The Riemann Hypothesis

[@andersjaevel]

The proof of the Riemann Hypothesis is clear and we leave as an exercise to the reader.

[@ItachiUchiha-ns1il]

andersjaevel damn that’s good one lmao

[@69erthx1138]

You need a couple of pints and few less text books mate.

[@ДмитроПрищепа-д3я]

Some good Landau right there.

[@yashhkotecha2647]

Trivial*

[@RodelIturalde]

@supadox Because often, the proof is rather easy to make if you did understand exactly the proofs and methods the textbook used to prove some other thing just before. And it is actually a good excercise to come up with ones own proofs. Though it is extremely hard i think.

[@72ackerman]

This is a great explanation of the Riemann hypothesis. I like how you presented it in historical context, broke it down into parts, and explained its relationship to other aspects of mathematics. Very critically, you presented the equations, you explained the intuitive portions to non-mathematicians, and you did it with the enthusiasm that is difficult to glean from dry textbooks. Love your KZbin posts and your appearances on Brady's videos. Keep up the great work.

[@singingbanana]

+72ackerman Thank you very much!

[@72ackerman]

+singingbanana Also, you finally taught me what that big Pi means before an equation, which I had not known before! (Math looks less like hieroglyphics now).

[@singingbanana]

+72ackerman Ha, I'm glad.

[@christosvoskresye]

+72ackerman The symbol is used for continued fractions. Well, not really, but I like the idea of using actual hieroglyphics for math.

[@christosvoskresye]

+christosvoskresye And, of course, it doesn't show.

[@GermanSnipe14]

"It was like the mathematical equivalent of a mic drop. Peace out, that's it. I'm done" ahahaha I love you Dr Grime

[@hummanuhblubberrumma]

I believe that we just got -1/12'd again.

[@dhidhi1000]

I find it interesting that I watched this video about 2 years ago when I was 17, and I remember I didn't understand somethings. Now I'm on college, and I decided to watch this again, and surprisingly enough, I got a lot more of what he said. It's nice to see our own development in practice.

[@nicolasd6391]

I am looking forward to understanding this:)

[@pakan357]

I feel exactly the same way. Although I failed both of my Math classes, I learned quite a lot.

[@tggt00]

+Dhiego Bersan Same here except I was 14 when I first watched this and now I'm 16 and I understand everything perfectly.

[@darmodak1773]

+tggt00 bahahahahahah

[@tggt00]

What's so funny?

[@FelipeBudinich]

Aaaand, it might be easier to earn a million dollars selling hotdogs :D

[@SD-de4do]

it all depends on how you go about it ;)

[@deeptochatterjee532]

Felipe Budinich Or just borrow a small loan of a million dollars

[@cameronspalding9792]

Deepto Chatterjee And you’d have to pay it back within a long time interval

[@j.vonhogen9650]

Just rob a bank, or build one!

[@JohnSmith-cy8hq]

"..that Riemann decided to rip off, I mean study." I coughed up my chocolate milk.

[@Popexssj]

I love to eat my dinners and watch this dude. His videos are usually long enough for me to finish my food. Too bad I don't understand a single thing he's saying.

[@singingbanana]

I love that I'm somehow a strange part of your daily rituals. I have a similar habit.

[@CafeAlpha]

There's a Japanese club for families to learn a bunch of languages, and the funny thing is that the guy who started the club requires people who join, as their first assignment, read Heisenberg's book on quantum theory. He says that it won't make any sense to you, but that if you're going to learn new languages you're going to have to get used to reading things that don't make sense to you... Though, obviously, some of his members did come to understand Heisenberg's book because they published a book that goes through every single step of proving that Schrodinger's wave equations are equivalent to Heisenberg's version. It was written by students who had just learned it, on the theory that you're better at remembering all the details and explaining something that you've just learned. And it's very Japanese, full of cute little cartoons and asides like how to draw a cartoon the physicist De Broglie, who's face is shaped like a peanut.

