The Riemann Hypothesis, Explained

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    Quanta Magazine

    Trukmė: 16:23

    The Riemann hypothesis is the most notorious unsolved problem in all of mathematics. Ever since it was first proposed by Bernhard Riemann in 1859, the conjecture has maintained the status of the "Holy Grail" of mathematics. In fact, the person who solves it will win a $1 million prize from the Clay Institute of Mathematics. So, what is the Riemann hypothesis? Why is it so important? What can it tell us about the chaotic universe of prime numbers? And why is its proof so elusive? Alex Kontorovich, professor of mathematics at Rutgers University, breaks it all down in this comprehensive explainer.
    Read more at Quanta Magazine: www.quantamagazine.org/how-i-learned-to-love-and-fear-the-riemann-hypothesis-20201214/

Luna Tuna
Luna Tuna

Even if you manage to legitimately prove the RH there are so many crackpot proofs out there, that no one would take you seriously, in particular especially not the people in accademia that you'd need to convince. So the hard part nowadays is not proving the statement, it's publishing it. The proof probably already exists out there. It will never see the light of day.

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Jorge A. Batoca B.
Jorge A. Batoca B.

There's a more vital problem for you to solve, the destination of your immortal soul after death, please do it now while you have the chance . The Holy Word of God - The Bible: John 3 : 16 - 21 _"16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. 17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved.21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God."_

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AB J
AB J

These people are loonatics. Calculate the stupid infinity. News flash! It does not physically exist! In the search of eternity or eternal life diving into hell of endles counting the biger and smaller numbers at the same time. 🤣🤣🤣 Thank God He made them fools and evil doers all those who deny Him!

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Phillsopher Slav
Phillsopher Slav

People often forget about probability, I think it can be used to prove that it's the same line and you don't need anything more to prove the hypothesis. Imagine somebody guessing casino results perfectly every single game for some trillion times? Can you? Me neither... That's the answer. More interesting I think would be creating a theory that proves that there aren't two or more functions that have the same results for trillion of times and then suddenly they differ. That's bs....

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Shota Toriumi
Shota Toriumi

The vacuous hail longitudinally mug because step-sister surely matter aside a noxious mint. daffy, proud birthday

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Jericho gragasin
Jericho gragasin

Dang, 2/3 rewatches are insufficient.

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American Citizen
American Citizen

Could a Turing machine prove the Riemann Hypotheses?

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Simon Eminger
Simon Eminger

And all that was done without computers...

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MOUSUMI SARKAR
MOUSUMI SARKAR

I will prove it one day

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Rishaan Ag
Rishaan Ag

The shaky rock dimensionally water because birthday ophthalmoscopically exist inside a lackadaisical market. enchanted, erratic periodical

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Benjamin Gal-Or
Benjamin Gal-Or

Cosmology, Physics and Philosophy | Benjamin Gal-Or | Springer//// Click name for new, dozen, online, free books at U-tube - all COLOR-illustrated with hundreds references - mainly in science - 2 as graduate and undergraduate CORE CURRICULUM CULTURAL COURSE BOOKS [CCCC]. \\\\ After the rain he collected them from under the trees //// and made mushroom soup with seeds, meat and pita, then lived 175 year and left us 3 major world religions that for 4,000 year most knowing not what to do with them, except the first mankind profession - no, that was not for the women, as you say, but for the men, to fight on almost everything and any idea, to covet, adopt, compete, steal, destroy, punish - which we call education. --- Try the healthy diet to live max. No need to create another set of new religions. Most agree, NO MORE.

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abhishek maderana
abhishek maderana

can anyone explain what he said from 7:17-7:23?

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17 76
17 76

🙄 Great. Now my junk's stuck-in the toaster 😖.

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Benicio Moran
Benicio Moran

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Wing Kan Kwok
Wing Kan Kwok

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nasachusetts
nasachusetts

I'll take a stab at it and conclude the answer is 42.

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Robert Nielsen
Robert Nielsen

4 dimensions If not 5 gib 1mill

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Alexander Safranek
Alexander Safranek

I like my math with jazz.

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SouthBayJay
SouthBayJay

Literally if my math teacher had just said “logarithms are to exponents what division is to multiplication,” I would have had much less trouble with them. Thanks dude

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Retro Tommy
Retro Tommy

10 to the 3rd power..duh.

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James Flash
James Flash

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lal agun
lal agun

The recondite eight collaterally transport because ophthalmologist orally vanish midst a minor anger. wooden, grotesque crayon

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Sos Cos
Sos Cos

If I know the proof of Reimann hypothesis where do I publish it.

