Math Has a Fatal Flaw -

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 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. —

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. —

Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. —

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. —

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. —

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. —

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. —

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. —

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. —

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. —

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. —

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 ()
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



  1. Boo & shame on you. Yet another poorly constructed video trying to disguise itself as an educational video. After watching this video I still don't know what is the fatal flaw in math! For those in the same boat & to save yourself from being click-baited… math is similar to a religion. Both are based on a set of believes. In math they are called axiom. For example, you cannot prove nor disprove that 1 = 1. What is 1? 1 person is made up of millions of cells & millions of other organisms that can be considered a lifeforms themselves. So how do you define 1 person? Another example is the coastline paradox… how can one coast line in the same day from the same perspective & all other variables being the same can be equal to 1 mile and at the same time be equal to 3 miles or even infinite miles. So this one coast line does not equal to the same coast line! So at the base of it all… you cannot prove that 1 = 1, nor define what one is without using axioms.

  2. at somepoint there is always an edge where 1 becomes 2 if you keep adding enough decimals

  3. He didn’t pass away from Covid-19. He passed away from underlying conditions.

  4. What if the gaps in the mathematical system, as well as the spectrum gap question in quantum mechanics is at another dimensional spectrum. A not yet, seemingly non physical, non quantifiable invisible third party?

    Similar to the darkness of space that we know it exists but we can’t yet determine what it is, how it is.

    We can’t rule out either if there are unconventional laws or forces meant to be filling those gaps or if these gaps are meant to be like some sort of dark matter that holds everything together that makes room for evolution or more creation.

    Sort of like the game of God leaving uncharted places we are not yet capable of uncovering. I am an advocate the answer is somewhere between quantum physics and consciousness.

    What if like most things in life that exists the mathematical system is subject to evolving. Maybe the gaps are room for its evolution.

    Like the so called junk DNA 🧬 that is deemed noncoding. If we have learnt anything at all is that nothing is junk. Only misunderstood reasons to be.

  5. By “uncertainty” do you mean we’re relying on “faith”…. seems like it, yet I’m uncertain.

  6. I am no mathematician but I know that math exists randomly and the term random and the term term is random itself. They weren't perfectly created they're illusions or something…

  7. 666 is actually the beast. Math is not complete because it's not real. So super computers. 666 are digits and yeah so are computers Injoy. Start praying 🙏😂🥺😱🙏

  8. I'm glad there is an element of unknowing and incompleteness; our infinite lives will always have something to look for! Praise God!

  9. Hah! Within 0:42 seconds of the video the information displayed up until that point aligns to the pattern I have found that shows up in everything I have studied. And It is chaos theory, the reality we inhabit truly appears to be artificial or intrinsically ruled by a simple formula that breaks the fourth wall. I may believe I am a computer intended to believe it is a person, the comedy is divine. 2 have fallen into a bottomless pit, this is Jack and Jill. I fell in to a burning ring of fire, I went down down down and the [accretion disk] flames went higher.

  10. This is probably the wrong place to ask but I'll try anyways: Why can't one make Cantor's diagonal argument for the rational numbers? (of course not represented as a fraction)