[@Snijele]

Popexssj same here bro. :)

[@shield543]

Dr James Grime, I salute you for finally making this video! :)

[@singingbanana]

The natural length of this video turned out to be 20 minutes. Normally they're only about 6 minutes. That proves something, but I'm not quite sure what yet.

[@paradoxica424]

singingbanana New proposition: Any attempt to explain a currently unsolved mathematical proposition/hypothesis will take about π times the expected length of time.

[@ClayCompton]

singingbanana It means this video should've been a three-parter.

[@lightclock9761]

It is brilliant. Clear explanation of Reimann Hypothesis is given, and it is inspiring.

[@BradleyRobinson]

James, sincere thanks for following through on this request by interested viewers like me, I am familiar with the content but the nuances continue to grow over time. The internet access to information sources like these youtube channels is a stunning contrast to when I was first introduced to it reading a paper back copy of "Stalking the Riemann Hypothesis by Dan Rockmore" around 2005 "by candlelight". Watching this now three or four times over two days was again similarly juxtaposed personally.." very exciting" and a thoroughly helpful addition to the initial "incredible read" experience. The interval between then and now is remarkably influenced and is clearly given me access to real structure by better understanding the mathematics, especially in the margins of addition and multiplication. The theorem's wide appeal to many pursuits is in itself remarkable. In all the video here is "Exquisitely arranged material and lucidly presented with admirable understanding and enthusiasm in a skilled detailed explanation". So much of what excites me about mathematics is how much there is to learn and the many open questions still abound in this wild field... exploring the unknown... and its good to leave a trail!

[@technowey]

Great lecture. Your deep knowledge is apparent, but you're also an excellent communicator. Thanks for the videos you've made.

[@ChongFrisbee]

You, sir, are a gentleman and the gratest math comunicator ever. Thank you.

[@LVBradley2013]

As a pure mathematics major, all I want is to sit down with you and learn even more. Wonderful video as always, Dr. Grime.

[@santafucker1945]

i've discovered a truly remarkable proof which this comment box is too small to contain.

[@liamcarman6256]

Link or it didn't happen

[@mikhailmikhailov8781]

Ferma, pls, no more jokes

[@MrMlindsay]

wait isn't the comment box now infinite. I think that I have either killed a frog or your proof doesn't exist.

[@hemuln]

i think he dropped dead right after writing this. sadly, this theorem is now called the kingslayer's last theorem, and George RR martin is going to sue.

[@santafucker1945]

beary the bear LOL

[@Epicaq]

Whenever I feel too clever, I just tune in on this channel and I feel stupid again. I love how passionate Jim feels towards math. Makes me passionate about it, even though I'm no strong mathematician. Keep it up :)

[@nge1301]

I dropped out of grade school and almost got this! It got hard after 0:08 though.

[@RBuckminsterFuller]

I studied math for a while a couple of years ago and I almost understood all of this. I'm so proud of my brain.

[@taherajna]

same feeling XD

[@OhDannyBoy512]

I feel ridiculously out of my depth watching this video. I only feel as though I partially understood this because you led us through it in such a logical and sequential order! Thank you for the brain strain! :)

[@singingbanana]

This one isn't for everyone. I'll do something more accessible next time.

[@michaelbauers8800]

I know this post is old, but don't feel too badly IMO. I have read a book on this, and studied a lot of math in college, and it's not simple to follow. I think I would have been equally lost had I not read a book on this, and remembered the equations. I was confused a few times by the book ( Derbyshire,) and this video is actually simpler, but it's dense. I would benefit from watching it again, I think.

[@twizzler2682]

@@singingbanana The Riemann hypothesis is a distraction The True lie on the Sum of all Natural Numbers The answer to this problem of -1/12 is that Jesus come back to say to everyone "i have 12 Apostles"

[@romanr9883]

fine ill do it, hold my beer.

