Why π^π^π^π could be an integer (for all we know!).

27 feb. 2021
1 109 519 Weergaven

Check out the Jane Street programs if you're considering a mathematics/finance/programming job:
Here is Tim Gowers's reply to the original tweet:
Start your Schanuel's Conjecture journey here:
3^3^3^3 on wolfram alpha:
And for completeness, here is pi^pi^pi^pi:
If you have opinions about my 2n conjecture, send an email to matt+puzzles@standupmaths.com
Here is my Numberphile video about types of numbers.
- None yet, let me know if you spot any mistakes!
Thanks to my Patreons who are also vital in keeping the videos coming. Stock audience clips don't come cheap.
As always: thanks to Jane Street who support my channel. They're amazing.
Editing by Alex Genn-Bash
Maths graphics by Sam Hartburn and Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback

  • why is 8 afraid of 9? 8:25

    John GroenJohn GroenUur geleden
  • U just wasted my 15 minutes..

    Ashutosh MishraAshutosh Mishra9 uur geleden
  • *laughs in spanish*

    André BretonAndré BretonDag geleden
  • pi tetrated by 4

    Unthinkable Time 47Unthinkable Time 47Dag geleden
  • x-pi=0 Solution: x=pi Pi is not "transcendental" (proof by counterexample).

    Fled From NowhereFled From NowhereDag geleden
  • =2^12

    Vastalasar OlusVastalasar Olus2 dagen geleden
  • Answer is 1.327049678×10⁵⁷ Trick convert π=22/7 and calculate in calculator ! EASY!!

    Life for LiveLife for Live3 dagen geleden
    • The goal is to find what it would be and not be very far away from it. pi^pi^pi^pi is way different to 22/7^22/7^22/7^22/7, because of the amount of times we raise it.

      SidgeSidge3 dagen geleden
  • I tried to do this and my calc Sai math error....

    Bill WhoeverBill Whoever3 dagen geleden
  • Irrationals are all non-rationals. You mean algebraic numbers.

    James LJames L4 dagen geleden
  • thumbs up for the stock audience

    Rylan AndersonRylan Anderson6 dagen geleden
  • I bet 2 dollars it's not an integer.

    Alexey DerevyankinAlexey Derevyankin7 dagen geleden
  • Here's my take on it. π^π^π^π... = x Since it's repeating infinitely, you can take the whole index of the first π and set it equal to x. π^x = x Now we can take the xth root. x√π = x (NOTE: 'x√π' isn't x multiplied by the root of π; it's the xth root of π)

    Umar RashidUmar Rashid7 dagen geleden
  • When is pi to the power of pi to the power of pi to the power of pi day?

    PetroleumalleyPetroleumalley7 dagen geleden
  • making Pi equal a nice round 3 in a machine is literally a side plot in a Pratchett novel

    Jules YoJules Yo8 dagen geleden
  • This video will literally causes a heart attack on Norman Wildberger (from Insights to math NLworld channel) LOL

    Diego Henrique ProfDiego Henrique Prof8 dagen geleden
  • I don't know what is better, the irrational jokes or the rational explanations

    Fernando FaviniFernando Favini8 dagen geleden
  • how root(2)^root(2) give root(2)*root(2)????

    Fantastic GamingTVFantastic GamingTV8 dagen geleden
    • What

      Damian FlettDamian Flett5 dagen geleden
  • Pi^logpi(3)=3

    Josiah CochranJosiah Cochran8 dagen geleden
  • 12:14 The answer is no we cannot get an integer number by rising pi to pi infinitely

    YassineYassine8 dagen geleden
  • Suddenly Electroboom outro start playing in my head

    YassineYassine8 dagen geleden
  • Give me 2 weeks and I’ll let you know if that conjecture is correct

    YunisYunis8 dagen geleden
    • Bet

      Damian FlettDamian Flett5 dagen geleden
  • Awesome !!! It almost reignited my interest in mathematics...

    Dheeraj VermaDheeraj Verma8 dagen geleden
  • My calculator: Math error

    Matt NaganidhiMatt Naganidhi8 dagen geleden
  • let's go 0:09

    jeanjean9 dagen geleden
  • The absence of evidence is not the evidence of absence.

    DRIF L00NDRIF L00N9 dagen geleden
  • Is the right side of the graphics on his shirt forming a straight line? That depends on the print resolution.. surely.. hm

    IJzervreter FIJzervreter F9 dagen geleden
  • 2:02 All transcendental real numbers are irrational. He seems to be using "irrational" to mean "irrational algebraic" which is not correct.

