There's a strange number system, featured in the work of a dozen Fields Medalists, that helps solve problems that are intractable with real numbers. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
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References:
Koblitz, N. (2012). p-adic Numbers, p-adic Analysis, and Zeta-Functions (Vol. 58). Springer Science & Business Media.
Amazing intro to p-adic numbers here: https://youtu.be/3gyHKCDq1YA
Excellent series on p-adic numbers: https://youtu.be/VTtBDSWR1Ac
Great videos by James Tanton: @JamesTantonMath
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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
Ok, but why? What does this information do for us?
@auntcissy Says:
I like the 5 squaring patern
@dpw0499 Says:
27:07 LMAOOOO
@renelepage5053 Says:
Great. Although I'll have to think it deeper.
@Y2K-b1k Says:
2:42
@luketorrence6425 Says:
i watched a video where this same guys showed me that there are bigger infinities and smaller infinities, and now hes trying to convince me that infinity + 1 isnt a thing.... get real
/s
@JohanKaewberg Says:
Threeadic? We call it trinary or ternary in computer science. Trinary computers existed at one point (USSR). Balanced ternary hardware used -1, 0, 1 times 3^n for trit values.
@littlefloss._. Says:
1:19 sorry the zack d films video changed this song for me
@zanezoucha5123 Says:
But like high-key 1/3 does not equal 0.666666667
@FrancescoMunafò Says:
This is one of the best mathematics content video ever, congrats to Veritasium for explaining an incredibly complex content in such an understandable and clear way
@nathankiwijoog1031 Says:
Why am I so uneducated but deeply love numbers 😅
@Mattt_or Says:
Bruh, the higher system invented this, we only noticed it
@toyinamodu3671 Says:
I mean anology
@toyinamodu3671 Says:
The stars apology was perfect . Thanks for the video
@AndijvieMetPatat Says:
So to destroy skynet, all we need to do is target Kurt Hensel, not protect John Connor.
@doomshroom7682 Says:
The ...999999999 ending up as -1 reminds me of the way signed integers work but if there was no bit limit.
11111111 in int8 means -1, and when you add 1 it switches every bit to zero from the right and trails off the left side resulting in 00000000 or just 0.
@JossoJJossoJ Says:
If we used a number system of prime number base from the beginning of human history, would we still get to find p-adic number system?
@AbyNeon Says:
What a stupid question..... the answer is obvious without using a calculator:
f^3 = 1
Mathematically, if you want a pure algebraic function that summarizes every possible way to square a frequency (f) and isolate a common denominator, you look at it as a generalized rational function:
f^2 = \frac{P(f)}{Q(f)}
Where:f^2 is the squared frequency.Q(f) is the algebraic denominator (which can be any polynomial, expression, or function of f).P(f) is the numerator.If you are treating the entire infinite process as a self-referential or recursive fraction where the denominator itself is generated by the squaring operations, it takes the form of a continued fraction or fixed-point equation:f^2 = \frac{1}{1 + \frac{1}{f^2 + \frac{1}{\dots}}}
Mathematically, if the infinite squaring process forces the denominator to equal the frequency itself, the system creates a self-referential loop.
When you set the squared frequency equal to a fraction where the denominator is the frequency (f), it forms a fundamental algebraic equation:f^2 = \frac{1}{f}
What Happens Next?
If you solve that equation by multiplying both sides by f, you get:f^3 = 1
Instead of blowing up to infinity or shrinking to zero, the infinite squaring collapses into a fixed point governed by roots of unity:f = 1 (A pure, stable unit frequency where squaring it forever changes nothing: 1^2 = 1).
Complex roots (representing perpetual phase rotation or oscillation, like
e^{i 2\pi / 3}).
By forcing the denominator to be the frequency itself, the infinite progression stops wandering. It locks into a stable harmonic anchor (1), where the frequency, its square, and its denominator all reconcile into the exact same value.
@Joemama555 Says:
lol, veritasium got 10 million people to watch number theory
@blakerhodes5024 Says:
let me guess.....it equals 1
@MauroGames_ofc Says:
Y not 😂 Why not
@Sonavlogs-vk6fc Says:
what is square root of n
@TechnoXD623 Says:
Good guy
@arturaslusnikovas8173 Says:
"take the number" 10 and square it :), repeat as long as needed (no fence). Decimal system.
@GuilhermeChacon-o6g Says:
Pq a afirmação de Fermat é uma das mais infemes de todos os tempos? Não entendi isso!
Wow. I have a master's degree in math (from 20 years ago) with an emphasis in abstract algebra and I don't remember ever working with p-adic numbers. I do remember going to a lecture about Fermat's Last Theorem, so I assume I must have heard of it, but it didn't ring any bells while watching this video.
@Leon-really-is-a-nerd-lol Says:
I was thinking the same.
5 is just really interesting.
@Rubikscubekid1234 Says:
67
@Worldisem1111 Says:
…99999999999999992+1=1×10¹⁷(That’s what it gave me)
@Worldisem1111 Says:
0, 1, 65536, the first three x^16 numbers 0^16=0, 1^16=1, 2^16=65,536.
@Worldisem1111 Says:
0^16+2^16=65,536 witch is x^16, so x^16+x^16 can equal x^16
@Worldisem1111 Says:
…99999999999973 = -27
@Worldisem1111 Says:
So …999999992 = -8
@guilherme6818 Says:
20:32
If we're working with mod 9, wouldn't that 15 actually be 6?
@actually_average Says:
whos here after messi missed the pen against egypt
@guili318 Says:
x^2=x, x=1, x=0, x=1/2+j/2 (j^2=1, j≠1, j≠-1), x=...890625, x=...6(I could not calculate the rest of the digits so could someone complete it for me?)
@BloxysBeats Says:
I’d rather work in the 10-adics than a p-adic because I LIKE THE FACT THAT THERE’S A NON-ZERO NUMBER THAT WHEN MULTIPLIED BY ANOTHER EQUALS ZERO.
@ozlembenli1072 Says:
42 lS NOT SpoiIer
@peksashipsa Says:
I dare Numberblocks to try this
@since91productions75 Says:
3:12 that would make sense because in that 10-adic number we can see the numbers “142857” and 0.142857=1/7
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