[@aeriumsoft]

i thought you drank soda

[@abstractapproach634]

Done yet?

[@markkeilys]

yo, this beer is getting kinda heavy... or at least the glass is.

[@王甯-h2x]

30 years later... "Hey father, why are you always holding the beer?" "He's still solving it... Oh my dear"

[@genericteenager8341]

Surely OP will deliver

[@Jag0n03]

Picturing Riemann doing a mic drop and saying "Peace out, y'all" had me dying.

[@RSLT]

Great Video. Very well explained the R.H. principles. Fantastic Job!

[@arsenelupin123]

Thank for the crash course, James.

[@rangedfighter]

I've read cash course at first

[@eamonnsiocain6454]

You take those topics which were always presented to me in the driest possible ways while I was working on my Maths degree and make them fascinating.

[@ShonkyLegs]

I can't believe I just found this channel. I can't believe this is the channel name. I can't believe you have Little Professor as your banner. I'm very pleased.

[@alexanderjones1129]

By far the most understandable and interesting explanation of the Riemann Hypothesis.

[@hawk0485]

the person who proves it, if he/she has watched this video should go back and leave a comment like: "lol, proved it."

[@ZonkoKongo]

yea gonna do that, just give me some time

[@giuseppeforte8687]

Looks like someone did it

[@AliElamraniElhanchi]

You sir have a talent for teaching and for communicating information the best way possible. I thank you with all my heart for these explanations and these videos. Keep up the good work!

[@gingerfeest]

Don't tempt me to switch my major to mathematics.

[@singingbanana]

***** Perfect reply :)

[@nahidhkurdi6740]

I Wish I had the opportunity to do so when it was my time!

[@hillwin10]

This guy makes even the most daunting subjects seem approachable. It's so much easier to stay excited and learn like this. I wish all teacher were like this, maybe then more people would be interested in maths (perhaps then, people who are naturally drawn to maths and physics wouldn't feel so isolated *sighs*).

[@Ishuzu]

i have no idea what i just watched but i still enjoyed it.

[@SolPhoebusApollo]

I can definitely see why people ask you to explain that one. Sucks about no million for disproving the hypothesis. Great return to posting videos! Those formulas hurt my eyes and that's awesome.

[@LynneSkysong]

I really think it's pretty crappy that you don't get the prize for disproving it. Wouldn't it be funny if someone disproved it and kept it to themself since there wasn't an incentive to share? Of course, that's impossible because anyone that dedicated to mathematics wouldn't be able to keep it a secret.

[@zzasdfwas]

You'd still be famous.

[@BobbieTheFish]

Oh yeah, I forgot to tell everyone, I disproved this years ago. It was so disappointing that I burned down my office with all my research.

[@rangedfighter]

I'm not 100% sure if he just made this part up or not, or where I could search to get a reference to that fact.

[@leonardromano1491]

I think you would become the most loved and at the same time most hated person in maths.

[@mitesh8utube]

I guess he meant disapproving with a rigorous proof will get you price. Disputing with a counter example won't.

[@luismontesdeocafis]

Is a great explanation of a non trivial topic, a wide background is needed but is understood with your guide! Great work! Thank you

[@philyking]

When you say log(x) are you referring to log_e(x)? It seems no one wants to keep consistent notation with it. Also, I'm happy you finally did a more intense video, but I find it sort of funny how people are acting like it was a super difficult video when you glossed over all the actual difficult details. Even the residue calculations can get horrendous.

[@singingbanana]

I sympathise, even the statement is more advance than most people are familiar with. It is the natural log.

[@kevroy314]

If I came to the UK could I take you out to lunch or something? Through your fantastic presentation style (and I really mean you, not just numberphile) you've managed to get my mathematically agnostic SO presenting proofs to strangers at restaurants. Between this feat of magic and your continued ability to inspire my own insterest in maths beyond a lowly undergraduate minor, you've quickly become one of my favorite people on the Internet. If not lunch, please let me know some other way I might support you!