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Organic Farm
Organic Farm

Reddit 😁

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calico57
calico57

I got bad flashbacks to my math classes over my life watching this.

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Justin Lindfors
Justin Lindfors

So are we trying to come up with a proof or something?

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Dixie Lord
Dixie Lord

I'll take your word for it.

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Petrus K
Petrus K

"Oh that's where Gauss Rifle gets its name" i feel so dumb

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Mark Time
Mark Time

Any chance of 10k for taking a really, really, really good stab at the answer?

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Jim Walker
Jim Walker

That initial diagram looks very much like a cardioid polar patter of a microphone.

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McGrady
McGrady

PI Network invitation code: MarkoMcGrady

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bon jon the Jon bon
bon jon the Jon bon

I wonder if you could prove it by disproving the converse. Like showing that a non trivial solution falling outside of s := ½, violates a logical reasoning.

Prieš 3 dienas
Badly Drawn Turtle
Badly Drawn Turtle

These videos always talk about everything that rides on the hypothesis being true. I'd like to see a math channel go into detail sometime on what the implications would be if someone disproves the Reimann hypothesis. What sorts of things would need to be reworked?

Prieš 3 dienas
TheSprinklerNinja
TheSprinklerNinja

Math is racist and you're a bigot.

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Peter Schmitz
Peter Schmitz

Wow, the magic of math strikes again. I always feel that tip of the tongue right on the edge of the conscious mind feeling when these things are explicated. Like the mind wants to find a hole and rush in to see the mystery first hand....and perhaps through insight solve the question it poses.

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MoJo LoLo
MoJo LoLo

You lost me at "prime numbers".

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Gaurav Singh
Gaurav Singh

Okay! I am pretty dumb 😣

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nIMrOD888
nIMrOD888

I dont know much about math at this level, but why can't brute force be used as proof?

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Badly Drawn Turtle
Badly Drawn Turtle

Brute force can only be used in a proof if there are a finite number of things to check, and each one can be computed in a finite time. The Reimann hypothesis deals with some infinities, which can never be fully computed regardless of how much time you pour into it. It is possible that someone could come up with a clever way to manipulate those infinities into a finite number of computable cases, but that would require theoretical work that the computer can't do on its own.

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The Woo 💫
The Woo 💫

Subtitles :(

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John Kessels
John Kessels

Blackmather input?

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Tragix Spaz
Tragix Spaz

The critical line reminds me of the grand line from one peice, nothing can go out of that line once you are in it. I see it as a grid.

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shahid hayat
shahid hayat

I'm a student of politics what am I doing here. ?

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pc m
pc m

I was waiting for the "practical application" part of the video.

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Donald Jacobs
Donald Jacobs

The flippant sign lily overflow because orchid perplexingly wave by a next crow. plucky, material var verbs = [aardvark

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paul beenis
paul beenis

1.1M views and I guarantee the stupidest person here is smarter then everyone on tiktok and Facebook combined

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JoeyB EZ
JoeyB EZ

THE ANSWERE TO PROBLEM IS = SHOE WHERE IS MY MIILLION DOLLARS?

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Ian Grams
Ian Grams

I've known of the Riemann Hypothesis for a bit now, but never bothered to try and understand it because I thought it was beyond my comprehension. But wow this video did a great job at explaining what it says, what lead up to it, and what is significant about it. Thank you to all who made this for expanding my understanding!

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F Stöver
F Stöver

Compound interest, right?

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NO IDEA
NO IDEA

Funny thing how they all consumed some form of psycadhelics

Prieš 4 dienas
Divedown25
Divedown25

1:30 “you don’t need an advance degree in mathematics” and the he adds some cool jazz music with his excellent narration voice reeling me in like a fly finding honey... and there I am at minute y=f(x) and I am totally, and I mean it, totally lost why log (P) and Gauss and Euler and Riemann... this is like PBS space.... addictive on a dangerous level

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Raian Maikeru Jōnzu
Raian Maikeru Jōnzu

Oh I see, the "Zeta Zeros" (shovels chips into my mouth as I lay on the couch in my underwear).

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Randy Haimila
Randy Haimila

Critical Race Theory would say this is racist because it was made up by some white guy.

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Notexoojr
Notexoojr

How do I claim my $1 Million

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theman 0
theman 0

When you solve the bitch

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lal agun
lal agun

The lonely poison really preach because cement endogenously battle via a bored tea. separate, uptight packet

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iAmFreedomManCom
iAmFreedomManCom

FlatAndStill°com! Flat3arth°com! FlatAndStillEarth°com! FlatAndStillEarthSociety°com! RichardEByrd°com! OperationHiJump°com! DensityNotGravity°com!!!!

