The Discovery That Transformed Pi 9,257,861 viewsMar 16, 2021

The Discovery That Transformed Pi 9,257,861 viewsMar 16, 2021 Veritasium 11.9M subscribers 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 https://brilliant.org/veritasium get 20% off a yearly subscription. Happy Pi Day! (for a few days ago...) References: Arndt, J., & Haenel, C. (2001). Pi-unleashed. Springer Science & Business Media — https://ve42.co/Arndt2001 Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley — https://ve42.co/Dunham1990 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 — https://ve42.co/Borwein2012 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 https://epidemicsound.com "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale" Thumbnail by Gianmarco Malandra and Karri Denise 17,362 Comments rongmaw lin Add a comment... Just Some Guy without a Mustache Just Some Guy without a Mustache 10 months ago "You can say he speedran pi" So Newton invented speedrunning as well 8.7K 76MUTiger 76MUTiger 4 months ago I was a "C" student and found math interesting but accompanied by a burden for homework that I could not bear. Your discussion of Pi today has been fascinating and I thank you! 986 Anshbeast Anshbeast 3 months ago The sheer way humans can do soooooo much with just 10 digits discovered from their fingers is extremely fascinating 477 Shawn Anderson Shawn Anderson 1 month ago (edited) Technically speaking, Newton's method is far superior. However, for me "dissecting polygons" was integral... an epiphany of sorts in visualizing the practical understanding of the math. 114 Diego G Diego G 5 months ago Most famous scientists, physicists, mathematicians are just regular people with a job that they are really passionate about, so they get very good results and publish papers and so on. Newton was one of few which I consider to be a true genius. 347 Teacher Homie G Teacher Homie G 4 months ago I tell my 8th grade science students that Newton was the most brilliant man to ever walk on Earth. Love teaching his Universal Law of Gravitation, and his three Laws on Motion. Einstein gets my vote for second most brilliant man to walk on Earth. 260 Kimi95 Kimi95 6 months ago Imagine having a career so illustrious that discovering a groundbreaking way to accurrately find pi is just one of your side achievements 8.5K Marko Apatović Marko Apatović 3 weeks ago I've implemented this algorithm in Java, almost solely based on information and formulae from this video. It's really cool, it can basically compute pi to any precision you want, provided you let it run long enough, but with how fast it's converging it's actually surprisingly fast. The biggest roadblock I've actually encountered was printing the whole thing to console. 53 Steven Robertson Steven Robertson 1 month ago This is so fascinating! I studied the binomial theorem and infinite series years ago (early 1970s) but there was no mention of Newton or the history of bisecting the circle to get π by previous mathematicians. This is so well done, entertaining, and easily understood! Amazing job! 36 Nour Art Nour Art 3 days ago I love the storytelling in your videos, even if a subject doesn't interest me, it's still entertaining to watch and in the same time informative. Truly amazing, keep it up. 3 K. C K. C 5 months ago This was EXCELLENT. I actually understood how we get pi with a clarity I never had before. 76 bhasky bhasky 2 months ago A standing ovation. Had this story be there before I had started to learning binomial theorem , I would have been more interested. This is like reading a detective novel. 29 Veritasium Veritasium 1 year ago Also shout out to Indian mathematician and astronomer Madhava of Sangamagrama, who in the 14th century had a different infinite series for pi that converged as fast as Newton's 8K ro3 ro3 5 days ago This is very interesting. I was fascinated on how creative Newton linked one thing to another thing that seemed to be unrelated, found a new pattern, found the bigger picture which finally led to a groundbreaking way of doing things. Amazing. 1 Zenocrat Zenocrat 4 months ago Even without understanding the math, here's what I learned: Newton was one smart dude. We all knew that his math was progressive, but I was also happy to see that he was socially progressive as well, as he was arguably the first to promote integration (although I hear there's sine German bloke making a similar claim). 8 Gil Galin Gil Galin 2 weeks ago if only your explanations would be shown during my schoole years - that would definitely not only produce fascination by the Maths itself but maybe even next level geniuses. Keep it up, words cannot expess my gratitude for all your work!!! Best regards, applied maths grad... 8 TheSoftwareJunction TheSoftwareJunction 2 months ago Newton was a genius and it's amazing that maths is actually about finding patterns 14 Rafael Rezende dos Santos Rafael Rezende dos Santos 2 months ago That's amazing, fortunately that we have people like Newton in humanity 12 TheRomichou TheRomichou 1 year ago The animator is the hidden hero here! 20K Veritasium SOOPERMEXICAN! SOOPERMEXICAN! 