.
howard baxter
howard baxter ヶ月 前
@_Nines pi = root (g)
garak55 3 ヶ月 前
Physicists be like : "fools to the left of me, jokers to right, here I am : stuck in the middle with you"
Mattical 3 ヶ月 前
yes, the more practical
Jarred Mosdal
Jarred Mosdal 3 ヶ月 前
Mathematicians: we must prove this equation. Engineers: Eh, it's good enough, we'll just use it. Lawyers: the evidence is inadmissible. But Godel's numbered cards are a gold mine. I'll add Bates numbering to each and consult until the funds available are exhausted.
Madhur Garg
Madhur Garg ヶ月 前
This incompleteness theorem completely changed my perspective towards mathematics. You are doing a great work.🙌
gome ben moshe
gome ben moshe ヶ月 前
Please do more math videos they are extremely fascinating!
Vlad Lazăr
Vlad Lazăr ヶ月 前
Absolutely fantastic video! Great work, my friend! 🤝🤓
Victor Rabinovich
Victor Rabinovich 2 ヶ月 前
What a window into the history of the 20th century, thank you!
Michael H
Michael H 9 ヶ月 前
Teacher: Your math is flawed. Student: No, math itself is flawed.
pyropulse 2 ヶ月 前
this doesn't show math is flawed, but I'm glad people still like making jokes of them being so dumb and trying to excuse it with super dumb jokes they think are clever
clash o clan
clash o clan 3 ヶ月 前
You missed the point of the video kiddo
Janis Thompson
Janis Thompson 3 ヶ月 前
My son tried that line in calculus, disputing his teacher. Was not spoken to, by the teacher, the rest of the year. Hes44 and just fine ❤️🇨🇦❤️
A Czech Man Going His Own Way
Bro, the school is about following and repeating what the teacher says. Not about discovering the ultimate truth (or about convincing/converting the average teacher).
Peter Codner
Peter Codner 6 ヶ月 前
Depending on how you define " flawed". Is a mirror not a mirror simply and only because it cannot reflect itself? It is axiomatic that a mirror cannot reflect itself. If axioms were not a priori they would not be axioms.
Ivan Bakin
Ivan Bakin ヶ月 前
This was a great and entertaining video, but I highly recommend Dr. Ron Eglash’s TedTalk on African Fractal Thinking to provide a greater depth to the preservation of the concepts of infinity and self reference. Even binary has strong roots from sand divination that came from Africa as part of the use of fractals in African societies.
Random Whisperer
Love these high quality informative videos
Isaiah Inman
Isaiah Inman ヶ月 前
i used to loath math, now after college its become one of my favorite subjects. lol wish math was taught like this
Proskillz ヶ月 前
This is why I love math. One of my favorite sayings is that math is the language of the universe.
Xavier Bergeron
Seeing the game of life being carried out in the game of life was a really impactful moment in this video
Mr. Yeet
Mr. Yeet 2 ヶ月 前
I came
ElectraLumen 5 ヶ月 前
Mateus Ferreira
Mateus Ferreira 9 ヶ月 前
mohamed amine khadhraoui
It was a really impactful moment of my life in general. Due to the music probably.
deejflat ヶ月 前
This easily should be JPvid’s #1 most watched video ever. Super cool! Everyone should watch this.
Kevin Bean
Kevin Bean 2 ヶ月 前
I liked this video! Since I liked it I also clicked Like so, like squared L(2). A lot of material that could become an entire quarter in college math ( perhaps also middle school ). Poor Turing, he was before his time, and did not respect his Era current laws and legal situations, not to mention being a bit paranoid. But those issues did not prevent him from the miracles he helped invent and promote. Perhaps we owe him a bit of slack? A posthumous pass? 😀
Proskillz ヶ月 前
This is why I love math. One of my favorite sayings is that math is the language of the universe.
Zaphod Beeblebrox
How are you so good at explaining things? You are just too good!
Kyriakos Mousias
Kyriakos Mousias 9 ヶ月 前
As a mathematician I haven't seen a more elegent presentation of these concepts,especially Godel's theorem. Amazing job thank you.
