The Riemann Hypothesis, Explained

Quanta Magazine
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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.

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Ciência e tecnologia

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3 Jan 2021



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Comentários 5 854
zhongning chen
zhongning chen Anos atrás
My math professor once said, “I’ve know the existence of these math problems for many years. And I assure you, there are a lot easier ways to make a million dollars”
Smeagol Karamazov
grigori perelman doesn't agree.
Ensieh Safary
Ensieh Safary 4 dias atrás
Even if the prize was a billion dollars, no one could solve it
Bailey Harrison
Bailey Harrison Mês atrás
@kruth 666 If you were smart (which you would be) and capitalised on it, you could make a hell of a lot more than a million dollars.
Shart Mês atrás
@kruth 666 "have you saved the entirety of mankind recently, including the possible future universe? if so, click here for your chance to win a new Kia."
Orphan Of Orbit
Orphan Of Orbit Mês atrás
So he was a millionaire then?
jose rojas
jose rojas 4 meses atrás
Thank you, Quanta Magazine. My understanding of the Riemann Hypothesis went from 0% to 15%. Great job (I mean it).
entity zero
entity zero 24 dias atrás
15%? sheesh, i guess ur a bit off by about +14.999997%
Evelyn Tromp
Evelyn Tromp Mês atrás
I really appreciate that you explain the more “basic” things (e.g. what a log function is). It makes the video feel welcoming to people who aren’t necessary very good at math (like me, lol)
EK 18 dias atrás
yeah but then other parts of it they just brush over like it's nothing
Faiq khan
Faiq khan 22 dias atrás
Log function is just a reverse function of exponential function.
theFishReloaded 24 dias atrás
@emigoldber i dont even think it was intended but it is pretty good
emigoldber Mês atrás
nice pun
Nath Thydanita
Nath Thydanita 11 meses atrás
Can I just appreciate how well the animation is? Literally, WOW.
Evan Patterson
Evan Patterson 19 dias atrás
Do you know where california is?
Houssam Alucad
Houssam Alucad Mês atrás
Ikr, as a motion artist myself my jaw was dropped throughout the video
FunkyyyT0wn _
FunkyyyT0wn _ 2 meses atrás
No, you cant
Kanglar 6 meses atrás
Figuratively, WOW.
Magic Carp
Magic Carp 6 meses atrás
Great production
Gerardo Piedras
Gerardo Piedras 2 meses atrás
"The proof of the Riemann hypothesis is trivial and left to the reader as an exercise" - Bernhard Riemann
GBSpiral 13 dias atrás
@Nen Master5 whats the epic sci-channel?
Deldarel 14 dias atrás
@Nen Master5 Owen is great, but please don't go advertise unrelated creators in the comments. it's considered spam.
Giggabiite 18 dias atrás
and he died before he could write it down... so sad, so sad
godsexdevil666 22 dias atrás
@Nen Master5 can we just have the epic sci channel instead?
A Giri
A Giri 27 dias atrás
@Emilio Prato its a satirical parody
Chase Denecke
Chase Denecke Anos atrás
Whoever does these animations, massive props to you. These are literally the best math illustrations I've ever seen.
ShadowNinja22 26 dias atrás
I@Hans Meiser y
ShadowNinja22 26 dias atrás
@John from tennessee i
Connie Pressley
Connie Pressley 28 dias atrás
@Hans Meiser 3Green1Red
J Trindle
J Trindle Mês atrás
Agreed - I'm an uneducated outsider - but my daughter loves math , even though she failed classes in high school because her strong synesthesia caused her to fail classes in high school because she's make arithmetic mistakes and couldn't finish the answers on time. She's always looking for ways to show me why she finds these ideas so "lyrical and lovely" ( her phrase") and this gives me some idea of what she enjoys
Mun Hwan Cho
Mun Hwan Cho Mês atrás
It says at the end Guan-Huei Wu Clay Shonkwiler
matthew Blanchard
matthew Blanchard Mês atrás
This is like becoming an astronaut, discovering a previously unknown planet, finding a river on that planet, and at the bottom of the river is the perfectly fitting other half to a broken rock you found in a river on Earth as a kid. The Universe sees the look on your face and laughs silently.
Wront Halen
Wront Halen Mês atrás
@Sasha Botalova LMAO
V Mês atrás
garbage analogy and nonsensical as well :)
Pissoff Puss
Pissoff Puss Mês atrás
@Ramaraksha He never mentioned a magic man.
Sumit Dutta Gupta
Sumit Dutta Gupta Mês atrás
When pure mathematics comes with lucid explanations, and the two are complemented by a perfect vanilla icing of aesthetic graphics. A million thanks for this amazing presentation.
Erald .C
Erald .C 3 meses atrás
Brilliant explanation. This makes me love math even more. There is so much beauty and mystery in mathematical patterns.
Mark Armstrong
Mark Armstrong Mês atrás
Really well done!! I am not a mathematician but it feels my brain was struck by lightning. Great feeling.
Artisorak Anos atrás
Proving the Riemann Hypothesis is probably one of the hardest ways to make a million dollars.
Luiz Esmiralha
Luiz Esmiralha 27 dias atrás
it's easier to open a casino in the North Pole.
NeilDieQualle 2 meses atrás
Nevermind! It´s fun!
John St Fleur
John St Fleur 5 meses atrás
Zamo Mthethwa
Zamo Mthethwa 6 meses atrás
If not the hardest…
Funny fails
Funny fails 6 meses atrás
Yet know it's been proved it's wrong
Mike Rawaan
Mike Rawaan 10 dias atrás
For the first time in my 46 years, I have truly understood what the Riemann Hypothesis actually is. Thank you!
Scott Carey
Scott Carey 17 dias atrás
Thanks for making someone who'd thought since 6th grade that he could live without learning more Maths that it can still be learned and had fun with whilst in the learning process.
