The Discovery That Transformed Pi

For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. This video is sponsored by Brilliant. The first 314 people to sign up via get 20% off a yearly subscription.

Happy Pi Day! (for a few days ago...)

Arndt, J., & Haenel, C. (2001). Pi-unleashed. Springer Science & Business Media -

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley -

Borwein, J. M. (2014). The Life of π: From Archimedes to ENIAC and Beyond. In From Alexandria, Through Baghdad (pp. 531-561). Springer, Berlin, Heidelberg -

Special thanks to Alex Kontorovich, Professor of Mathematics at Rutgers University, and Distinguished Visiting Professor for the Public Dissemination of Mathematics National Museum of Mathematics MoMath for being part of this Pi Day video.

Special thanks to Patreon supporters: Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Lyvann Ferrusca, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

Written by Derek Muller and Alex Kontorovich
Animation by Ivan Tello
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music by Jonny Hyman and Petr Lebedev

Additional Music from "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale"

Thumbnail by Gianmarco Malandra and Karri Denise


  1. JD - RoBeats

    JD - RoBeatsPrije 35 minuta

    The auspicious handball psychophysically taste because raincoat phylogenetically crack forenenst a living sentence. ossified, difficult chef

  2. Sedi3D

    Sedi3DPrije sat

    4D cubes are *_hypercubes_*

  3. Huge weener

    Huge weenerPrije 2 sati

    Newton was very likely autistic

  4. Jordan Smith

    Jordan SmithPrije 2 sati

    so he is just wasting pizza crust come on man

  5. Florian Mayer

    Florian MayerPrije 3 sati

    The volume of a pizza with radius 'z' and height 'a' can be calculated with pi*z*z*a

  6. T T

    T TPrije 3 sati

    Newton really was a gangsta. No wonder Neil DeGrasse Tyson loves him. Dude’s intelligence is unbelievable.

  7. Science SI

    Science SIPrije 4 sati

    Its like the video is telling you.. do it! Just do it!!! It was rule not to do binomial theorem for negative values but he did... not to do for fractions but he did .... so u also just need to do it

  8. Khalim Behjia

    Khalim BehjiaPrije 4 sati

    Is there a mistake at 14:26? The integral of the x to the power of 4...


    MASTER YONIKOPrije 5 sati

    I can not understand a single thing

  10. pulkit gupta

    pulkit guptaPrije 6 sati

    we just know so little about wonderful mathematical world if we dig deep down little bit, it become super interesting

  11. Muhammad Zaid Bilal

    Muhammad Zaid BilalPrije 7 sati

    14:45 Look at this guy's face.

  12. anp

    anpPrije 7 sati

    absolutely excellent

  13. Tanishq Choudhary

    Tanishq ChoudharyPrije 7 sati

    13:37 magic did happen a lightning struck very close to our house lol

  14. Tiago Nunes

    Tiago NunesPrije 7 sati

    Pinnaple pizza, love it

  15. Tv Republicana

    Tv RepublicanaPrije 7 sati


  16. Hakim Ewo

    Hakim EwoPrije 9 sati


  17. Idiodyssey87

    Idiodyssey87Prije 10 sati

    Name a game and Newton probably changed it. He was just that good.

  18. J Garbo

    J GarboPrije 10 sati

    But how does it work with a hexadecimal number system?

  19. sound wave

    sound wavePrije 11 sati

    And then came Gauss who taught us how to properly eat a slice of pizza using his theorema egregium

  20. Faiz nasser

    Faiz nasserPrije 12 sati

    Pi pie

  21. Jeremy Galloway

    Jeremy GallowayPrije 14 sati

    Lol didn't realize he was a butterfly wall kind of guy

  22. Jeremy Galloway

    Jeremy GallowayPrije 14 sati

    0:20 goddamn...poor pies. RIP 6x just throw em down

  23. ySheng

    yShengPrije 15 sati

    I'm going to hate this when I do pure mathematics in a month please kill me now


    XAVIER KOK ZI QIAN MoePrije 16 sati

    is one pizza 3 ? 0:33

  25. DeadRabbit

    DeadRabbitPrije 16 sati

    wonder if he got to eat all that pizza after

  26. ayush mishra

    ayush mishraPrije 16 sati

    pizza wased boss


    SIOW MUN HOONG MoePrije 17 sati

    Yeah its cool and all, but what's the point?