2 months ago Fantastic video. It is to Newton's credit that it's actually difficult to explain just how brilliant the man was. 7 Mohit Singh Mohit Singh 1 year ago Imagine working on something for 25 years only to find out that someone did it while playing with an equation during a pandemic. 2.2K Varun Krishnan Varun Krishnan 4 months ago (edited) Thanks @Veritsasium. This video has transformed me from a math failure, who hated maths into the one who uses math in astrophysics & DSA. This has made maths interesting to me and inspired me to learn more. This 20 mins video did something what schools & colleges failed to do. Maths is now a lot interesting. Maths is a tool, it is a way expressing your thoughts on paper & validating it. I would like to meet & thank you in person. 6 stischer47 stischer47 2 months ago If I had had this type of instruction when I was in high school and interested in mathematics, I would have probably majored in math. Instead, I was taught to memorize formulae and to do things "the right way". A try in college ended up with a teaching assistant in calculus who couldn't solve the problems he gave us to solve (or were unsolvable but he didn't know). 7 Ariya Ikhsan Ariya Ikhsan 2 months ago This presentation is amazing, I'm not even interested in math, and i could barely understand what they're talking about, but i found my self at the end of the video still watching. And i love how they're so excited to talk about math, like a kid talking about their Christmas presents. Bravo 5 KC Batista KC Batista 2 months ago Math is beautiful. So bad that it is actually crushed through the educational system. 3 Unknown Variable Unknown Variable 5 days ago I've watched this video so many times, and I love it each time. I find Newton's brilliance inspirational in taking a process that everyone thought was well known and, quite literally, rewriting the book. At least here we can all come together to appreciate the beautiful work of a genius expanding humanity's capabilities, instead of hating one another for frivolous things. 1 atell atell 8 months ago in all honesty, i never realized how much of a genius newton really was. i feel a bit ashamed now, dude practically made hundreds of years worth of discoveries in a few decades and i never cared much for him at all. somehow this is insanely impressive. imagine being this guy. 2.4K Mirrorwarrior Mirrorwarrior 1 month ago The explanations were so easy to understand but very interesting too! Awesome!! Keep making such great learning videos!! 2 Rahuldeb5 Gaming Rahuldeb5 Gaming 1 month ago Thank you so much for this video. Even though I'm still learning algebra, your video was very interesting and taught me a lot. 6 Attila Bertok Attila Bertok 2 weeks ago Great video! I've really enjoyed it, but I think it would be very important to mention the radius of convergence for x (=1) because of course the binomial formula stops working for just any number. And... I mean the following comment in a funny way, but I would like to see you doing the integration using Newton's original method with fluxions. That would be a much longer video. It is a bit ironic that for the integral you have used the notation given to us by Leibniz' which is much clearer than the fluxions stuff. Still great work though. 1 David Emerling David Emerling 5 months ago (edited) "The thing that fascinated me when I started looked at those old documents (ancient Chinese) - like, I don't speak those languages, I don't know those number systems - and yet, it is obvious - it is clear as day that they're all writing down the same thing which, today, in the Western World, we call Pascal's Triangle." This reminded me of the movie "Contact," starring Jodie Foster. Aliens from Vega send a seemingly cryptic message to Earth. Ellie (played by Jodie Foster) explains to a senate committee, "Mathematics is the only truly universal language, Senator. We think this may be a beacon -- an announcement to get our attention." 6 J Faleiro J Faleiro 4 months ago This was a fantastic way to use a trivial topic to introduce a bunch of very important math fundaments. This is how math should be taught. Good job. 1 Peter Siri Peter Siri 1 year ago "He was quarantining at home due to an outbreak of bubonic plague." ...what a great time to do math 3K DaCash DaCash 2 weeks ago I really struggled in calculation (geometry was a breeze but algebra and I had our moments) and then calculus was a weird beast. I always seemed to get the concept clearly and fast enough, could even look at my answer and know if it was right, but the calculation was always painful. So later, when I taught math (as a science teacher), I was so excited to discover manipulatives for teaching binomials (essentially legos to make squares). I thought: why did no one show this to me when I was learning? I feel the same way about your pizza example. The first bit I knew and shared (by diagram) but the second part where you made a rectangle of the slices! Thank you! I no longer teach, but that would have been a beautiful insight. I'm sure I'll use it (and other bits of your video as well) helping someone someday, even if I no longer do it professionally. 