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

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
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
US book:
UK book:


  1. Bluemushroom44


    21 mínútu síðan

    = Poodiepie

  2. Tasty Pie

    Tasty Pie

    43 mínútum síðan

    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)))

  3. Daichi Audios

    Daichi Audios

    2 klukkustundum síðan

    Oh hell yeah Parker Conjecture

  4. Ashay Gupta

    Ashay Gupta

    12 klukkustundum síðan

    Why don't you take a little help from complex numbers?

  5. Dark Knighte Apologeticz

    Dark Knighte Apologeticz

    18 klukkustundum síðan

    That was interesting. I like math.

  6. Eason Liang

    Eason Liang

    20 klukkustundum síðan

    2:36 Complex numbers: I'm 4 parallel universes ahead of you

  7. Tiger 1x1

    Tiger 1x1

    Degi Síðan síðan

    6:30 reminded me of Gogol, I learned that in some video.

  8. Prime Phoenix 6174

    Prime Phoenix 6174

    Degi Síðan síðan

    Is the value of this expression greater than Graham's Number?

    • Prime Phoenix 6174

      Prime Phoenix 6174

      18 klukkustundum síðan

      Wait. It is not.

  9. Tyler Lizeé

    Tyler Lizeé

    Degi Síðan síðan

    I have a feeling it equals 7

  10. ꧁𓆩F.B.I ༒ I.G.X𓆪꧂

    ꧁𓆩F.B.I ༒ I.G.X𓆪꧂

    Degi Síðan síðan

    2:28, (x - π)(x - e) = 0 or, x = π,e

    • ꧁𓆩F.B.I ༒ I.G.X𓆪꧂

      ꧁𓆩F.B.I ༒ I.G.X𓆪꧂

      Degi Síðan síðan




    Degi Síðan síðan

    I don't know why this video is on my suggestion list. I think he should try on comedy shows

  12. Fr3p Oooo

    Fr3p Oooo

    Degi Síðan síðan


  13. Douglas Boffey

    Douglas Boffey

    Degi Síðan síðan

    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.

  14. JimmyTulip1


    3 dögum síðan

    It's probably something around 42. Call it Jimmys Conjecture.

  15. ostmana1


    3 dögum síðan

    Just A total waste of my time

  16. drisbain


    3 dögum síðan

    disappointed no e^iπ

  17. C8Sasquatch


    3 dögum síðan

    Taking my engineering approach looks to me like 3^3^3^3

  18. Insouciant


    5 dögum síðan

    Ramanujan: is that a challenge?

  19. Emile Heskey

    Emile Heskey

    5 dögum síðan

    "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

  20. ThalesPo


    5 dögum síðan

    I calculated it. Not only it's an integer but it's also prime.

  21. Viggo Ny Thomassen

    Viggo Ny Thomassen

    6 dögum síðan

    I am wondering what to do with me life, but I am not remotely mathematically oriented. I watch these videos for fun.

  22. Paul S

    Paul S

    6 dögum síðan

    I really like the 31.4 trillion digits of pi calculated.

  23. amaraojiji


    7 dögum síðan

    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.

  24. Ich verrate Google doch nicht meinen Namen

    Ich verrate Google doch nicht meinen Namen

    7 dögum síðan

    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.

  25. Max Qubit

    Max Qubit

    7 dögum síðan

    Pi defines (or is an expression of) Creativity. Creativity is inherent to Everything for Everything to exist ... So, if God, who could be seen as the 'Creator', wanted to calculate 'his' Pi to the last digit, God would have to spend infinite Time and still not getting there. Yep that's what Creativity does. Pretty clever stuff of God to invent Creativity ... Let it run and himself disappearing into Nothing without a trace as if he was never there ... Which actually is True😁

  26. Joseph Doe

    Joseph Doe

    8 dögum síðan

  27. Jar Jar Binks

    Jar Jar Binks

    8 dögum síðan

    I like how you can hear brady out at 1:52

    • Muskaan Kaur Deol

      Muskaan Kaur Deol

      7 dögum síðan

      I hear him now haha

  28. IO gamer

    IO gamer

    9 dögum síðan

    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 gamer

      IO gamer

      9 dögum síðan

      Teacher: So, does anyone else have any questions? =)

  29. Little Miss JLK

    Little Miss JLK

    9 dögum síðan

    the parker conjecture

  30. inyobill


    9 dögum síðan

    I note that the title of this episode is not nearly as Click-Baity as suggested in the introduction.