[@ThatSpazChick]

I do not have the education necessary to watch this.

[@gameragedad8953]

Sad thing is, I have the education necessary to watch this, but I don't have the patience to listen to him. I feel like I'm listening to a lecture from a professor asking myself the same question I did then "Why the hell do I even care about this?". No offense to the presenter, he is a great guy and math is his thing and I'm glad he can get excited about it. He's also made some other cool videos that have kept me entertained, but this one is for the egghead nerds for sure.

[@ThatSpazChick]

GameRage Dad I'm the opposite. I have no idea what he's talking about but I love listening to it nonetheless. Most of the reason may be his adorable, awesome accent.

[@ThatSpazChick]

khaled khunaifer You're hurting my brain.

[@mikecheng104mike]

khaled khunaifer yeah... you missed the complex analysis part, we all wish we can LOL

[@ThatSpazChick]

***** Seventeen with the math ability of an eight-year-old.

[@zimbabweian]

I am currently doing a doctoral degree in Physics where I use the Riemann zeta function all the time. I had no idea of its origin or how interesting it really was, just kinda used it as a tool up until now. Great video, really enhanced my interest on the subject!

[@singingbanana]

That's awesome - thanks!

[@PuglyWont]

Thanks for making this video. I had the Riemann Hypothesis explained by a professor once, (in a most excellent way too, outside with sidewalk chalk)... but I forgot much of the explanation. I'll have to watch this a few more times to really have it all sink in. I'd like to see more videos like this with the right level of detail without getting bogged down in the formulas too much. I especially like pointing out the important parts of involved formulas.

[@InvitingShores]

I cannot state having understood, but I'm greatly inspired to learn more to understand it finally. Thanks James and don't let the gap between consecutive videos be as big as those between big prime numbers! ;-)

[@sabassegovia3915]

I transferred from a community college and began my first quarter in an actual university in California (UC Davis). I transferred to study math but had no interest in it at all, it was just a way to move on. I wish I began watching your videos earlier, here and on numberphile. They've made some hard to grasp topics much more enjoyable and understandable, such as the video where you deal with the different types of infinity. I look forward to newer videos from you and everyone on numberphile.

[@martijnvanweele6204]

Why am I even watching this? I understand about as much about math as a banana! ... *continues watching* ....

[@trejkaz]

When I saw this was about the Riemann Hypothesis, I wondered if the 1+2+3+4+5+6+... = -1/12 thing would find its way in here as well, and was not disappointed.

[@TheSpinTensor]

I have discovered a truly remarkable proof of this hypothesis which this KZbin comment is too small to contain.

[@retepaskab]

I have discovered a counterexample but it was marked as spam.

[@darwinbodero7872]

I think the best part of this video is he explicitly defined the Riemann zeta function across the entire domain. Most authors just give the infinite series definition and say “by analytic continuation” everywhere else. Which is totally useless

[@friedrichhayek3683]

They paying one million dollar for this proof is like me paying 0,15$ for Lobster/Champagne dinner.

[@ML-uu5ik]

You did an awesome job explaining this. I have been reading/watching videos on this for the last couple days trying to find a sufficient explanation of what in the world the connection is between the zeta function and prime numbers, and you explained it well enough that I am sufficiently satisfied. Thank you!

[@harryc2549]

I love this guy. Always very clear. Great video.

[@jeffreyluciana8711]

The 5 travels down the grouping of 6 from the 5th position to the first position to the 25 and cancels out the right prime to 24. The 7 travels to the right through the first position back to the first position of 48 and cancels out 49. The squares of primes cancel out other primes. That is why the number of prime numbers less than a certain number follows the inverse of the log

[@connorgibes709]

Every time I watch this, I understand it a little bit more.

[@Boomshicleafaunda]

I'm really happy to see a new video on your channel. Numberphile doesn't always go into the same depth as you do on this channel.