Aisha 7 ヶ月 前
Any tips on becoming good at math as a high schooler?☹️
william mabon
william mabon 7 ヶ月 前
@Dayton Robar What's naturally good? Opinions are endless.
Dayton Robar
Dayton Robar 7 ヶ月 前
Presentation is everything for people that are not naturally good at math.
Michael Salisbury
Michael Salisbury 7 ヶ月 前
This is the perfect medium for this stuff.
william mabon
william mabon 8 ヶ月 前
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.
yash 2 ヶ月 前
I don't know a lot of maths but I can prove that these 34 minutes of mathematics have taught me more than 13 years of schooling
KEMNS Art 2 ヶ月 前
This video is just amazing. This is the third time I watched it in a few months and I never get bored thinking about it.
Iso bOOl
Iso bOOl ヶ月 前
Math is the most compressed simulation of the universe. Since the universe is infinite and not a perpetuum mobile it is completely reasonable that math deviates from the outdated human assumption that there might not be perpetuum mobiles when we take parts of the universe into focus - but not the universe itself. Therefore this hole never will get patched without creating another one. It's like imagining the borders of the universe - only that a border by definition consists of at least two sides - so what's on the outside if this border if not even more of that sweet little universe.
Saltysenpai 2 ヶ月 前
Cantor's diagonalisation proof, cheats by offering an impossible scenario. Think about it for the example to be true we must have a comple list with every real and natural number, let's say for the sake of argument that storing something infinite is even possible. Then it asks us to perform yet another impossible task in the diagonalization test of adding +1 and moving to the next number and so on and proceeeds to explain to us that when we are done the number resulting would be different than any of the listed numbers. But for us to be done in the first place the list has to end and if it end and we extract a number all we have done is make a really long list and made a number that would be on that list had the list continued. Here is another example so you can picture what im tryinig to say amke the same naturals and real numbers list but stop at the first natural number, now apply the diagonalization test by adding one to the first number (let's say again that you can be done with such a task ), what you are left with is a number that would be on that list had you continued to make it. What im trying to say it's that the Example plays with our minds limited capacity for understanding what infinite really means. Feel free to tell me if I missed anything
Epic Marschmallow
You're very (obviously) wrong. It's also pretty arrogant to assume you know better than the entire mathematics community
pyropulse 2 ヶ月 前
you are wrong because you introduced a further, unneeded assumption, which is that we need a complete list for the 'proof' to be valid We are working in logic, not actual computation..... If you were right, then integral calculus wouldn't work, and yet it does. We never 'carried out the infinite sums."
Niklas 年 前
This is basically my whole computer science studies in 34 minutes.
Eric McKinley
Eric McKinley ヶ月 前
@kotzpenner cs degree is a waste of time anyway
Zoran Matijević
@Brandon puntin One of the first things general science methodology and logic professor explained to us.
kotzpenner 年 前
@a set theory and all that is what I struggle with the most
a 年 前
@kotzpenner what math are you in rn? Just got my CS degree so maybe I can give some insight
kotzpenner 年 前
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.
Isaac John Padilla
Isaac John Padilla 2 ヶ月 前
This was one of the craziest videos I've ever had the attention span to actually sit through! I'm not going to lie I was definitely lost halfway through I had to watch it two or three times.
Menthols ヶ月 前
This was an amazing video, really got me thinking. Thank you.
Michael Epp
Michael Epp 2 ヶ月 前
Even if I watched this an infinite number of times, my brain would always reach its elastic limit.
수과학애호박 MathScienceFancier
Really massive and complex for me to understand, though I've already watched and somewhat understood this topic.
Jean le Ronde d'Amelbert
If there was an Oscar for JPvid videos, I have absolutely no doubt this would be nominated. Well done sir!
Gabriel Carvalho
@Jean le Ronde d'Amelbert lol, here's my like sir
Jean le Ronde d'Amelbert
@Gabriel Carvalho you can like it now :)
Jean le Ronde d'Amelbert
@pottyputter05 I commented without much thought but I absolutely agree. Some (emphasis on some) of the content on JPvid is absolutely on par with Oscar nominated films, especially some of the lower budget ones
Simon B
Simon B 年 前
So we have the rewind or whatever it is but we don’t have YT oscars? Ricky we need you
Gabriel Carvalho
I was going to like your comment, but it says 404...
