Check out the Jane Street programs if you're considering a mathematics/finance/programming job:

www.janestreet.com/join-jane-street/our-programs/

Here is Tim Gowers's reply to the original tweet:

twitter.com/wtgowers/status/1346212151581700096

Start your Schanuel's Conjecture journey here:

mathworld.wolfram.com/SchanuelsConjecture.html

3^3^3^3 on wolfram alpha:

www.wolframalpha.com/input/?i=3%5E3%5E3%5E3

And for completeness, here is pi^pi^pi^pi:

www.wolframalpha.com/input/?i=pi%5Epi%5Epi%5Epi

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.

nlworld.info/key/video/loyce8qZZ7BjfYA

CORRECTIONS:

- 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.

www.patreon.com/standupmaths

As always: thanks to Jane Street who support my channel. They're amazing.

www.janestreet.com/

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

U just wasted my 15 minutes..

*laughs in spanish*

pi tetrated by 4

x-pi=0 Solution: x=pi Pi is not "transcendental" (proof by counterexample).

=2^12

Answer is 1.327049678×10⁵⁷ Trick convert π=22/7 and calculate in calculator ! EASY!!

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.

I tried to do this and my calc Sai math error....

Irrationals are all non-rationals. You mean algebraic numbers.

thumbs up for the stock audience

I bet 2 dollars it's not an integer.

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)

When is pi to the power of pi to the power of pi to the power of pi day?

making Pi equal a nice round 3 in a machine is literally a side plot in a Pratchett novel

This video will literally causes a heart attack on Norman Wildberger (from Insights to math NLworld channel) LOL

I don't know what is better, the irrational jokes or the rational explanations

how root(2)^root(2) give root(2)*root(2)????

What

Pi^logpi(3)=3

12:14 The answer is no we cannot get an integer number by rising pi to pi infinitely

Suddenly Electroboom outro start playing in my head

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

Bet

Awesome !!! It almost reignited my interest in mathematics...

My calculator: Math error

let's go 0:09

The absence of evidence is not the evidence of absence.

Is the right side of the graphics on his shirt forming a straight line? That depends on the print resolution.. surely.. hm

2:02 All transcendental real numbers are irrational. He seems to be using "irrational" to mean "irrational algebraic" which is not correct.

Just brilliant!!! Thanx

If you say ‘pi to the’ over and over again you become a dance DJ.

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)))

Oh hell yeah Parker Conjecture

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

That was interesting. I like math.

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

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

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

No.

Wait. It is not.

I have a feeling it equals 7

2:28, (x - π)(x - e) = 0 or, x = π,e

jk

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

8:15 EINSACHTSIIIIIEEEBEN

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.

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

Just A total waste of my time

disappointed no e^iπ

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

Ramanujan: is that a challenge?

"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

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

Wow

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

I really like the 31.4 trillion digits of pi calculated.

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.

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.

nlworld.info/key/video/rWmWl8y5i651iWc

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

I hear him now haha

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

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

the parker conjecture

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

Excellent. Thank You.

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?

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."

well the title wasnt misleading, it told you all that

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

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.

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

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.

Peh. Work out 2π^2π^2π^2π instead.

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?

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

The clickbait worked.

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

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?

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

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

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

E

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

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.

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))

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

1:32 of course you said 42

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.

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.)

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

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

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

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

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

c# is exponentially faster than python

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

*Menacing*

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

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

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

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

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.

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

Good content, but your transitions offend the ears

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

racist

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

2.598.761.979.625.197,5214462849737795

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

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