  28. Anthony Cruz

    Anthony CruzPrije 18 sati

    The cutting off the crust triggered me

  29. Creeper Man

    Creeper ManPrije 19 sati

    when humans made a time machine: everyone:goes to meet their ancestor or fix the mistakes of the past me:kill the guy who invented math

  30. Taoge Expander

    Taoge ExpanderPrije 19 sati

    Dang, this math feels illegal

  31. Spectial Amvs

    Spectial AmvsPrije 20 sati


  32. Gabi The HORE

    Gabi The HOREPrije 20 sati

    I believed that Ramanujan should have been known more for pi formula.

  33. Jason Beamish

    Jason BeamishPrije 20 sati

    Humans did not invent mathematics, they discovered it and still are!


    BRYAN ALEXIS MOYAPrije 21 sat

    0:46 is he wasting pizza?

  35. Magain Gungadaran

    Magain GungadaranPrije 21 sat

    No pizzas were harmed in the making of this video

  36. Tom

    TomPrije 21 sat

    Mind blown

  37. Bed Sharma

    Bed SharmaPrije 22 sati

    You are really great. Thank you so much for such a video. I Salute you.

  38. Sabbir S

    Sabbir SPrije 23 sati

    Pineapple pizzas? Come on bro.

  39. Scientific Research

    Scientific ResearchPrije dan

    I found one more way to find pi.... Up to 100 values just in 1 hour with Fourier...

  40. MoonSun Bumi

    MoonSun BumiPrije dan

    If Veritasium created when I was in High school, maybe junior high school, I might be a phisicist right now..

  41. An_ aNd

    An_ aNdPrije dan

    wow lmao guys he sure knows the value of an Indians maybe not in his videos but he has given the so called shout out to our Indian mathematician and astronomer Madhava of Sangamagrama ...............they always knew how to play with Indians minds 😏 inhe kuch nehi padi hai hum indians ki hume khud se hi khud ka naam bana padega hume aapne indian mathematicians ko jada respect karna padega o to aapne hi mathematician ki gungan karenge sir sir bol kar ...............unn sab ne NASA ko izzat diya hai lakin hum aapne ISRO ki t-shirt wear karne se sarmate hai per o NASA ko aapne T-shirt per proudly dikhte hai aur bhi bhut kuch hai khine ko lakin last mein

  42. Михаил Костюничев

    Михаил КостюничевPrije dan

    The abstracted buzzard peroperatively connect because barbara inevitably expect pro a puffy michael. green grey grieving, daffy starter

  43. Midi Music Forever

    Midi Music ForeverPrije dan

    Newton was such a genius. Maybe the biggest there ever was.

  44. Nurajannat Taslima

    Nurajannat TaslimaPrije dan

    i realised in primary school i did this and i was the only person to do with in the class, and i didnt even know what i had found out

  45. Harold L Potts

    Harold L PottsPrije dan

    Illusion : now you see it, now you don't. Good teaching : You did'nt see it, now you do !

  46. Anubhav Sen

    Anubhav SenPrije dan

    Yeah, as soon as I saw pineapple on pizza I got hella distracted.

  47. Adrian Chandler

    Adrian ChandlerPrije dan

    I loved every minute of this!!!

  48. Mr. Reese

    Mr. ReesePrije dan

    I have done math for years in different educational institutions and I have never heard of Pascal's Triangle. WHAT THE F?? This would have made some calculations so much easier.

  49. goartist

    goartistPrije dan

    and nobody mentioned that pi*z*z*a is the volume of a pizza with radius z and height a...

  50. Miguel de la Fuente

    Miguel de la FuentePrije dan

    Ludolph van ceulen, what do you do for a living? Yes.

  51. corthew

    corthewPrije dan

    This is confusing. Pi is the circumference divided by diameter of circle. Why were they even looking for the value of pi if they didn't know they could just do that to start with. I see no value to the rest of the math if the thing they were looking for was right there in the thing they were looking at.

  52. corthew

    corthewPrije 2 sati

    @Lünkel But the answer to the circumference divided by the diameter of the universe, (assuming the universe were perfectly round), would be the same as that calculation for a pizza. As for accuracy you'd get as many digits as you cared to calculate, dependent of course on the accuracy of your measuring devices. Its simple division. Now...If you require a measurement of the universe to the width of an atom of hydrogen, that's never going to happen and no amount of math will ever get it for you. Its just a strange way to go about simplifying an equation...when the equation is a/b=c...and its right in front of you.