    PureExilePureExile9 dagen geleden
  • Just brilliant!!! Thanx

    Francisco GarciaFrancisco Garcia10 dagen geleden
  • If you say ‘pi to the’ over and over again you become a dance DJ.

    Mister BruhhMister Bruhh10 dagen geleden
  • It would be fun if mathematicians start dividing into 2 groups: the one who BELIEVES that pi^pi^pi^pi is an integer and the one who doesn't)))

    Tasty PieTasty Pie10 dagen geleden
  • Oh hell yeah Parker Conjecture

    Daichi AudiosDaichi Audios10 dagen geleden
  • Why don't you take a little help from complex numbers?

    Ashay GuptaAshay Gupta10 dagen geleden
  • That was interesting. I like math.

    Dark Knighte ApologeticzDark Knighte Apologeticz10 dagen geleden
  • 2:36 Complex numbers: I'm 4 parallel universes ahead of you

    Eason LiangEason Liang11 dagen geleden
  • 6:30 reminded me of Gogol, I learned that in some video.

    Tiger 1x1Tiger 1x111 dagen geleden
  • Is the value of this expression greater than Graham's Number?

    Prime Phoenix 6174Prime Phoenix 617411 dagen geleden
    • No.

      Damian FlettDamian Flett5 dagen geleden
    • Wait. It is not.

      Prime Phoenix 6174Prime Phoenix 617410 dagen geleden
  • I have a feeling it equals 7

    Tyler LizeéTyler Lizeé11 dagen geleden
  • 2:28, (x - π)(x - e) = 0 or, x = π,e

    ꧁𓆩F.B.I ༒ I.G.X𓆪꧂꧁𓆩F.B.I ༒ I.G.X𓆪꧂11 dagen geleden
    • jk

      ꧁𓆩F.B.I ༒ I.G.X𓆪꧂꧁𓆩F.B.I ༒ I.G.X𓆪꧂11 dagen geleden
  • I don't know why this video is on my suggestion list. I think he should try on comedy shows


    Fr3p OoooFr3p Oooo11 dagen geleden
  • One could come away from this with the impression that transcendentals aren't irrational, but of course, they are. The set containing the roots of polynomials, like root 2, is the set of algebraic numbers, so the name that should have been used is the algebraic irrationals.

    Douglas BoffeyDouglas Boffey12 dagen geleden
  • It's probably something around 42. Call it Jimmys Conjecture.

    JimmyTulip1JimmyTulip113 dagen geleden
  • Just A total waste of my time

    ostmana1ostmana113 dagen geleden
  • disappointed no e^iπ

    drisbaindrisbain13 dagen geleden
  • Taking my engineering approach looks to me like 3^3^3^3

    C8SasquatchC8Sasquatch14 dagen geleden
  • Ramanujan: is that a challenge?

    InsouciantInsouciant15 dagen geleden
  • "Everyone remembers where they were, the first time they noticed that" Yeah, on the toilet about 10 seconds ago, what a beautiful moment that was

    Emile HeskeyEmile Heskey15 dagen geleden
  • I calculated it. Not only it's an integer but it's also prime.

    ThalesPoThalesPo16 dagen geleden
    • Wow

      Damian FlettDamian Flett5 dagen geleden
  • I am wondering what to do with me life, but I am not remotely mathematically oriented. I watch these videos for fun.

    Viggo Ny ThomassenViggo Ny Thomassen16 dagen geleden
  • I really like the 31.4 trillion digits of pi calculated.

    Paul SPaul S16 dagen geleden
  • There is a special number _p0, which is, by definition, equals to the minimal number of pies in power stack to make a rational number. There is an unproven conjecture, that a set _P, consisting of all numbers of power-stacked pies been rational, is finite. Some guys even claims that there are 42 members of that set.

    amaraojijiamaraojiji17 dagen geleden
  • Title: Why π^π^π^π could be an integer (for all we know!). Me: Oh, that sounds interesting, because it's definitely too big to compute directly. Video: Well, I have no idea if it's an integer, because I can't compute it.