2 goldensilver goldensilver 1 month ago (edited) Always wondered how to figure out pi...bought a Math encyclopedia and going through it one day, came across a recursive routine the Sumerians used way back in the day to calculate pi... I wrote a recursive C routine to calculate pi using the Sumerian formula and the results were no different than using my calculator... 1 Ralston Robertson Ralston Robertson 3 months ago The entire video was very enjoyable. Newton’s insight and problem solving skill was remarkable. I especially liked the connection between the Binomial Theorem and Pascal’s Triangle. Generally, one just uses the Binomial Theorem but seeing this historical connection is one of those things one puts in one’s math “toolbox” - thank you so much for this historical connection. 4 Hink Hall Hink Hall 5 months ago Isaac Newton is my hero but I still hadn’t heard about this story so I truly enjoyed this video. Thank you! 11 Amanda Penner Amanda Penner 1 month ago I really enjoyed this video. I’m not a mathematician and while I loved algebra I nearly flunked geometry so I never tried physics or calculus. 😭 This has helped me remember I can still learn as a mom of three. Don’t ever give up. 9 saddlepiggy | The Purple Pig saddlepiggy | The Purple Pig 1 year ago “Luckily, Newton had just invented Calculus.” Bruh chill out Newton leave some discoveries for the rest of us. 4.4K Dave Jung Dave Jung 1 month ago Learning calc 2 right now and these series expansions are so fascinating. It's refreshing to relate my learning to something tangible like pi. TimeBucks TimeBucks 1 year ago Very clear and easy to understand 372 Brodie Eaton Brodie Eaton 5 months ago One of the greatest mathematical developments in history, made by one guy who was bored during quarantine. What a chad. 2 Wenwu Xu Wenwu Xu 4 months ago On my god, I felt like I was watching those old days discovery documenting series!!! very interesting and amazing how smart Newton was! 4 Don Marco Don Marco 2 months ago It‘s so awesome and motivating to see, how you both „live“ that!! 👍🏼 2 nuller87 nuller87 4 months ago It's mindblowing to me, that this was discovered and done so many years ago. Percy Percy 3 weeks ago Newton is by far and undeniably has the biggest contribution to science or Mathematics. 2 AJ AJ 11 months ago "Luckily he had just invented calculus" unbelievable 3K Utkarsh Kumar Utkarsh Kumar 1 month ago Newton tried to find extent of things by challenging there rules . I bet he must would have failed many times in challenging those rules and somewhere he would have got stuck , but in some of them he made new rules . So we learn from him that we should challenge things in our life . 2 Random Human Random Human 1 month ago (edited) Breathtaking really. Hiding in plain sight for the right set of eyes. This sort of genius gives hope for mankind. 1 Wissle Wissle 1 month ago Starting this video with Pizza was brilliant, I watched all of it after that intro Interesting stuff, Newton was such a genius it's really mindblowing 12 sakke sakke 4 months ago These Veritasium videos are the best educational material on these topics that I've ever encountered anywhere. Exemplary work on how to educate. Thank you. 1 unept96 unept96 1 month ago Wow! Thank you! I asked my calculus teacher how Pi was determined 30 years ago and never got a decent answer! It's a ratio- circumference to diameter. 2 Priya M Priya M 1 year ago If math in schools was taught like this, dearth of STEM candidates in the western world would drop within a decade! Loved it 😊 944 Mr. Lengo Mr. Lengo 4 months ago I made a simple loop program in C++ to calculate Pi and once you get past a handful of digits even the computer starts to take minutes, tens of minutes, hours and eventually years to calculate pi. Can’t imagine doing those calculations by hand back then. It took my computer like 20 minutes to get only 12 digits (I think), so 30+ would be insane to do. Each correct digit takes orders of magnitude more iterations to get. 2 Bobby Adams Bobby Adams 2 months ago I follow you with the math until I reach my limit where my head is about to pop then find myself a little jolted back to reality at the end when you look and talk like a normal human, I guess I was expecting a robot! 😂 1 Bill Miller Bill Miller 2 months ago I alway found it funny that differentiating the area of a circle over r gives the circumfence and differentiating the volume of a sphere over r gives you its surface. 1 patchesdf patchesdf 2 months ago I love trying out these equations on my own and finding out they work. Go Home and get your shinebox! Go Home and get your shinebox! 4 months ago Newton and I are very similar - We both quarantined at home due to an outbreak and did some basic math 2 The Knightikins The Knightikins 5 months ago