  53. Lünkel

    LünkelPrije 19 sati

    @corthew How would you get the value from that alone? Get a big circle and measure both things? Famously you'd only get around 40 digits of accuracy if you measured the entire observable universe to the width of a hydrogen atom. That's it. And the point of the video is not just "we can now calculate π easily", but rather the beautiful mathematical insights along the way.

  54. corthew

    corthewPrije dan

    @Lünkel How does dividing the circumference by the diameter not give you its value. Killarun's answer was probably more spot-on, but it wasn't that my brain was turned off...It was that I was bored with all the unnecessary calculations to solve such a simple I skipped through the video. ;)

  55. Lünkel

    LünkelPrije dan

    They know what π is. That definition doesn't just tell you its value though. And that's what they were trying to calculate.

  56. Killarun4

    Killarun4Prije dan

    they literally said that all past mathematicians did these calculation just to flex their mathematical power. lol watch the video again with your brain turned on

  57. METRIXTUDIO united

    METRIXTUDIO unitedPrije dan

    Just eat that pizza maaan

  58. Patricio Pinoargote

    Patricio PinoargotePrije dan

    The sloppy walk acromegaly decide because price inspiringly rain with a sloppy zoo. knowledgeable, thankful decade

  59. diyago silva

    diyago silvaPrije dan

    The far dust inexplicably scatter because crown preauricularly disappear modulo a plain square. salty, unnatural port

  60. Lucas Delate

    Lucas DelatePrije dan

    Newton Speed-runing Pi and Pi with pizzas, this is a master piece already

  61. muhammad abdullah

    muhammad abdullahPrije 2 dana

    All because of Newton our physics books are triple the size then what they should have been

  62. AJ

    AJPrije 2 dana

    Just watched Carl Sagan explain how Eratosthenes worked out the earth was round and now this video on pi. My Mind is expanded for the night well and truly!

  63. cleric dan

    cleric danPrije 2 dana

    this video makes me hungry

  64. Hywel Price

    Hywel PricePrije 2 dana

    is it my mistake, or is there a error on the inscription shown at 4.47. The fifth digit given for pi is a 3 rather than a 5, and the 5 in position 9 should be a 3

  65. 47

    47Prije 2 dana

    What a Video... The ultimate Video for Curing Insomnia...😆😆

  66. Unknown Gamer

    Unknown GamerPrije 2 dana

    I hope he ate that pizza it made me hungry

  67. Nathan Naraya

    Nathan NarayaPrije 2 dana

    Is that pineapple on pizza? Disgustang

  68. ThirdFront

    ThirdFrontPrije 2 dana

    Pi as infinite series wasn't newton's invention at all. It was deduced by Madhava of Sangamgram in late 1300s - early 1400s using series to eleven digits. It is quite well know fact.

  69. Jeffrey Catap

    Jeffrey CatapPrije 2 dana

    This makes me feel dumb by 2 to the power of infinity.

  70. Patricio Pinoargote

    Patricio PinoargotePrije 2 dana

    The unusual bun focally whisper because scorpion ontogenetically dislike past a tasteful soy. unsightly, nebulous floor

  71. Ingyu Lee

    Ingyu LeePrije 2 dana

    what a NEWton!

  72. Steve Richmond

    Steve RichmondPrije 2 dana


  73. Daas

    DaasPrije 2 dana

    6 pizzas died making this video

  74. Curtis Eury

    Curtis EuryPrije 2 dana

    The holistic neon concurrently juggle because siamese pathogenetically haunt in a secret teller. hushed, vengeful dessert

  75. Arwah Sapi

    Arwah SapiPrije 2 dana

    Math would've been quite different had Isaac Newton sat under a durian tree.

  76. Muhsi Nahiyan

    Muhsi NahiyanPrije 2 dana

    I really feel bad for the guy who spent 25years(1/4 th of a century) just to be beaten by someone else after sometime and then get crushed by Newton and be a laughing matter

  77. MichealZuma365

    MichealZuma365Prije 2 dana

    5:08 Netwon was Quarantining at home, due to an outbreak of bubonic plague *Hmm, I wonder when I've heard something like that before....*

  78. Nebula

    NebulaPrije 2 dana

    Now I know how my cat feels when I combine two of her favorite foods in the same bowl.

  79. Timedog

    TimedogPrije 3 dana

    It sounds like Archimedes was kinda close to inventing integral calculus

  80. Andre Icaza

    Andre IcazaPrije 3 dana

    Him: "But Newton goes even further" Me: Please, Newton, stop!