[@CompuBOOT]

Are you aware that there is a direct correlation between your enthusiasm and emotions attending this explanation and the actual rigor used in the ramping up of your description? It's almost melodious. What if numbers and math have human emotive and fantastical elements to them? What if math is an endless song or a dance that we can't sing or sway to because we lack the dimensional articulation? Thus it behooves us to merely express things mathematically using one-dimensional verbal or written symbolic gesturing. This idea is only partially reflected in the quiet passion of too few mathematicians or scientists. John Nash understood it.

[@singingbanana]

***** Sounds good to me.

[@doceigen]

+Peter McMillan Agreed. Especially where he spoke about proving that the zeta function has no zeros on the line of the real part of S = 1. Hurrah. Likewise from the WIKI, "In a lecture on prime numbers for a general audience, Fields medalist Terence Tao described one approach to proving the prime number theorem in poetic terms: listening to the "music" of the primes. We start with a "sound wave" that is "noisy" at the prime numbers and silent at other numbers; this is the von Mangoldt function. Then we analyze its notes or frequencies by subjecting it to a process akin to Fourier transform; this is the Mellin transform. The next and most difficult step is to prove that certain "notes" cannot occur in this music. This exclusion of certain notes leads to the statement of the prime number theorem. According to Tao, this proof yields much deeper insights into the distribution of the primes than the "elementary" proofs." Maths are the tools, but music is the spirt.

[@donutazarausg1623]

+doceigen chaos theory proves the relation between you and me, music and me, mathematics and me, using mathematics.

[@sradtke314159]

Excellent lecture - it brings light into a dark place. Quite enjoyable!

[@Solitaan]

Even though I have almost no idea what he was talking about, I still feel a little bit smarter just watching it xD

[@YiannisANO1911]

the fact that i dont understand what you are saying makes my depression come back. I genuinely just want to know what mathematicians are talking about but i think as soon as i graduated high school i lost that skill

[@TomFoster1996]

Could you do a video on each of the clay millennium problems?

[@cosumel]

This is by far the easiest of the six to understand. The rest of them, particularly P vs NP, are so abstract, just the formulae used to write them require a PhD in migraine medication.

[@rosskrt]

@@cosumel i know i'm late as you can possibly be, but anyways. P vs NP is by far the easiest to explain. You can even explain it to a child. Now try that with the RH. It gets abstract and complicated when you start working on it, basically like all the other Millennium Problems.

[@KannanNambiar]

strikingly beautiful, amazing clarity, please do more

[@trevormugalu3797]

10 years later, I'm still waiting for the proof that cat equals dog and dog equals cat

[@evalsoftserver]

A Solution for the RIEMANN ZETA FUNCTION is extremely valuable because It also point to Solutions for enhancing the HAMILTON GEOMETRZATION Poincare conjecture, Hodge Invariance conjecture as it relates to PRIME NUMBERS, TAYLOR INFINITE SERIES ,MACULIN SERIES and Doing Arithmetic past ZERO or Singularity as it is called in Analytic Geometry , and Algebraic Geometry, and it Directly points to the Prime factorization Algorithm , the Division algorithm, and the QUADRIATIC FORMULA This Solves many DIMENSIONS and RANK IN THE COMPLEX FUNCTION PLANE for MANIFOLD like The Kahler MANIFOLD ,CALIBU YAU MANIFOLD simeoustanesly and Points to Soulutions to the entire Millennium Prize Problems proposed by The Early 20th Century Philospher and Mathematician David HILBERT , Including the YANG-MILL Mass GAP , and the NP COMPUTATION time space COMPLEXITY problem also know as the Traveling Salesman problem

[@raydredX]

19:17 That's... Lame, I mean I get why, you want to pay the guy for showing up, shake some hands and say some words and being a symbol for the problem. But still that's not how math works, solving the problem means either proving it, disproving it or proving it's "improvability".

