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

@ItachiUchiha-ns1il

5 жыл бұрын

andersjaevel damn that’s good one lmao

@69erthx1138

5 жыл бұрын

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

@user-xh9pu2wj6b

5 жыл бұрын

Some good Landau right there.

@yashhkotecha2647

5 жыл бұрын

Trivial*

@RodelIturalde

4 жыл бұрын

@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.

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 KZread posts and your appearances on Brady's videos. Keep up the great work.

@singingbanana

8 жыл бұрын

+72ackerman Thank you very much!

@72ackerman

8 жыл бұрын

+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

8 жыл бұрын

+72ackerman Ha, I'm glad.

@christosvoskresye

8 жыл бұрын

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

@christosvoskresye

8 жыл бұрын

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

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

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

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

8 жыл бұрын

I am looking forward to understanding this:)

@pakan357

8 жыл бұрын

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

@tggt00

8 жыл бұрын

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

@darmodak1773

8 жыл бұрын

+tggt00 bahahahahahah

@tggt00

8 жыл бұрын

What's so funny?

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

10 жыл бұрын

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

@CafeAlpha

10 жыл бұрын

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

9 жыл бұрын

Popexssj same here bro. :)

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

@SD-de4do

7 жыл бұрын

it all depends on how you go about it ;)

@deeptochatterjee532

7 жыл бұрын

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

@cameronspalding9792

5 жыл бұрын

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

@j.vonhogen9650

3 жыл бұрын

Just rob a bank, or build one!

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

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

@singingbanana

10 жыл бұрын

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

10 жыл бұрын

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

@ClayCompton

10 жыл бұрын

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

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

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

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 :)

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

10 жыл бұрын

same feeling XD

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

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

10 жыл бұрын

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

@michaelbauers8800

6 жыл бұрын

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

Жыл бұрын

@@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"

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

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

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!

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!

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.

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

10 жыл бұрын

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

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.

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*).

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!

fine ill do it, hold my beer.

@aeriumsoft

8 жыл бұрын

i thought you drank soda

@abstractapproach634

6 жыл бұрын

Done yet?

@markkeilys

6 жыл бұрын

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

@user-mv4oh8yp1y

6 жыл бұрын

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

@genericteenager8341

5 жыл бұрын

Surely OP will deliver

Thank for the crash course, James.

@rangedfighter

10 жыл бұрын

I've read cash course at first

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!

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.

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

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

9 жыл бұрын

***** Sounds good to me.

@doceigen

8 жыл бұрын

+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

8 жыл бұрын

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

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

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

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

@liamcarman6256

9 жыл бұрын

Link or it didn't happen

@mikhailmikhailov8781

9 жыл бұрын

Ferma, pls, no more jokes

@MrMlindsay

9 жыл бұрын

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

@hemuln

9 жыл бұрын

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

9 жыл бұрын

beary the bear LOL

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

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

strikingly beautiful, amazing clarity, please do more

great to see you back with a video :D

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

@cosumel

4 жыл бұрын

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

Жыл бұрын

@@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.

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

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.

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! ;-)

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

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

10 жыл бұрын

That's awesome - thanks!

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

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

@ZonkoKongo

6 жыл бұрын

yea gonna do that, just give me some time

@giuseppeforte8687

5 жыл бұрын

Looks like someone did it

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

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.

Beautiful complete explanation. The visuals are very well timed and helpful. Thank you.

This has been solved by a Professor in India recently.

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.

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

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

5 жыл бұрын

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

I do not have the education necessary to watch this.

@gameragedad8953

10 жыл бұрын

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

10 жыл бұрын

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

10 жыл бұрын

khaled khunaifer You're hurting my brain.

@mikecheng104mike

10 жыл бұрын

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

@ThatSpazChick

10 жыл бұрын

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

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.

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

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

@amirabudubai2279

7 жыл бұрын

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.

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

This may have just saved my IB HL Mathematics IA! I am so glad I found this amazing video.

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!

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!

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

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! :)

Thank you for this video, I really enjoyed it. Hopefully you'll do more videos like this on interesting problems.

Yay youre making videos again.

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

I love maths, and Dr james! you made me love maths even more. With love from egypt

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

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

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

@retepaskab

10 жыл бұрын

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

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

10 жыл бұрын

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

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|

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

@singingbanana

10 жыл бұрын

***** Perfect reply :)

@nahidhkurdi6740

5 жыл бұрын

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

Am I correct to assume that those symmetrical non-trivial zeros that you plotted do not in fact correspond to any actually known zeros because otherwise the whole Riemann hypothesis would have been disproven already? Isn't it a bit confusing then to just put them there?

