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

“We set pi equal to 3” Engineers: applause

The year is 3021. Computing power has finally advanced to the point that we can confirm that pi to the power of pi to the power of pi to the power of pi is not in fact an integer. The Intergalactic Society of Mathematics is hosting a party to celebrate. Suddenly, someone speaks up from the back of the room. "But what about pi to the power of pi to the power of pi to the power of pi to the power of pi ? Is that an integer?" The room falls silent.

6:48 I love how Matt just casually referred to the two people as Emma and Timothy like if they were close friends

2:00 – calling them "irrationals" is indirect, since π or e are irrationals as well. Numbers like √2 are algebraic, an antonym to transcendental.

This reminds me of 8 year old me trying to repeatedly multiply 9999 to itself in my calculator. I too was limited by the technology of my time.

“Everyone remembers where they were when they noticed that” Ah, yes. This takes me back to two seconds ago.

Great video. Although I expected some kind of argument for why we would expect this number to be an integer. But as I understand it, there is no reason to believe that it is anything in particular. We simply don't know. Although I am inclined to think it is probably not an integer, it is true that you can get integers or rational by operating irrationals and transcendentals in certain ways. But there is always, I think, a good explanation for it, it seems that you have to be deliberate about it. Kind of like when trying to convert rationals into integers, if you multiply randomly, you will fail in even a vast majority of cases, when multiplying by the inverse for instance, you succeed. But of course, I don't know much about it, it is just the impression I got from watching the video. Pretty interesting question.

I remember the moment I realized what the word trigonometry meant..! I started looking at the word "polygon", meaning "several corners". I then thought of what a triangle would be called, "probably Tri-gon". Then it absolutely struck me, "Tri-gono-metry = The measurement of triangles"!

"We set pi equal to 3” I felt a great disturbance in the force.

My math teacher used to say, “if you don’t like natural logarithms just e-raise it. Then you don’t have to deal with it”

This was such a fun video to watch. Definitely one of my favorites from Matt.

Thank you for making complicated math concepts fun and entertaining. Peace and Love Matt <3

"Say what you want about 3, at least we know it exactly. It's equal... to 3." This is what we call high-quality educational content.

I'm surprised that you didn't save this for March 14.

It's remarkable how modern mathematics can produce amazingly powerful and accurate results for physics, engineering, computing and essentiatially all fields of applied science, yet remarkly simple statements in number theory, combinatorics, transcendental number theory and other pure math branches are not only unproven but seem to be utterly unpproachable by every mean know to mathematicians today and many see no progress for decades, sometimes more ...

This video was amazing. So many fascinating thoughts. Absolutely loved it!❤

Never before have I seen someone have so much fun with a stock studio audience, and I love it so much

"How about we start by setting pi equal to 3..." What is this, stand-up engineering?

This is amazing. I love that you led with Tim Gowers' response, to reassure all the mathematicians in the audience: this isn't as simple as it might look, keep watching! 😅

Actually, we can apply number theory to this, in particular, Fermat's Little Theorem. We have methods of calculating the nth digit of pi in binary without having to calculate all the previous digits. In the appropriately chosen modulus, this is all you need to determine if the number is integer or not.