Mathematicians Use Numbers Differently From The Rest of Us

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References:

Koblitz, N. (2012). p-adic Numbers, p-adic Analysis, and Zeta-Functions (Vol. 58). Springer Science & Business Media.

Great videos by James Tanton: @JamesTantonMath

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Special thanks to our Patreon supporters:
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Written by Derek Muller and Alex Kontorovich
Edited by Trenton Oliver
Animated by Mike Radjabov, Ivy Tello, Fabio Albertelli and Jakub Misiek
Filmed by Derek Muller
Additional video/photos supplied by Getty Images & Pond5
Music from Epidemic Sound & Jonny Hyman
Produced by Derek Muller, Petr Lebedev, & Emily Zhang

[RenaudAlly]

These are literally scientific documentaries of the highest quality at this point. It's amazing that I'm able to watch this stuff for no cost at all. Thank you so much Veritasium

[rrrfaa]

I took a graduate course on p-adics in university and it felt like all I did was manipulating symbols on paper without understanding what is happening. This video finally made me understand what is going on.

[einargs]

As someone who does computer science, it was extremely cool to suddenly make the connection to how we represent negative numbers using two's complement.

[andy]

The level of quality in these videos is sublime. You never insult the audiences, by not going as deep as is required. Excellent work as always

[imtiazsameer]

My Granddad used to play P-adics numbers game with me. He started by asking me to write any random numbers before decimals and he used to write his random numbers below them, And sum of them always comes Zero. His techniques and methodology amazed me and fascinated to learn More Math. Miss you Granddad ! And Thank you Veritasium for this Video

[LeoLeahy]

As an engineer and video editor, I am absolutely mind-blown by the production quality of this video. I can't even imagine the number of hours put into the editing alone. It's amazing that content like this is available for free. Not that your other videos aren't great as well, but this was something else.

[johnchessant]

I don't normally think of Veritasium as a math youtuber, but with videos on Newton's calculation of pi, Godel's incompleteness theorem, discrete Fourier transform, logistic map, Penrose tiling, Hilbert's hotel paradox, and various probability puzzles, he definitely should be. I mean, this video alone (p-adic numbers, Fermat's last theorem, Hensel lifting) would be an extremely ambitious topic even for a math-focused channel, and he and Alex Kontorovich did a great job with it!

[saltytriscuit]

Me and the boys finding the last digit of Pi by calculating it backwards:

[jessejustice]

I can’t focus for 5 mins at school but can watch a full 30 minutes video from you no problem

[ZacharyVogt]

This video is the perfect example of encouraging the audience to rise to the level of the content (the exact opposite of talking down to the audience.) Very inspiring.

[CyclingGeo]

I’m a geologist so my maths is questionable at best.

I find it utterly fascinating how well I can follow along with this, yet still be completely bewildered and confused.

[aurunemaru]

0:24
"so, does this pattern continue?"
me immediatelly:
"patterns fool ya, paterns fool ya, ..."

[TerryBollinger]

As a computer scientist, your comparison of p-adic numbers to two's complement negative numbers was extremely helpful for getting this topic to finally "click" in my head. Thanks!

[neerajwa]

I couldn't imagine someone could do a youtube video on this topic. Complete with graphics and engaging commentary. It takes a very special level of film making skill plus top notch scientific knowledge to do such a thing. I am a phd in maths. At one time sixteen years back, i was entranced by p-adics. Used to organize student level lectures on it. Slowly my interest wore off and i moved on.

Thanks for reminding those days again.

[Pyrozoid]

I'm jealous that Derek gets a personal lecture from such an amazing mathematician.

[poly_hexamethyl]

I'd heard of p-adic numbers and was vaguely familiar with their definition, but didn't know much about their motivation or applications. After watching your excellent video, I'm motivated to learn more about them.

[TimeBucks]

Thanks for bringing this amazing topic to us

[meep]

learning about math without the pressure of college is pretty nice. i still feel completely lost after a certain point but the crushing pressure of needing to pass the class and putting stress on myself doesn't exist

[greatjojek]

Fascinating topic! I am so glad it got more traction.
Fun fact, some p-addic systems have really interesting properties. For example in 5-addic the number:
…04340423140223032431212
Multiplied by itself gives:

Which is a representation of -1 (add 1 to it and you get 0).
This means that 5-addic system has the sqrt(-1), the imaginary unit, in it!

[manOmanyTrades]

Bravo! You covered in 30 minutes what took me semesters to master in my youth. I am totally inspired.