Janice Hadley
Janice Hadley 2 ヶ月 前
I have to yet again admire the great thinkers, philosophers, etc.
Sachin Meel
Sachin Meel ヶ月 前
Although I dont understand some part of this video. But eventually I thought this is really great video for scientific persons and the editing of video was also nice.
Nishad Dixit
Nishad Dixit ヶ月 前
I wish I could understand all this. And it is scary for me that this has been easily understood by so many people.
Andrew far
Andrew far ヶ月 前
I understood the video, what scare me the most Is that some people can write math demonstration of this concepts and these are basic things. Humanity Is Amazing.
Mohammad Oskuie
Mohammad Oskuie 2 ヶ月 前
Amazing and informative. Thank you.
justtrolin 2 ヶ月 前
the completeness bit seems to reflect the"begging the question fallacy". it seems to stem from an implied static state, that the paradox is because of duplicity inherent in the work itself. if the definition is relaxed enough to imply scenarios where the reference palettes from which the word gets its "form", then the static state and the comfort it grants to the mind in its finite form changes. it is this dynamic inference that grants the joke of Jim being his own enemy its hilarity. as it is required for the joke to ignore the circumstances that make Jim his own enemy to be verified, or even true.
Jamie Crookes
Jamie Crookes ヶ月 前
I always hated maths lessons at school because I couldn't wrap my head around them, but i've always been fascinated by things like this due to my work with computer. Only found this channel today. Keep up the great work.
Kyla Evelyn
Kyla Evelyn 2 ヶ月 前
Thank you for mentioning Turing's tragic end... Whenever people talk about how brilliant he was or his contributions during and after WW2, they often leave out the injustice that was done to him simply because he was gay. It's sad to think about how much the world lost out on his brilliance due to this ignorance, and I think it's important to remember so we don't repeat these tragic mistakes.
Katie Larsen
Katie Larsen 16 日 前
I see math as another language, where you have to just agree on certain things in order for it to make sense. If you look too closely at any object, it is made of energy, so in a way it ceases to "exist" in the conventional sense. I see math the same way: if you look too closely things get weird.
Lemon D
Lemon D 年 前
I don't know why but I love the idea of mathematicians gathered in a room yelling and hurling insults at one another
MrKotBonifacy 7 ヶ月 前
@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 7 ヶ月 前
@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 9 ヶ月 前
“Corrupter of youth” 😂
Grevoron 10 ヶ月 前
the mic drops could've been the hottest known to mankind
J K 10 ヶ月 前
Oh Reginald.... I DISAGREE
dubmaster z
dubmaster z ヶ月 前
Derek, this is really great content. I’m going to coin a term now called “Content Disease“. Meaning = A content provider of any kind using mediums such as JPvid, with an extreme addiction for the need to constantly produce content. Usually at the risk of devolving themselves from life, family, relationships and social constructs. “ Is there a mathematical proof in that Derek?
Matt Smith
Matt Smith 2 ヶ月 前
Then there's my favorite type of number: the reccit reverse exclusion clause, a number that can only by defined as being anything other than itself. Brought to us by the great philosopher Douglas Adams who gave an example of of arrival time for a party at a restaurant is therefore the one time in which it's impossible for anyone to arrive.
Mokshith Kumar
Mokshith Kumar 5 日 前
I am watching mathematics!!! Never thought I'd do that! Awesome job man
Raj Pandey
Raj Pandey 23 日 前
i always come back to this video after every few months to see whether i have developed enough to understand everything in it completely 100%. nit there yet.
jonasba276 年 前
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.
AR 4 ヶ月 前
@Peter Codner Horrible attempt at sounding smart. Did you feel bad this video didn't including anything about your field of expertise which you could flex. Sit down buddy, you've successfully cringed me out.
Peter Codner
Peter Codner 6 ヶ月 前
@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 6 ヶ月 前
​@Peter Codner Damn you sound like a nice guy
Peter Codner
Peter Codner 6 ヶ月 前
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 年 前
You like conflating. Well that sums up this whole video. Have fun!