  31. Steve Menegaz

    Steve Menegaz

    9 dögum síðan

    Excellent. Thank You.

  32. Carsten Lervad

    Carsten Lervad

    9 dögum síðan

    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?

  33. Peter Stalman

    Peter Stalman

    10 dögum síðan

    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."

    • Gerald


      7 dögum síðan

      well the title wasnt misleading, it told you all that

  34. dalex641


    10 dögum síðan

    Oh, come on! Of course it's not an integer.

  35. Nathaniel Kilmer

    Nathaniel Kilmer

    10 dögum síðan

    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.

  36. Kephalo Pod

    Kephalo Pod

    10 dögum síðan

    e^(i * pi) = - 1! Hey, an integer!

  37. 80s gamr

    80s gamr

    10 dögum síðan

    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.

  38. Carbon Roller Caco

    Carbon Roller Caco

    10 dögum síðan

    Peh. Work out 2π^2π^2π^2π instead.

  39. Matthias Bolliger

    Matthias Bolliger

    11 dögum síðan

    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?

    • Eric Burgess

      Eric Burgess

      9 dögum síðan

      It is almost certainly not an integer, but the point is it's really interesting that we can't rule it out!

  40. 89Aurum


    11 dögum síðan

    The clickbait worked.

  41. Artur Souza

    Artur Souza

    11 dögum síðan

    Isn´t the probability that that´s an integer really low though?

    • Artur Souza

      Artur Souza

      11 dögum síðan

      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?

  42. sportsquid


    11 dögum síðan

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

  43. ThatEditingBaka


    11 dögum síðan

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

  44. Matthew Stuckenbruck

    Matthew Stuckenbruck

    11 dögum síðan

    Easy. Set pi equal to 2, answer is 65536. Integer.

  45. God


    11 dögum síðan


  46. Ralf Büscher

    Ralf Büscher

    12 dögum síðan

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

  47. OcelotJungle


    12 dögum síðan

    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.

  48. Alex Taunton

    Alex Taunton

    12 dögum síðan

    And 1:42 of course you said -1/12

  49. Alex Taunton

    Alex Taunton

    12 dögum síðan

    1:32 of course you said 42

  50. Trevor Koch

    Trevor Koch

    12 dögum síðan

    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.

  51. chx1975


    12 dögum síðan

    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.)

  52. Ators Channel

    Ators Channel

    12 dögum síðan

    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

  53. Herr Zeit

    Herr Zeit

    12 dögum síðan

    This video opened my eyes. We have to explore the transcendentals!1!

  54. LeonG


    12 dögum síðan

    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

  55. TymexComputing


    12 dögum síðan

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

  56. abhishek patil

    abhishek patil

    13 dögum síðan

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

  57. RedEyeRecords H

    RedEyeRecords H

    13 dögum síðan

    c# is exponentially faster than python

  58. BaufenBeast


    13 dögum síðan

    There's always the fun one where e^(pi*i)=-1

  59. BadAtLosingVideogames


    13 dögum síðan


  60. Benny Blue

    Benny Blue

    13 dögum síðan

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

  61. Lei Yu

    Lei Yu

    14 dögum síðan

    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

  62. Amonimus


    14 dögum síðan

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

  63. Руслан ,

    Руслан ,

    14 dögum síðan

    ещё бы субтитры на русском и других языках, наука должна быть доступна каждому (

  64. Søren Hedegaard

    Søren Hedegaard

    14 dögum síðan

    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.

  65. Raziel Angelos

    Raziel Angelos

    14 dögum síðan

    We know that at least one of (e+pi) and (e*pi) is transcendental.