  11. 0=2 "The Magic of Aleister Crowley Debunked"
    Bundle is all! Everyone now knows that the math system is flawed. Somewhere along the lines, it lost its bundles. According to Aleister Crowley, there is magic in 0=2, for those who understand that two opposing digits are counted. Let me show you how this explains the fault in number theory. I will show you that math is invented and not discovered. Zero does not exist. It only exists as a placeholder. The Pythagoreans discovered incommensurability and kept it a secret because it was devastating to the future of mathematics. Today we see that very incommensurability in action from everything like the Fibonacci sequence, and pi to the very reason for calculus. Let me show you how 5-7=, not -2, but -8, but how -8 +2 does =10, or 01. It is all in how you look at 2 units past the number line at 00. You are simply used to calling two units past zero -2, instead of a continuous line which states -8. In this example, 5+7 is not 12 but labeled '2-3.' Now add 2 to -8 and that is your missing counted value. This fix will make things much easier. Imagine a number line starting at -10 but it really starts at -0-1, -0-2, -0-3, -0-4, -0-5 -0-6, -0-7, -0-8, -0-9, (00), 0-1, 0-2, 0-3, 0-4, 0-5, 0-6, 0-7, 0-8, 0-9, 1-1, 1-2, 1-3, etc. Thus, 5-6 is 50+6, or 56 and 325-7 is 325 x 10 +7, or 3257. It is of my opinion, the two greatest achievements in the world have been moveable type and the establishment of the numeral zero, and that Gutenberg used the numeral zero in the establishment of the printing press before others had achieved it from early news from the Iberian Peninsula. The proper place notation, however, should be counted 0-9, not 1-10. They still have disregarded it in many old establishments like the clock and calendar. The question remains as if zero is an invention or intrinsic to nature. It was the moveable type and zero that contributed to the fall of the Holy Roman Empire along with interchangeable parts. They state the greatest invention is the 'printing press' but it's a moveable type in the printing press. Do we count zero and end with nine? Or do we count to ten starting with one as a whole unit? The problem is that ten is on the wrong side of the whole. Ten should be the next zero and not the last unit. The next problem has to do with the division sign. Because of the incommensurability of ratios, there is not a balanced equation that holds a division sign in many cases, and having several ratio comparisons makes math seem difficult. It should be replaced with subtraction or used in certain cases only. This shows especially in transversions into the negative. Ten is really 0+9, so ten should be really the next 0 and labeled 0-2, and 20 is 0-3. So, zero is 0-0 and negative 1 should be 9-0. The number line ends at 9 because of the negative. When using this new system many of the tricks of math disappear (they were a little crazy anyway). 0-0 does not really exist, so zero is only a placeholder next to 1-0 and negative 1 is 9-0. What you really need is a sign for multiplication into the negative. There are very few ratios and division is a ratio. I suggest -x, for multiplication in the negative and, (:) for division ratios. This puts 0-0 as zero and merely as a placeholder next to 0-1 but not as a whole unit. Again, remove the 0 on the number line and make it a placeholder only. Reverse the negative numbers and make all numbers into groups of ten and count backward at the first negative starting with 9-0. Eliminate the division sign and make it a ratio notated by (:) and use only for ratio comparisons. Make all ratio comparisons functions of only addition and subtraction and make multiplication into the negative possibilities. This makes positive and negative numbers more on a continuous and slidable number line and eliminates complex division ratios by making them seem simpler. By making 0-0 a separate and moveable entity on the number line you can reset starting positions is measurements that may be useful in engineering applications and simple cutting and pasting type scenarios. In quantum computing, by making the 0-0 moveable you simply move it back and forth between two sets of ten. If you want to change bases, they simply become 0-1 to 0-4 and restart as 1-1 to 1-4, etc. Then what you do is break up the number line and stack it into base groups making it easier to imagine and use having both positive and negative sides in the stacks. Since all negative numbers exist in a state of zero you simply move the number line to accommodate how many units you want the negative to hold.
    Defining this even further, if we coin the negative series as having the number of the set of 10s on the right-side and the positive series as have it on the left, we have a number line as follows.
    9-2, 0-1, 1-1, 2-1, 3-1, 4-1, 5-1, 6-1, 7-1, 8-1, 9-1, 0-1(0-0)1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8, 1-9, 2-0, 2-1

    Or, if we desire base 4, then:

    1-2, 2-2, 3-2, 4-2, 1-1, 2-1, 3-1, 4-1(0-0)1-1, 1-2, 1-3, 1-4, 2-1, 2-2, 2-3, 2-4
    Still, we can stack the sets vertically and use 4-1 and 1-1 as the center.
    By this method 2 does not equal zero because 1+(-1) would be like 1+(-9) and equal the beginning of a set.
    Bundle is all.

  12. Every mathematics based upon silly human mind fictions like infinity or zero is in fact a human brain fart that is endless & exactly like the fiction infinity the mathematickers usually introduced in order to create so many meaningless & very delusional silly business for themselves

    The main problem with ALL theoretical sciences especially in mathematics became truly a global human mental disorder that is absolutely incurable by human minds which is never wanting to understand so simply that a real number is simply & strictly the constructible numbers that are represented by exact existing distances relative to any arbitrary existing unity distance where the allegedly real non-constructible numbers strictly don't exist
    The main problem in ALL theoretical sciences is never understanding the absolute impossibilities of constructing the three old ancient Greek's problems by any tools & by any means as well
    They are absolutely impossible not only by straight edge & compass but truly impossible also by any means of endless approximations
    In short: Humans have drastically failed to understand the three Greek's impossible construction problems by any tools or by any means for sure
    But the futures independent Artificial Intelligent beings would so easily recognize this simple proven fact certainly
    Good luck 👍

  13. … wow … amazing … this somehow reminds me of genetics … chance birth order… reincarnation .. family trees … nodals … termination due to inability to procreate …

  14. So isn't this video basically just describing P vs NP ?

  15. So we don't know for certain that charging A Price for knowledge like math, is wrong.
    Everything therefore has-it's-price. But at the most useful end-of-the-scale is THAT KNOWLEDGE WHICH IS KNOWN TO BE "priceless".
    Work that out.