Yuri the YouTuber
Yuri the YouTuber 2 ヶ月 前
26:00 perhaps im missing something, but i cant see how this is a paradox, yes it gives the opposite output from what the initial h+ does, but thats what h+ was programmed to do, so in my mind this isnt necessarily an issue with h+ being flawed, but rather how it was programmed being flawed. Im not an expert in math btw, but I am taking programming courses so im quite familiar with programming stuff that ends up not working for whatever reason. But that reason usually boils down to, "It's not the machine that made the mistake, it just did exactly what you told it to," which seems to be the case here. h+ is forced into an infinite loop if it halts, which makes 'h' do as it's programmed and loop as per the program code used. However, because its part of h+, the output ends up being a halt, because that's what the machine 'h' is part of is programmed to do. And of course the inverse would be true as well. Please do correct me though, i would love to learn why im wrong and expand my knowledge👍
Parniyan I
Parniyan I 2 ヶ月 前
And I'm supposed to plan my whole Year 2 and 3 DigiTech units, lessons, assessment, transdisciplinary themes, etc. for the term but I'm watching this coz I LOVE MATHEMATICS!!!!
Alfin Dpr
Alfin Dpr 2 ヶ月 前
I wish i have this kind of explanation 30years ago. But its never late for clear explanation of fundamental law
Adnan ヶ月 前
One of my favourite Veritasium videos❤️
stephan Roche
Ironic that Godel's death was the result of a self-referential paradox: he died in order to not die
Aayush Srivastava
Aayush Srivastava 9 ヶ月 前
Niranjan 9 ヶ月 前
@Matthew N AMEN!
Shayer S. Utsho
Shayer S. Utsho 9 ヶ月 前
@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 10 ヶ月 前
ctrl 10 ヶ月 前
Great, now I have to clean my brains off the ceiling.
Neom ヶ月 前
Ok, this was my second video of Veratisium I ever have watched...the first was about the impossible measuring of light in one way...combined with this here i would say, "that's brain fxxxing". But that's not the point, the point is, I am loving it! And the game in game declaration is another milestone to the point that we are simulated. An other theorie that is also not to be checkable...
Michael Anderson
Michael Anderson 12 日 前
I like your simulation take.
Naterkix 2 ヶ月 前
"Words is hard sometimes" is a phase I use and have used on me when something has been said if it doesn't quite come out right. I think for math we could use "numbers is crazy" but you'd prolly hafta re-title "math" to just "numbers is crazy" or something.
Naterkix 2 ヶ月 前
@pyropulse .......Yes, that was the joke. If somebody says something weird and you correct them with a completely correct statement, that's not really a joke. Also, something something capitalization and punctuation.
pyropulse 2 ヶ月 前
when a word is plural, you use 'are,' not 'is,' so yes, words clearly ARE hard for you
Rum 2 ヶ月 前
I may not be able to grasp everything in this video but it feel so fun to watch it.
mknomad5 2 ヶ月 前
Probably the third time I've watched this. Thank you for all your work.
Judy Petree
Judy Petree 年 前
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.
2 minute vape reviews
I'm 104, male. I'm grateful I watched this video
Peter Codner
Peter Codner 6 ヶ月 前
"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 6 ヶ月 前
"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?
blue sewage
blue sewage 10 ヶ月 前
@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.
Shayden Foran
Shayden Foran 3 日 前
I always though 9/9 was an interesting mathematical problem. Does it equal 1 or .999(repeating) 1/9=.111(repeating) but any number divided by itself = 1. So .1×9=.9 so is it 1 or .999(repeating) or is it both?
Tomas 3 日 前
0.999... and 1 are different representations of the same number
Em K
Em K 2 ヶ月 前
Continue to be among the best videos out there!
nan0S 2 ヶ月 前
I think the only thing to mention regarding decideability of maths is that we have to say that Halt problem for a Turing Machine can be expressed as a mathematical formula, which if proven (by a Turing Machine) would be the algorithm for halting problem which we know it doesn't exist.