    Ich verrate Google doch nicht meinen NamenIch verrate Google doch nicht meinen Namen18 dagen geleden
  • nlworld.info/key/video/rWmWl8y5i651iWc

    Joseph DoeJoseph Doe18 dagen geleden
  • I like how you can hear brady out at 1:52

    Jar Jar BinksJar Jar Binks18 dagen geleden
    • I hear him now haha

      Muskaan Kaur DeolMuskaan Kaur Deol17 dagen geleden
  • Random student in class: So why are we acting like idiots trying to calculate this again? Teacher: * throws him out the window and therefore out of the class

    IO gamerIO gamer19 dagen geleden
    • Teacher: So, does anyone else have any questions? =)

      IO gamerIO gamer19 dagen geleden
  • the parker conjecture

    Little Miss JLKLittle Miss JLK19 dagen geleden
  • I note that the title of this episode is not nearly as Click-Baity as suggested in the introduction.

    inyobillinyobill19 dagen geleden
  • Excellent. Thank You.

    Steve MenegazSteve Menegaz20 dagen geleden
  • Yes, very very poor clickbait indeed! - Firstly because π^π^π^π does seem like quite a lot of π. Therefore you would expect that getting a free slice or two wouldn't really be that big of a deal. - Secondly, a rather important question, which I feel wasn't covered at all: if it was raspberry, then could it be programmed to jam someone's radar, say while they are having coffee?

    Carsten LervadCarsten Lervad20 dagen geleden
  • I want my 15 min back. "Here's an equation, we don't know the answer, it might be this but it also might not be."

    Peter StalmanPeter Stalman20 dagen geleden
    • well the title wasnt misleading, it told you all that

      GeraldGerald17 dagen geleden
  • Oh, come on! Of course it's not an integer.

    dalex641dalex64120 dagen geleden
  • I thought I could be slick by setting x=pi^pi^pi^pi and then taking log base pi (pilog) of both sides twice to "spread out" the computation. Then I just have to find x such that lp(lp(x))=36.4622..... turns out that lp(lp(x) is practically a horizontal line and getting up to 36 is an exercise in futility (I was looking at it in Desmos). Back to the drawing board.

    Nathaniel KilmerNathaniel Kilmer20 dagen geleden
  • e^(i * pi) = - 1! Hey, an integer!

    Kephalo PodKephalo Pod20 dagen geleden
  • I thought we'd get an analog answer... not proofs using digital measures. If I can't divide 1 by 3 on a digital machine and then multiply the answer by 3 on the same machine and get 1 then it's not the device to use... at least in theory.

    80s gamr80s gamr21 dag geleden
  • Peh. Work out 2π^2π^2π^2π instead.

    Carbon Roller CacoCarbon Roller Caco21 dag geleden
  • What makes you (or someone) think that the answer could be an integer? Is it "could" just in the sense "it's not impossible", or has someone proposed something that makes it seem likely?

    Matthias BolligerMatthias Bolliger21 dag geleden
    • It is almost certainly not an integer, but the point is it's really interesting that we can't rule it out!

      Eric BurgessEric Burgess19 dagen geleden
  • The clickbait worked.

    89Aurum89Aurum21 dag geleden
  • Isn´t the probability that that´s an integer really low though?

    Artur SouzaArtur Souza21 dag geleden
    • Like, if I put apple juice on a blender 4 times, what are the odds I get some apples at the end of the process?

      Artur SouzaArtur Souza21 dag geleden
  • Everyone is joking about setting pi = 3 but only real engineers know pi = e. (Yes I had a professor actually do this)

    sportsquidsportsquid21 dag geleden
  • I prefer Emma's calculation of Pi, for the sheer fact of it being 31.4 trillion, or Pi*10 trillion digits...

    ThatEditingBakaThatEditingBaka21 dag geleden
  • Easy. Set pi equal to 2, answer is 65536. Integer.

    Matthew StuckenbruckMatthew Stuckenbruck21 dag geleden
  • E

    GodGod22 dagen geleden
  • How often do you have to calculate the factor of pi until you end up with a prime number as the result?

    Ralf BüscherRalf Büscher22 dagen geleden
  • Well, I used Windows calc to PI^PI^PI^PI. And the answer equals 2'598'761'979'625'197,521(...), which really doesn't look like an integer. Literally a middle between two neighbor integers. Will I get an integer if I will use PI with much more precision? Sadly I can't easily check it because Windows calc doesn't understand numbers with higher precision than 31 digits after comma and JS has much lower precision.