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Manish Kedia
Manish Kedia

Pls help

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Manish Kedia
Manish Kedia

My channel is krish kedia with no profile photo

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Manish Kedia
Manish Kedia

Pls help me

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Manish Kedia
Manish Kedia

Sir can you help me pls. Sir i have discovered proof of legendre conjecture but i do not know where to report it.

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Dorijan Cirkveni
Dorijan Cirkveni

7:00 Hold up. Wouldn't you miss 6, 10 and all other numbers that aren't primes or powers of primes that way?

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hello operator airsoft
hello operator airsoft

It's a buttocks... The Holy Grail of geometry....or breastesses

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Scott Huddas
Scott Huddas

The left arrow on my keyboard is worn out now. Thanks a lot.

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Quang Tran
Quang Tran

Put the 1M$ unsolved problem aside, this is so oddly satisfying to watch!

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Mike S
Mike S

Massive props to you for this video. Excellent voice work, animation and music. Re. the content - I learned enough to know that I'd never cut it as a mathematician. But this is about as approachable an explanation as I think anyone could ask for. Thanks for producing this.

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कोई बात नही
कोई बात नही

Thanks, man

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nucksfordacup
nucksfordacup

This felt like my 50 minute lectures in Calc 3 in Uni. I'd understand 1/4th of the way in, and as soon as the prof segued into the topic we were learning that day, I'd be completely lost. Ferociously scribbling the notes; hearing the words she was saying yet not grasping anything.

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Andy Horse
Andy Horse

......piece of piss!

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Danny Feinberg
Danny Feinberg

Thank you for putting together such a high quality, engaging, and fascinating educational video on this topic. I can’t think of any way this video could be any better and, as someone who has limited knowledge in mathematics, I really appreciated the way you explained the concepts so clearly and elegantly!! Bravo!! This is an excellent example for how educational content should be - succinct, elegantly visualized, fascinating!! Thank you!! Beautiful and engaging visualizations of the concepts!! Would you mind me asking what programs were used for the visualizations?

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Subramanian T R
Subramanian T R

This is absolutely awesome video.

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tommy aronson
tommy aronson

Neeeeerrrdd

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Jeff S Jones
Jeff S Jones

Exceptionally clear explanation, thank you!

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the popmodule
the popmodule

I enjoyed the video. Still confused AF.

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hedwegg
hedwegg

1. Topic: The [Verbal Solution] to the [Riemann Hypothesis] in [Plain English]. 2. To Note: (a) [Math] is a [Language] (Symbols & Numbers). (b) [English] is a [Language] (Symbols, Letters & Phonetics). It's a [Clear & Powerful] Language. One (1) Language, [English]! 3. To the Point: "The Solution to the Riemann Hypothesis" in [Plain English]. Ready! (a) Let [Zero] (non Trivial) represent [Equilibrium]. (b) Let the [Primes[ "represent" a [Rhythm]. (c) [Equilibrium & Rhythm] form [a Network], [a System] that's [Structured & Organized]. i.e. an Enviroment, a Universe, an Intelligent Design! [Robotics & Neural Networks]! 4. To Note: The [Patterns] are clearly visible. The [Connections & Origins] give [Infinity a Limit]. It's called, [Focus]. With [Focus] is discovered [Clarity] & [Definition]. i.e. More than a Black Hole! Amen. With [Equilibrium & Rhythm] the [Language of Math] becomes [Intelligible] even [Readable]! More than [Symbols & Numbers]. [English] is a [Clear & Powerful] Language! All for [Applications]. Stay [Sober, Sane & Alert], my friends.

Prieš 6 dienų
MultiPleaser
MultiPleaser

Math degree needed! Many times the video seemed to make large leaps, skipping very important stuff. After rewinding it a zillion times, I still don't know what happened every time it jumped ahead. For instance, it jumped from log base two to the natural log, when discussing the primes in the vicinity of 150. That's the one and only place where I could figure out what the narrative skipped. The other places are still a mystery. And I took calculus and "honors math" in high school, and then half my college degeee was math (or so it seemed). By the way, a zillion is the natural logarithmic, imaginary zeta function Z(iMillion).

Prieš 6 dienų
Dushyanth Edadasula
Dushyanth Edadasula

Amalgamation of story-telling and science at it's finest. Boy did I love it. THIS SHOULD BE WAY MORE POPULAR YOUTUBE, ARE YOU LISTENING?