OpiatesAndTits 2 ヶ月 前
So if I’m understanding this correctly the contradiction is that a system can’t prove itself? Like no system you can devise can prove the validity of the system you devised. Which sort of makes sense. You can’t measure a ruler with itself but you can use that ruler to make consistent measurements. It’s unprovability is evidence of one thing - it’s arbitrary. A formalized system of mathematics is still useful though it can do amazing things: provide answers and make predictions about the real world making it inductively true just not deductively true. I believe in philosophy this is like perfectly basic beliefs. At the end of the day things like the law of non-contradiction being deductively provable isn’t relevant so long as they hold up in practice which is perhaps what it means to be turning complete? I dunno lol
mike johnston Bob
Godel's friends: "No one's trying to kill you Godel" Godel: "You can't prove that!"
Chinedu Atisele
Chinedu Atisele 2 ヶ月 前
Frank Pembleton
Frank Pembleton 9 ヶ月 前
The irony that he was a living Godel's theorem. He died, so that he wouldn't die, but the statement 'he wouldn't die' is false as he did die. But he died because he didn't want to die. Damn.
Wesley Jones
Wesley Jones 9 ヶ月 前
Jean-Christophe Le Bayon
@Lavabeard No, that would make him become his own wife
bradOZ 9 ヶ月 前
@Mooney Makes think he just stated a fact. The guy died from something else he would have said that too.
Ryan Schlegel
Ryan Schlegel 2 ヶ月 前
Although it appears unthinkable, if the models were allowed to go on forever the premise of life would eventually expire. As it is for numerology it would be correct in saying that each scenario is true. Probably, if prime numbers get rarer and rarer over time there will be vast expanses where there are no prime numbers. The probability of one will decrease and decrease. The question would then become how long you would be willing to wait until one appears. If the probability of one manifesting is longer than the amount of time left in the universe, then reasonably the relative nature would suggest that it is insignificant and therefore both answers would be correct. There is an end to prime numbers but technically there is no end. -you're welcome.
christopher mccaul
Wow man this is some of your best work yet Tom top notch!
EdgyShooter 2 ヶ月 前
Wasn't Cantor's diagonal argument based on a binary number where when you created your diagonal each digit was complimentary (ie, if it was a 1 originally it was changed to zero)?
Greg Anderson
Greg Anderson 2 ヶ月 前
Fascinating and brilliant! I pulled Godel Escher Bach off the shelf thanks to this.
tuomas rönnberg
"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.
jameson44k 4 ヶ月 前
@Wassup Rocker Totally false, set theory is universally taught to undergraduate maths students and is regarded as foundational to modern mathematics.
Wassup Rocker
Wassup Rocker 11 ヶ月 前
to my knowledge set theory is still regarded as a mini disease today. rare universities teach it if not just an introdduction to make know people it exist.
l1mbo 年 前
@Electro_blob 2 Sorry this post is going to be a mess because it consists of random points I thought of, rn I'm too tired to organise them all into a structured reply; if it's too incoherent I'll try to restructure it "Maths relies exclusively on intuition for its results" where are we getting this from? Other than geniuses (which tbf consists of a much larger than normal proportion of mathematicians) who say they 'just know' I don't think most mathematicians rely on intuition. I at least for sure don't 90% of the time whenever I do any math. Intuition is logic our subsconscious thought of that we can't find a rationalisation immediately for. But it exists. However we have no reason to choose the decision of our intuition over logic as it is only able to choose because it leans into our biases. You can explain why you get a certain intuition with logic but not the other way round There is nothing that intuition can tell us that logic can't given enough time; intuition is just efficient guessing so in a way it could be said it completes things in Polynomial time which would take logic NP time. The intuitionists also, obviously, used logic to demonstrate to others in form of their proof and used intuition only to guide them. Intuition may have ended up being indispensable, but that's not because it's somehow more fundamental, but rather that without the efficient guessing we simply cannot reach a conclusion with logic alone in enough time. 1. But we can't intuitively "know" beforehand whether a system will terminate or not either. In others words we don't have intuition for things that can't be proven logically. 2. So this would mean that logic may not be the most fundamental thing but intuition isn't the best word to describe the thing that is. 3. But, because we intuitively derive basic rules of logic doesn't somehow suggest that intuition is more fundamental, (side note this intuition would be quite different to what I had been referring to till now) it could simply mean that we are just wired to think this way. Why not some other way? Well, because this is how the world works! This is what is beneficial for survival. Same reason as why we see "visible" light and not X ray, we adapt according to how the world is 4. ; Also it might be that there is not something more fundamental than logic but something else just as fundamental 5. We can still describe the Turing machine each moment follows the next according to only logic of the fundamental rules Also that was very interesting to read, thanks for writing an in depth reply. Do you know if current mathematicians are working on reformulating mathematics
Rumford Chimpenstein
@Electro_blob 2 In this case it wasn't JPvid auto-deleting it, or else we wouldn't have gotten the notification. Its more likely he thought it through, changed his mind, and deleted them himself.