  66. Zack Lawrence

    Zack Lawrence

    14 dögum síðan

    Good content, but your transitions offend the ears

  67. Jones


    14 dögum síðan

    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

  68. Clair de Lune

    Clair de Lune

    15 dögum síðan


  69. I Kap

    I Kap

    15 dögum síðan

    i did wrong calculations in excel powering from bottom to top and got an INTEGER number ((π^π)^π)^π. WHY??

  70. mister Knister

    mister Knister

    15 dögum síðan


  71. ale mutasa

    ale mutasa

    15 dögum síðan

    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

  72. Kien Thinh Tran

    Kien Thinh Tran

    15 dögum síðan

    The protective minibus periodically whirl because europe immunohistologically nail till a aback condition. evasive, versed badger

  73. Lubos


    15 dögum síðan

    Fantastic popularizing presentation. I have not seen anybody speaking from mathematics so lively and with so much passion. Thank you....

  74. Alan Miner

    Alan Miner

    15 dögum síðan

    Actually, pi^pi^pi^pi IS an integer. Go ahead, prove me wrong. :)

  75. Jack HandMa

    Jack HandMa

    15 dögum síðan

    Engineers are just laughing because they know it's an integer.

  76. John Sausage

    John Sausage

    15 dögum síðan

    It's really interesting and cool video though but I still don't get the point of its existence

  77. Almost Brilliant

    Almost Brilliant

    15 dögum síðan

    I might be pretty ignorant to think this, but doesn't Pi being transcendental rule this out? If not, I'm curious why not.

  78. January First-of-May

    January First-of-May

    16 dögum síðan

    @8:20 it should say 1683, not 1618. An integer power of 3 cannot be an even number.

  79. dvkJoe


    16 dögum síðan

    Every engineer: I don't understand your confusion. PI is an integer, so ...

  80. John King

    John King

    16 dögum síðan

    This maths is White Supremacist and Integers are racist. LOL!

  81. Peter Lawrey

    Peter Lawrey

    16 dögum síðan

    e^i*pi = -1 (an integer)

  82. Android Lg

    Android Lg

    16 dögum síðan

    Perhaps the real integers were the friends we made along the way

  83. Tubemanjac


    16 dögum síðan

    One alien to the other: "i just can't figure out why they don't see it".

  84. E L

    E L

    16 dögum síðan

    Pi divided by pi could be an Integer too

  85. Alex S

    Alex S

    16 dögum síðan

    Asking the other question - why would someone come up with the assumption that pi^^4 could be an integer?

    • E942


      14 dögum síðan

      Overall a proof on this could give some insight. If you answer this question, then you would automatically answer it for a large group of numbers. And mathematicians do things just for the sake of it. On a note an irrational number to the power of an irrational number can be an integer.

  86. Dan Ellis

    Dan Ellis

    16 dögum síðan

    So there's absolutely no reason to even suspect it's an integer?

  87. Brian Cannard

    Brian Cannard

    16 dögum síðan

    "It's too big".

    • Brian Cannard

      Brian Cannard

      16 dögum síðan

      424GB long number.

    • Brian Cannard

      Brian Cannard

      16 dögum síðan

      Funny that 2^42 is so close to the number of BINARY digits necessary to represent π^π^π^π's number of digits 3,638,334,640,025. How many bytes are necessary to store that large number? Let's see... 512GB exactly. Isn't that weird that it's the most popular "big enough" storage format nowadays?

  88. Orazmyrat Rejepgeldiyev

    Orazmyrat Rejepgeldiyev

    16 dögum síðan

    am i just trolled???🤔

  89. Lyokoheros


    16 dögum síðan

    The moment when You have calculated how many times power fo Supercomputer from Code Lyoko was increased due to about 2700 events which doubled it's power and already knew that this 3638334640025 will be number of digits and how insanely those number will grow (as knowing 2^2700 has over 600 digits already, yeah most probably creators didn't realize how insane number this in-universe lore element will produce)

  90. Jeff Guarino

    Jeff Guarino

    16 dögum síðan

    Pi is the distance around a circle divided by the diameter. So I just defined pi and did not need an infinite series to do it. Trouble with mathematicians is that they are using classical physics to construct their math. Classical physics does not exist. So what is a circle ? It is a curved line drawn so that it is equidistant from a point, which is called the center. In Quantum Physics we have the uncertainty principle. So the point in the center is moving around. How do we make sure the distance to the circumference is constant? Use a light and mirror and then time the round trip. The uncertainty principle will cause small uncertainties in the time also . So the center is moving around and the radius is fluctuating. So What is a circle? No one can make one so what is it ???? You can't even define a circle , it is not possible.