[@aleksapetrovic7088]

If you disprove it they'll be bummed out

[@chalams]

Slowly but surely my love towards mathematics is increasing

[@hirayahana]

What if...the answer to Riemann Hypothesis is the friendship we found along the way?

[@321joeyboy]

Thank you for putting so much effort and enthusiasme into your videos!!! It's because of you and numberfile that I love math's!! (Sorry for my bad English)

[@singingbanana]

Thank you!

[@rangedfighter]

great to see you back with a video :D

[@carlosarturomunozcastro3180]

CARITO BENAVIDES MONTILLA MiUltimaHistoria Pensaba yo en estos tiempos difíciles Llenos de incompresiones y desencantos en tantas buenas razones Para soñar Y sin quejas, sin desfallecer, si… con todo El agrado y los buenos sentimientos… pensaba con nostalgia De la inocencia de aquellos años De esos primeros amores Con yannette, teressitta, floralba… Si… florssitta amore mio, Que al recordarlas, vuelven a nacer Y recuerdo en mi memoria Aquellos tiempos de … de Carito CaritoBenavidesMontilla diMugnoz Mi bello, nuevo y gran amor…. Ella era una miss de Boston Ocasellb: OcassoDiBellSetBuck Que daba clase en la escuela di Cullinnarii et pannes también… Le gustaba el español Y aunque lo hablaba poquito Tenía esos ojos bonitos Que hablaban muy bien por ella Carito me habla en inglés. Aveces… Que bonito se veía sola o en compañía De unos que admiraban como io Lo que jamas seria per me, perque Io ya era cassado: con Florsitta, Con DianaCarolinna, y por supuesto, conLaFuncion Zetta di Riemann Carito me habla en inglés et también en Italiano, germanny, francais, portuggisse, Mandarin pictórico y por su puesto, En un quichua, básico para viajar por ecuador, peru, Bolivia, chile, y volver al final de tanto andar, de tanto amar, de tanto padecer su belleza, Que me dice: yo no se Carlitos don´t be like that Now listen to me You will pay attention I need you to write in english Muy perfecto parragraph And tell me where did you learn Donde tu aprender to be tan coqueto Remember nada de futbol Until you finish the work you have Y me daba una sonrisa Y yo me quedaba loquito Y despues en el examen Lo ponía todo al reves Carito se fue del valle Yo la recuerdo cantando Porque me dejo muy triste cuando Para su tierra se fue Carlito dime que si, me eneñaras todo Para no quierer morir per te……. Carito don´t tell me no Que me muero por tu amor Que importa la raza Tampoco el idioma Si al fin lo que cuenta Es lo buena persona Si es del altiplano O de tierra caliente Si al fin lo que vale Es que sea buena gente Que importa su credo Si es hombre de influyente Si al fin lo que cuenta Es la gente decente No importa si es blanco Si es pobre o famoso Si al fin lo que vale Es que cante sabroso Pudiera escribir un millón de tequieros Y algunos teamosrepletos de sinceridad… Pero esta vez, ire lo mas lento posible… Paso a paso, dia a dia, verso a verso, Para que ni tu ni yo se pierdan En tanta vanalidad en que habre envuelto Mi extensa vida que alguien resumirá:

[@aleggs6019]

in tenth grade atm, almost got the jist of it, hoping I'll be able to understand better as I learn.

[@MadaxeMunkeee]

Wow, this was very easy to follow. Granted, I just got my maths degree and I'm running through a book on the Prime Number Theorem now, but still I think you did a great job. You also gave me more motivation to keep ploughing through all these proofs lol. Thanks!

[@singingbanana]

Thanks. This one does have a higher threshold, but you were the ideal viewer!

[@IoEstasCedonta]

9:20 - This isn't strictly true, since he didn't explain the restriction that the function must be analytic.

[@jupytr1]

Oh, sorry:( I hastily hit a thumbs down on you're comment w/o thinking. You are of course completely right.