l1mbo 年 前
@Electro_blob 2 ik it's a lost cause but iirc in his second reply he said that the game of life you saw in this very video was also literally just that- emergence, do you think that is also magic? Don't remember the first reply though Kinda insane even this got deleted he didn't even say anything offensive
Diego Arriaga
Diego Arriaga 2 ヶ月 前
As a computer scientist, this blew my friggin mind
Dark Knight
Dark Knight ヶ月 前
7:05 the answer of the limit is -π/2
Jason Holloman
Jason Holloman ヶ月 前
Best video on the subject. The visual aides help so much.
Zombie 1005050
Zombie 1005050 ヶ月 前
I'm taking a class in abstract and linear algebra, and we heard of this before.
Arthur Barbosa Câmara
I'm a PhD in computer science. This is a full-on Discrete Mathematics intro course. This is amazing.
My dad's best friend at Cambridge university was Dave Masser. Do any of you know that guy? Formulated the abc conjecture..
Kevin Rinkanya
Kevin Rinkanya 2 ヶ月 前
Some poor kids are about to be forced to watch this
Joseph Smith
Joseph Smith 2 ヶ月 前
I have a basic math knowledge but do to videos like this I understand some theory
Zarth Sajuuk
Zarth Sajuuk 3 ヶ月 前
There is a fundamental flaw in the real vs natural numbers challenge. The way Veritasum is presenting it - is a trickery. It is presented as if natural numbers N are being opposed to the real numbers with the length of N, which is wrong. Obviously, the natural numbers from 1 to 100 will have fewer combinations than a real number with 100 digits in length. But that is wrong comparison. The correct one is comparing natural numbers with K (infinity) number of digits in it vs real numbers with K digits in it. So, if this task is presented properly without tricking the viewers into substituting of the natutal number count with the real number length, then it will be obvious that this task has a valid conclusion (see below). In other words, lets say the "infinity" (or "lim") is N, and assume it's 2-digit value (K=2). That means on the natural number side you have 100 possible values between 0 and 99. On the real side you have got "random" non-repeating values between 0.00 and 0.99. Please note, the trick in the video lures you into an impression that you would have more digits in the real numbers row, e.g. you could use 0.991 value, but it is wrong because of the premise that you have reached the N (in the natural numbers) and that is the "infinity". Otherwise you could say "well, whatewer is the last natural number, I will add 1 in front of it and I will get a new unused natural number". But the idea is - you have reached the limit. But this means, you are supposed to reach the same limit in real numbers that will tell you that there is no more digits to continue your real numbers. Therefore, we are playing in the same field and the limit is the same. So if we go back to our 2-digit "lim" for natural 0 to 99 where you have 100 variants or real of the same lim between 0.00 and 0.99. Now you can try applying "adding 1 to the digit" in the real row. What do you get? And the answer is - you get it duplicated. Or you have to violate the limit. So, the conclusion is - there are as many natural numbers between 0 and 1 as there are real ones. The importsnt understanding is that natural number 1 and real 0.1 are in fact: 0000...infinity...0001 and 0.1000...infinity...0000 And if their length is the same - they have have the same number of combinations. Thanks for reading this if you reached this line :)
BAZM0 🇬🇧
BAZM0 🇬🇧 3 ヶ月 前
Whats a PhD in computer science? Isnt that called a geek 🤣
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