  91. Pamela Santos

    Pamela Santos

    16 dögum síðan

    why e^e^e^e^e could be an integer

  92. Guilhem Ané

    Guilhem Ané

    17 dögum síðan

    We set pi equal to 3 Statisticians: applause

  93. 3 mOn3y

    3 mOn3y

    17 dögum síðan

    The second traffic controversly slip because clerk additionly relax upon a gray greasy great burglar. jittery, crowded argentina

  94. Sasuke Uchiha

    Sasuke Uchiha

    17 dögum síðan

    8:15 moment mal das ist doch die 187 Straßenbande

  95. Laika Husky

    Laika Husky

    17 dögum síðan

    "For simplicity's sake, why don't we start with setting pi equal to 3." Engineers everywhere rejoiced

    • Peter Anon

      Peter Anon

      13 dögum síðan

      .... and cried....

  96. scicodude


    17 dögum síðan

    Dont the irrationals INCLUDE the transcendentals? What you're classifying as "irrational numbers" would actually be real algebraic numbers, no? Is this a british vs american english thing?

  97. Micheal Dean

    Micheal Dean

    17 dögum síðan

    OMG! After about 10 minutes in I think my brain exploded. So I stopped watching. The pain is receding but I may still need some aspirin. Or it could be the shitty transition noise that is giving me this headache...hmmm.

  98. Jonny Rocket

    Jonny Rocket

    17 dögum síðan

    Why are we obsessed with Pi ? do we need to know Pi to the Pi(n) is an integer ? would this benefit society ? Reminds me of Fermat's last theorem... when this was finally solved did it benefit us in any way, or was it just a puzzle ? I'm asking these things provocatively as I'm fascinated by Math, but I'm no Mathematician, I'd just like to understand what motivates Math people

  99. Ayk Borstelmann

    Ayk Borstelmann

    17 dögum síðan

    "We set pi to 3" Astrophysicists: Wait what, thought the approximation was 10?

    • Carbon Roller Caco

      Carbon Roller Caco

      6 dögum síðan

      @朕是神 Cutting things in half is one of the most fundamental geometric and physical operations. Triangles are the most basic type of polygon. Right angles are one fourth of a full turn, and right triangles are key shapes. One circle can be surrounded by six others the same size. What does 5 get? The simplest 2D star with a unique shape, and the ability to be cut into either 1 and 4 or 2 and 3. Huzzah.

    • Carbon Roller Caco

      Carbon Roller Caco

      6 dögum síðan

      @P JMU It's still ironic that scientific notation, which is supposed to be unbiased, uses a scientifically wonky base informed by culture only because of evolutionary happenstance. But it is understandable in a sense as they need to quickly relate things to what's already convenient, even if it's an anachronism. Even still, it sounds wrong as THE base for magnitude.

    • 朕是神


      8 dögum síðan

      @Carbon Roller Caco Because other people use 10. No number is better than another in a vacuum. Same reason why you use lightyear instead of inches to talk about astronomy, despite the calculation to change basis is trivially easy.

    • P JMU

      P JMU

      10 dögum síðan

      @Carbon Roller Caco I guess because base 10 is the standard in scientific notation. If a star has mass x * 10^y, astronomers usually can't precisely measure x, so they don't care about. They only care about y, the order of magnitude, which they can estimate properly.

    • Carbon Roller Caco

      Carbon Roller Caco

      10 dögum síðan

      Why do they of all people use 10, anyway? Everyone knows base 10's just a cultural bias inspired by our hands. And 3×3 squares, but those aren't that much more relevant to physics.

  100. Gary McNicol

    Gary McNicol

    17 dögum síðan

    But what about e^(i pi)???