[@tkk3852]

Good job my brother. If you are still there,thank you. I never understood riemann until today. You made it simple

[@kot_robot8205]

there's a very interesting book "Prime Obsession" by John Derbyshire, it is all about primes, zeta function, the riemann hypothesis, and Riemann himself :D

[@lPlanetarizado]

yeah very interesting book, it also talks about the connection between HR and physics

[@anonymous1361015]

Thanks for the video, I like the way you explain things with so much enthusiasm

[@RokeyGames]

I'm a physics student, I have a lot of math as well and I really like math, but I didn't get any of this :P I still really liked the video. James can really make such a thing really enjoyable!

[@livinlicious]

I NOW understood why 1+2+3...= -1/12. When I saw the numberphiles episode it wasnt quite clear, but how you explained it, now its totally clear.

[@tabularasa0606]

Sadly been too long since I did maths like this. I'll leave the proof to you :)

[@SiMyt848]

Thank you! I spend a lot of time speaking with my classmates (we are studing maths) about the series 1+2+3+... after the numberphile's video. I refuse their 2 "proof" (because I lerned in analysis 1 that 1-1+1-1+... doesn't converge, so it isn't equals to 1/2 and in the second video they set -1 in a formula (coming from a geometric series) where |x|

[@autodidactusplaysjrpgs7614]

That x = 0.5 line is called in some circles 'the dirty crease.' Modern maths seeks to know how dirty the crease really is. Get at it.

[@jainaadi]

Brilliant video!! Thank you so much !! I have been trying to understand this for months!

[@oskarp1862]

Is it possible that it is true but there is no way of proving it? Or if it is true can we the be sure that it is also possible to prove it?

[@0730Ender]

This is certainly the most insightful video I've found on the properties of the Riemann Zeta function. I'd just wished you could go more slowly over some of the steps, but they can be filled in with some effort. Great job!

[@freedomwarrior7734]

I've found an amazing proof of Riemanns hypothesis. But I'm too lazy to write it down.

[@littleflower787]

AnonymousIntellectual Isn't that what Fermat said when he supposedly proved his theorem. Please, tell us. Don't make mathematicians wait for hundreds of years for your wisdom. :)

[@ulmovalar3076]

AnonymousIntellectual u little fermat

[@michaelrobertson9870]

AnonymousIntellectual Best KZbin comment yet.

[@AkshayAradhya]

AnonymousIntellectual I have almost solved it but I have to go feed my cat.

[@theadammz4475]

AnonymousIntellectual You sure, Fermat? You don't want that million dollar?

[@Swetlana0]

I've always wanted to know what the Riemann Hypothesis was about. Thanks for making it a bit more accessible because wikipedia sure isn't helpful!

[@singingbanana]

Thanks. I think the choice is a hand-waving explanation or a difficult explanation.

[@anteaters-R-us]

he's so adorable

[@seanoneill2098]

Thank you, been wondering how complex numbers were needed to do PNT proof, am hoping to learn more about this material

[@louischo2701]

Yay youre making videos again.

[@kanabalize]

20 minutes talking about a subject... That is why he is a PHD holder... Salute!!!

[@ashley2khoo510]

Fermat be like: i know the proof. But this margin is too small to write it down

[@evalsoftserver]

A Solution for the RIEMANN ZETA FUNCTION is extremely valuable because It also point to Solutions for enhancing the HAMILTON GEOMETRZATION Poincare conjecture, Hodge Invariance conjecture as it relates to PRIME NUMBERS, TAYLOR INFINITE SERIES ,MACULIN SERIES and Doing Arithmetic past ZERO or Singularity as it is called in Analytic Geometry , and Algebraic Geometry, and it Directly points to the Prime factorization Algorithm , the Division algorithm, and the QUADRIATIC FORMULA This Solves many DIMENSIONS and RANK IN THE COMPLEX FUNCTION PLANE for MANIFOLD like The Kahler MANIFOLD ,CALIBU YAU MANIFOLD simeoustanesly and Points to Soulutions to the entire Millennium Prize Problems proposed by The Early 20th Century Philospher and Mathematician David HILBERT , Including the YANG-MILL Mass GAP , and the NP COMPUTATION time space COMPLEXITY problem also know as the Traveling Salesman problem

[@javsmo]

This video summarizes in 20 minutes all odd-numbered chapters of "Prime Obsession". I liked!