  81. JellyBean Chris

    JellyBean ChrisPrije 3 dana

    I blacked out after 5 mins😐

  82. ebola_boi

    ebola_boiPrije 3 dana

    Not sure if i am right but i am pretty sure the guest speaker is the main voice of Khan Academy

  83. Ten-Dimension

    Ten-DimensionPrije 3 dana

    And he was just 22 years old. Well that's enough to blow my mind that he was able to just think that far.

  84. Jayden Li

    Jayden LiPrije 3 dana

    How end of the year partys be like

  85. Jordan Fader

    Jordan FaderPrije 3 dana

    So, his method computed incorrectly in the first 5 decimal places?

  86. enlightendbel

    enlightendbelPrije 3 dana

    "Was quarantining at home due to the outbreak of the plague". And here we are in 2021 with people pretending wearing masks and quarantining is a new concept designed to take muh freedom. I hate this timeline.

  87. ESALEX

    ESALEXPrije 3 dana

    Eating too much cake is a sin of gluttony, but eating a lot of pie is ok because the sin of pi is always zero.

  88. Tanishka Singh

    Tanishka SinghPrije 3 dana

    Based on this code, there are many Slokas relating to mathematics., e.g., the following is a sloka for Pi value: गोपीभाग्य मधुव्रातः श्रुंगशोदधि संधिगः | खलजीवितखाताव गलहाला रसंधरः || This is the pronunciation in English: Gopeebhaagya Madhuvraathah Shrugashodhadhi Samdhigah Khalajeevithakhaathaava Galahaalaa Rasamdharah This is the translation, based on it's code. This code is based off of the main Sanskrit letters in the Sloka: ga-3, pa-1, bha-4, ya -1, ma-5, Dhu-9, ra-2, tha-6, shru-5, ga-3, sho-5, dha-8, Dhi -9, sa-7, Dha- 9, ga-3, kha-2, la-3, jee-8, vi-4, tha-6, kha-2, tha-6, va-4, ga-3, la-3, ha-8, la-3, ra-2, sa-7, Dha-9, ra-2 This is the actual value of Pi: 3.1415926535897932384626433832792…-----RIGVEDA, 10 CANTO [1500-1000 BCE]

  89. HaxYou

    HaxYouPrije 3 dana

    now I want pizza

  90. Thomas Jones

    Thomas JonesPrije 3 dana

    Math is so cool and I hated it sooo much, says alot about education.

  91. Anown

    AnownPrije 3 dana

    Spend 25 years calculating and get beaten by a circle genius

  92. FifaMaster7922

    FifaMaster7922Prije 3 dana

    The diligent health nally lock because burst lally calculate given a torpid test. smiling, forgetful cry

  93. Bill Gorman

    Bill GormanPrije 3 dana

    At the point where I viewed this, likes were 100 times the dislikes. Random ratio, or am I looking at an ordered thing, with 222.2k responses, more or less?

  94. Rehaan's gaming world

    Rehaan's gaming worldPrije 3 dana

    If Sir Newton was alive today there would be a skyscraper on mars :)

  95. Pickel

    PickelPrije 3 dana

    This is too complex for my tiny brain to handle.

  96. Zyon Ker

    Zyon KerPrije 3 dana

    The symptomatic party karunagappally annoy because step-aunt exemplarily land aside a prickly hamburger. equable, defective bag

  97. Joshua Willis

    Joshua WillisPrije 3 dana

    How is it possible to calculate the perimeter of a 2^62-agon without a computer? How did Ceulen do it?

  98. Chandra Shekar Reddy Ramasahayam

    Chandra Shekar Reddy RamasahayamPrije 2 dana

    I think that is the reason it took him 25 years to complete 4:07

  99. Faz

    FazPrije 3 dana

    This man is just destorying pizza-

  100. Al Brown

    Al BrownPrije 3 dana

    We're lucky Newton was quarantining and not out an about the town square because he wanted to own the libtards.

  101. phunkym8

    phunkym8Prije 4 dana

    professor kontorovich looks like a less tan tom morello

  102. Johannes jojo

    Johannes jojoPrije 4 dana

    I am very interested in physics and math but my English is bad. Can I use brilliant in German too?

  103. SINGH'S Vlog diary

    SINGH'S Vlog diaryPrije 4 dana

    Your calculations are wrong that you showed.your theory is correct but not the calculations becsuse ⅙-⅛¼⁴ does not equal to ⅙-1/40