@matthewcooke4011

10 жыл бұрын

Yes, you are correct. I guess he was just illustrating the fact that IF they were to exist as shown, they would have to be symmetrical about the ½ line. I agree that it may have been a little confusing to some people and he could have made it clear that he was showing hypothetical zeros. But a good video generally.

@TheWeco

10 жыл бұрын

At that point in the story, we had only achieved that information. It was only later with the Zeta function that we got the idea of them beeing on a single line. Furthermore, that proves a point. Never trust a mathematician, and never ever trust a picture! :)

He's BACK!!!!! We missed you James :)

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.

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

@jupytr1

10 жыл бұрын

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

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

8 жыл бұрын

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

Wow thank you for taking the time to make this!! Finally I know what it's all about. :)

I wonder whether you can do a series on "The Congruent Number Problem" and some Algebraic Geometry. I have learned quiet a lot from this.

he's so adorable

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

Ok, it took me a few minutes of goggling to realize you're not "Numberphile", just a part of it! But let me tell you, you MAKE Numberphile what it is! Love your enthusiasm and videos!

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

10 жыл бұрын

Thank you!

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

10 жыл бұрын

You'd still be famous.

@BobbieTheFish

10 жыл бұрын

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

10 жыл бұрын

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.

@BiophysicalChemist

10 жыл бұрын

What? That's incorrect. A proof OR disproof of the Riemann Hypothesis is a solution to the problem. The Millenium prize awards 1 million dollars to anyone who provides a solution to the Riemann Hypothesis, not just an affirmative proof.

@leonardromano1491

6 жыл бұрын

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

Do the Hodge Conjecture next! :)

I'm learning about infinite sums at university nowadays im learning chemical engeneering at Budapest. But i just got in love with this kind of maths and i was amazed by riemanns state about the Conditionally convergent sums ! i wish i could count better with complex numbers to do tricks like he did with the dzeta function :D i mean thats amazing that you can get the sums of divergent series i mean if the dzeta function is extended by this way and it has such a huge impact on the real numberline and the prime numbers then i'd say that the sums that can be got out of divergent series can be really useful in other sciences :D!

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

10 жыл бұрын

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

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

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

5 жыл бұрын

If you disprove it they'll be bummed out

Awesome video. I haven't seen you deal with PDE's much, but I would love you to do a Navier-Stokes video like this one, thanks.

How did I miss you channel before? I really like seeing you on Numberphile. Subscribed.

@singingbanana

10 жыл бұрын

Hello!

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

Why is the English notation off the natural log just 'log'? Where I live, 'log' means log base 10 while 'ln' is used for the natural log.

@lamudri

10 жыл бұрын

I usually see “ln” in English, but I guess “log” just looks nicer and it's fairly obvious that we're not dealing with base ten logs.

@MultiplyByZ3r0

10 жыл бұрын

It depends on whether you're an engineer or a mathematician, the former uses ln for natural log, the latter, log and they say log 10 when they mean log 10.

@deskgo

10 жыл бұрын

Because the natural log is more important in maths and log10 is better for applications. You are right that log should mean log 10 but log 10 is not very useful in math theory so log tends to mean natural log which is much more useful.

@singingbanana

10 жыл бұрын

Exactly what Ryan said. Mathematicians always mean the natural log.

@joffysloffy

10 жыл бұрын

singingbanana Jeroen J Exactly. And Jeroen, presuming you're from the Netherlands as well; I study mathematics at the Utrecht University and we use log as in base e, but in high school I was taught log was base 10 and ln was base e.

I love your videos. Especially the numerphile ones. You should make one video for the 8 problems of the Clay Institute (and if you have time, about 23 Hilbert's Problems). This comment is from Argentina!

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

Define it for quarternions

@nahidhkurdi6740

5 жыл бұрын

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.

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

@IlBoiaChannelGamer

6 жыл бұрын

lolzomgz1337 the curse of numberphile

This is really an excellent video. Many KZreadrs try to sacrifice facts and reality to make content more presentable/watchable. You didn't and that's why this video is a fest for me😂. Please make more videos like this!! Live long and prosper 🖖

Slowly but surely my love towards mathematics is increasing

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