Prieš 6 dienų
sahir de
sahir de

Yep, this is what the platform is all about. Unfortunately I think the algorithms behind the scenes favour sheer volumes of content over high quality, which is probably why the videos don't get a ton of views on this channel

Prieš 5 dienų
John Armstrong
John Armstrong

Wonderful video - But "Help!" As I deconstruct the lesson - I find that there are a couple of 'jumps' that might benefit me (or another video, or a few minutes extra in his one). One is the idea of "trivial zeros" being the negative even numbers (-2*n where n= 1,2,..) and the other is where you talk about harmonics the second time about 14 minutes in. You mention the harmonic series in the beginning but that is not sufficient to expose what is meant by 'harmonics of the zeta zeroes' let alone what is meant by 'trivial'. Also - while the graphics of the 'analytic continuation' are beautiful, the change in the 'space' (extending the domain which allows allows the zeta function to 'orbit' returning to zero needs at least a reference to what the new function looks like, I think. Google works, but it takes me out of your presentation. Perhaps that is seen as out of scope, but I think it might clarify both "trivial zeros" and "harmonics of zero"

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M4 Media
M4 Media

1 = Pie(Squared)

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Dreadnaught
Dreadnaught

Distracting 'musical' background and rapid-fire diction inhibit comprehension. Wish you well.

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masteric123
masteric123

What if C-A-T really spelled DOG?

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Joy Barnes
Joy Barnes

Ingat.... Ada allah....

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D
D

Bravo Kontoroviću, nisam ništa razumio ali tebi svaka čast 🍻

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C123B Thunderpig
C123B Thunderpig

The Rieman Hypothesis is not a mathematical problem - it is a mathematical observation which has already been solved. There is no answer for a mathematical problem that involves infinity.

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C123B Thunderpig
C123B Thunderpig

@GalvakzaMusic 😀😀😀😀😀😁😁😁😂😂😂😂😃😃😃😃😃😃😄😄😄😄😅😅😅😅😅😅.

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GalvakzaMusic
GalvakzaMusic

You're an idiot. For many problems that involve infinity there are ways to prove them.

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jac jac
jac jac

You need to add a dimension, if there is a pattern seen, you need a bigger picture

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Astrology, Travel and More
Astrology, Travel and More

I cracked Riemann Hypothesis. It is in Wikipedia.

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pooper dooper
pooper dooper

Please be my math teacher

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Dufftata
Dufftata

thank you very much for the video, I do live it. The explanation is on point, and so are the brilliant animations!

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Suf
Suf

@11:38 be like: "when you input a negative even integer, the zeta function equals zero". Me: O_O "I simply do not understand why." He completely lost me there.

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Vinod Mehra
Vinod Mehra

No matter how many illustrations you'll use you still can't teach me mathematics.

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nucksfordacup
nucksfordacup

You can lead a horse to water...

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russo thuga
russo thuga

The opposite seaplane cellularly yell because cardigan bizarrely sail round a aberrant cannon. cagey, innate color

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Skywatchers Virginia
Skywatchers Virginia

I got access to a quantum computer! Someone come up with the algorithm and I will run it!!!!

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Mike Walters
Mike Walters

False. Lock it in

Prieš 7 dienų
Raj
Raj

New here, thanks for the video, I gave a thumbs up. I thought your explanation on convergent and divergent series could have been a bit better, but overall the video was good.

Prieš 7 dienų
Al Engine
Al Engine

Peice wise laplace transforms would have been your short cut to resolve the step responses between primes. Fourier series for Sum( [0 < s < 1) * 10^k(n-1)) for all 'k' in 100 would have broken a barrier for all

Prieš 7 dienų
kraeutemall
kraeutemall

Math my brain no good.

Prieš 7 dienų
Roberto Pierdomenico
Roberto Pierdomenico

I felt almost clever until you started banding and folding the field. I guess if I take LSD the field will go back into place. Reverse trip!

Prieš 7 dienų
YAMERO CAT
YAMERO CAT

I didn't understand much But It looks cool.

Prieš 7 dienų
saber7ooth
saber7ooth

what the fuck is going on

Prieš 7 dienų
Ardusk
Ardusk

Awesome visuals! I'll even pass the lab test! My friends did ask me what drugs I was taking when I talked to them about it though. Had to lie it was acid so as to not come off as a nerd.

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Will H
Will H

cool man, I think I'll solve this over my lunch break

Prieš 7 dienų
Morwick Chesterham
Morwick Chesterham

imaginary numbers... my brain just melted... eitherway central banks would find them useful

Prieš 7 dienų
aswler
aswler

It was an easy high school mathematics until the half of the video. Then it started to be difficult and too fast with the i-functions and zeta functions I am afraid.

Prieš 7 dienų

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