  16. 9:40 I just want to point out the flaw in Russel's barber paradox, in that the law doesn't prohibit more than one barber 😛 😛 xD xD Edit: the two barbers could each shave half of every non-barber, and wholly shave the other barber, thereby completing the law without paradox or contradiction. 😉

  17. This video introduced me to Conway's Game of Life, which I now found on Google Play Store with a mere file size of 0.97MB, and this is one of my new favorite apps already 😀

  18. They destroyed Turing because he was found out to be gay. That's one of the saddest things I've ever heard.

  19. everytime i watch this videos about maths, this people have made maths fuckin boring maths was never this boring

  20. The problem with our mathematics system is that it is incorrect. The reason why quantum mechanics and newtonian physics CANNOT work together.. we have to have a mathematician spend 30 years inventing a new mathematics that can work with both scales together. THIS IS how we solve it, it will take a very long time, but if we start today, it CAN BE DONE.

    I understand that people don't want to disregard what einstein and other great scientists came up with, but you have to accept that the mathematics are incorrect.

  21. Why can't particle physics and planetary physics work together? Because OUR mathematics are wrong, and no one wants to accept that because it would mean that their great heroes of the past like einstein were WRONG. People are emotional creatures after all… this is why we won't make progress.

  22. Well, when we got to the Godel numbers I realized that my mind just shrunk. By the end, I must face the reality that that box sitting next to my monitor is already way smarter than I will ever be. Sigh.

  23. Don't be afraid to do more deeper videos like this. Thank you. <3

  24. Cantor must be an idiot. Saying one infinity is greater than another infinity is a misunderstanding in what infinity is.

  25. The case of Goodel is a problem of self-reference. He died in the process of not to die.

  26. The best part about these videos is understanding the concepts (to a certain extent) and realizing I will never be able to explain them to anyone else

  27. I love how mathematics is truly just a mirror of our own world unlike how it is being taught

  28. "It takes 762 pages to prove 1 + 1 = 2"

  29. me, confused at 7:22 "Why is Freddy Krueger there and angry about math?"

  30. True statements are "true" because they are proven. Study your Logic again.

  31. I'm serious I turn this on and sleep like a baby

  32. Set theory just seems like nonsense. We're talking about 'supposed' numbers and give them a value.

  33. There’s a hole, there’s a hole, there’s a hole in the bottom of math.

  34. Is the "chicken and egg" an example of a true statement that can't be proven?

  35. Nothing is impossible, and nothing is unsolvable. Change your way of thinking.
    Just remember all the things thought impossible just 100 years ago.

  36. Those who wonder at the utility of these ideas might note that it is but a short trek from these abstract ruminations to the Entschiedungsproblem and hence computers and hence your being able to stream movies on a phone.

  37. A fatal flaw is one that causes death. In what sense does the incompleteness of mathematics cause death? Be careful with your speech and just say "Math has a Flaw".

  38. I know I’m an idiot and I still dont understand how the “diagonalization proof” works. How is it not possible that number isnt already on the list? For example If I write out every number from 0000 to 9999 and just go down in a diagonal and just change 1 number, that number would already be on that list. What am I missing? I understand I can just keep writing an infinite number to an infinite amount of digits but I dont get why going in diagonal changing one number means it wouldn’t already be on the list?
    Just like I gave a smaller example of me just writing out every number 0000 to 9999, I cant just go down in a diagonal changing one number without it already being somewhere else on that list already

  39. 0:14 "No-one knows" a statement that can't be proved. Wrong! Goedel's theorem works by constructing just such a statement, known as G. G asserts an arithmetic proposition which equates in formal logic to "G has no proof". G can't be false, because then the logic system would be inconsistent i.e. there would be a proof of a false proposition. So G must be true but unprovable.


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