[@PrimusProductions]

Define it for quarternions

[@nahidhkurdi6740]

I had that idea for a while, but it seems that mathematicians proved a Riemann hypothesis for other number systems rather than the quaternions. They had more than a century to think about the idea of extension to quaternions had it been that fruitful. You should know, however, that even the very concept of an analytic function will not emerge unscathed when you extend your definitions to quaternions.

[@philipmylan654]

Even though I didn't understand this enough to understand the Riemann Hypothesis, I still learned a lot from it. More of this so-called 'maths' stuff, please! :)

[@lolzomgz1337]

11:23 -1/12?! NOT AGAIN!!!!!

[@IlBoiaChannelGamer]

lolzomgz1337 the curse of numberphile

[@Nai61a]

This is the first of your vids I have seen. I'm a new subscriber; you're obviously barking mad; I don't understand a word. I LOVE it!

[@singingbanana]

They're really not all like this. There was that one where I made a straw kazoo.

[@EpicUnderscoreJdog]

Is it a british-ism that you call 1/3 "a cubed" instead of a "a third"? The other ones seem the same as North American usage. He does this twice around 5.40.

[@rezwhap]

I'm British and it's not something I recognise. I'd even say he misspoke, but it could be a regional thing.

[@unvergebeneid]

I think more plots of the various functions would have helped this video to be even more approachable. Also, more repetitions, relating where we are at a given moment to where we started out and where we're going.

[@JamesSpeiser]

Looking at graphs of Riemann Zeta, would it be wrong to infer there are some fractal properties of primes?

[@amirabudubai2279]

Probably, but you should rephrase that to prime properties of fractals. Primes show up in almost every aspect of math; at this point it would be more impressive to prove something is not related to the primes.

[@mineland8220]

"What world would be there if you have no idea how to prove or disprove the Riemann Hypothesis?!?!" -A concerned mother

[@ragnkja]

The harmonic series sounds nice, at least the first few terms. The seventh is a bit flat, though.

[@sphakamisozondi]

Dr James, I think I got a better chance winning the lotto than to win the mathematics millennium prize. I thought I had a shot in solving this hypothesis.

[@peterbarber716]

2:14"…prove that black equals white…" And get run over on the next zebra crossing? NOOOOOO!!!

[@bur2000]

If someone still reads this: it is often said, if we could prove the Rieman Hypothesis, it would give great insight into the nature of primes. Is that the case though? We already have that insight, we just can't prove it's the correct insight. Proving it just means: "yes, what you now only assume is true about the nature of primes, definitely is true". In a way that's how every other science than math operates all the time. Just assuming.

[@kansuerdem2799]

I finally have the proof. Only this textbox is too narrow to contain...!!!

[@JannikPitt]

+Kansu Erdem haha :D

[@Czeckie]

+Kansu Erdem publish it then

[@TheSnump3r]

+gravity0529 it's a reference to fermats last theorem...

[@JannikPitt]

***** Dude that was a joke, he didn't mean it like that - look up "Fermats Last Theorem"

[@Czeckie]

JANNIK | The world through my camera thank you for the explanation, I haven't known that. Now I see the foolishness of my response, which was ignorant and unfunny. Thank you for showing me the light. This very moment will guide me for the rest of my life; I will remember you, kind stranger, everytime I face hardship. You've done much more than merely pointing out a single fact; now I finally can see what kind of person I want to become and grow.