    OcelotJungleOcelotJungle22 dagen geleden
    • windows calc is stupid and does exponentiation wrong. What you have calculated is ((pi^pi)^pi)^pi. What you had to calculate is pi^(pi^(pi^pi))

      AthenriAthenri6 dagen geleden
  • And 1:42 of course you said -1/12

    Alex TauntonAlex Taunton22 dagen geleden
  • 1:32 of course you said 42

    Alex TauntonAlex Taunton22 dagen geleden
  • Since pi is a property of circles, could you construct a model in a higher dimensional plane, and just look at the property of that new shape to see if is clean and integerial at that dimension.

    Trevor KochTrevor Koch22 dagen geleden
  • that sqrt(2) tower is a neat solution to a riddle: is it possible two irrational numbers say a and b are such that a^b is rational? The answer is yes. Let b be sqrt(2), we just need to find an a. Let's look at sqrt(2)^sqrt(2). If that's rational, we are done with a being sqrt(2). If it is not rational then let sqrt(2)^sqrt(2) be a and then a^b equals 2 which is rational. So we know there's such a pair but we don't know which! (BTW using much higher maths we can prove sqrt(2)^sqrt(2) but this doesn't matter for the above high school level proof.)

    chx1975chx197522 dagen geleden
  • If anyone really wants to calculate that, I know the answear is lying somewhere in between 3^3^3^3 and 4^4^4^4. Have fun. :D

    Ators ChannelAtors Channel22 dagen geleden
  • This video opened my eyes. We have to explore the transcendentals!1!

    Herr ZeitHerr Zeit22 dagen geleden
  • 6:30 ... pi expontential has a finite number of digits ? no thats the digits left of the decimal point... the integer, wholenumber bit.. you make it clearer later on

    LeonGLeonG22 dagen geleden
  • The most important thing is that it is already such a big number that it doesnt matter 2 598 761 979 625 197

    TymexComputingTymexComputing23 dagen geleden
  • using wolframalpha i get solution to the above problem as z =e^-(10000W(-3183/20000))/3183

    abhishek patilabhishek patil23 dagen geleden
  • c# is exponentially faster than python

    RedEyeRecords HRedEyeRecords H23 dagen geleden
  • There's always the fun one where e^(pi*i)=-1

    BaufenBeastBaufenBeast23 dagen geleden
  • *Menacing*

    BadAtLosingVideogamesBadAtLosingVideogames23 dagen geleden
  • What’s with the fluctuating values in the rightmost column of the chart at 10:30?

    Benny BlueBenny Blue23 dagen geleden
  • Gee, after spending 15 mins on this video, it just tell me that it doesn't know how to prove or overthrow the statement it makes? WTF

    Lei YuLei Yu24 dagen geleden
  • tl;tr: "Read about Schanuel's Conjecture not here, that isn't even proven for just pi^pi." What a clickbait.

    AmonimusAmonimus24 dagen geleden
  • ещё бы субтитры на русском и других языках, наука должна быть доступна каждому (

    Руслан ,Руслан ,24 dagen geleden
  • 1x10^9 = 1,000,000,000 = Short scale 1 billion = Long scale thousand million or 1 milliard 1x10^12 = 1,000,000,000,000 = Short scale 1 trillion = Long scale 1 billion For those who also don't use English number system.

    Søren HedegaardSøren Hedegaard24 dagen geleden
  • We know that at least one of (e+pi) and (e*pi) is transcendental.

    Raziel AngelosRaziel Angelos25 dagen geleden
  • Good content, but your transitions offend the ears

    Zack LawrenceZack Lawrence25 dagen geleden
  • At what point does "PI" make that many numbers that you can make a loop every time numbers repeat by at least 1/to the most loops it has made or try to make it smaller if it isn't stupid news

    JonesJones25 dagen geleden
  • racist

    Clair de LuneClair de Lune25 dagen geleden
  • i did wrong calculations in excel powering from bottom to top and got an INTEGER number ((π^π)^π)^π. WHY??

    I KapI Kap25 dagen geleden
  • 2.598.761.979.625.197,5214462849737795

    mister Knistermister Knister25 dagen geleden
  • I always thought that "rational" meant "a number that's possible but, in order to get what that actually represents, you have to take a leap and realize that not everything is an integer". I love my idiocy

    ale mutasaale mutasa25 dagen geleden
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    Kien Thinh TranKien Thinh Tran25 dagen geleden
  • Fantastic popularizing presentation. I have not seen anybody speaking from mathematics so lively and with so much passion. Thank you....

    LubosLubos25 dagen geleden