Frank McCann
Frank McCann 3 meses atrás
Thanks. Wonderful ☺️. When you're working with waves and need figures as we require, a reduction of complexity makes subjects understandable as you've so aptly done.
Nikhil Desai
Nikhil Desai 8 meses atrás
Thanks for making this video, even though its only touching the surface it was really informative and easy to understand this problem and even harder to solve.
ClemensAlive Anos atrás
WHO WANTS TO BE A MILLIONAIRE?! Mathematicians: "No thanks..."
Maciej Kulczycki
Maciej Kulczycki 28 dias atrás
They do not use proper tools to solve the problem.
EconAtheist Mês atrás
@Jack Schwartz the issue is convergence-divergence -- infinitely many 'infinite equations' can be solved.
EconAtheist Mês atrás
@ONXsDITTU WAT no. still an outstanding problem. cripes.
Jack Schwartz
Jack Schwartz Mês atrás
Lets see if I get deleted again
Jack Schwartz
Jack Schwartz Mês atrás
@H B I pointed out that it's unsolvable due to the fact that the answer is an infinite equation thus unsolvable, and they deleted it. SMH Take Care All
Neuro Fiber
Neuro Fiber 22 dias atrás
I can't believe I understood this. I've heard about this for years, but this is the first explanation I've seen that makes sense. Great video.
Jason Lee KY
Jason Lee KY 7 meses atrás
Im so glad I found this video when it was released. Rewatching this now made me appreciate the language of math so much more now that I'm taking a math degree.
tartarus216 4 meses atrás
Brilliant explanation. This video will help add many different layman’s perspectives on this problem, if only for a few moments, and hopefully help crack it.
Fernando Rocha
Fernando Rocha 17 dias atrás
I loved this video and the math explanations. I could like it 10 times if possible. Great explanation. That is an example of how math should be taught. I am an engineer and at university I had a few good professors, but no professor was as good as this video.
Miguel Eduardo Sánchez
I have watched countless videos about the Riemann Hypothesis, the Riemann's Zeta function, etc. And this is only one that actually explains the connecction between this function and the distribution of prime numbers. The harmonics part has never been explained to me before. Well done, now I can finally truly understand why this is such a big deal for mathematicians. Well done!
Louis-Philippe Chiasson
I was going to say the same!
The Kaveman
The Kaveman Mês atrás
You are on the right track ..
Sir Pumpington Of Dumpenshire
Odd harmonics create square waves, I learned this in audio engineering. So cool to know the mathematical basis for music.
HelixCarinae 2 meses atrás
@dodo meme you're going to have a FIELD day when you find out about quantum mechanics
CosmosNut Mês atrás
Well done! Great animations go a very long way to illuminating the discussion which is as relatively simple and clear as possible. Thank you.
Paul Pedersen
Paul Pedersen 4 meses atrás
Look at 13:21. At each prime p, the value of the function does not increase by log(p), as stated in the video. If that were the case, each step would be larger than the one before. Instead, the steps increase sometimes by large amounts, sometimes by small ones. For example, the step labeled "log(p)" at 13:21 is at the prime 13, i.e., the size of the step is log(13), but the step at 17, which should be log(17), is smaller. It should be bigger. What am I missing?
John Richardson
John Richardson 22 dias atrás
I feel the puzzle has more to do with frequency like that of synthesis in musical synthesizers utilizing different filters(analog) or digital(no filter) and how noise can be represented A pulsar can even be represented as a pulse(control voltage) Fast Radio Bursts hold priority in the realm of spirits… And Really the secret answer is: Oscilloscope
John Richardson
John Richardson 23 dias atrás
Function Hypothesis: Twos Thirds (inverted Fourths), fifths, half an octave (6), 7 the magic number… 11 the interloper… Sexagesimal and roots or functions using pi … etc… Wolf Rayet Star Longevity of a White dwarf/ Magnetar/ Pulsar/Neutron Star Erratic Red Dwarf star Highly Metallic Star (remnants of large rich 2nd/3rd generation stars) Quark Star Boson Star (Dark Matter star) (Stars surrounded by a Hydrogen and Helium bubble (early universe) Primordial Black Hole Interlocked Universe Ringularity vs. gyroscope
Paul Pedersen
Paul Pedersen Mês atrás
@Kappa Lock Ah. That makes sense. Thanks. I'm going to have to re-watch the whole video now, because it seems like I missed something important.
Kappa Lock
Kappa Lock Mês atrás
In the video he said that we also gonna jump by logp when we encounter p squared, p^3, p^4, etc... So the small jump you talked about was at 16 which is 2^4, so that is log2, and that's why it's smaller
Adrien Sawyer
Adrien Sawyer 3 meses atrás
I hope they answer, I’m gonna comment to attract attention ⚠️
This is the best video explanation of the Riemann Hypothesis. Thank you for taking the time and effort to produce it.
Nic Flatterie
Nic Flatterie 11 meses atrás
These videos are so well done and are so much better then the way I had to learn some of these concepts. It used to be just a mess of fuzzy equations without context or explaining. I guess I was stuck with poor teachers...
SouthBayJay Anos atrás
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
nicomopo Mês atrás
​@InfluxDecline It depends on the underlying function, i.e. if 2^3=8 is the application of the function f(x)=x^3 to the argument x=2 then its inverse function (in the R domain) is g(x)=cbrt(x). If it is the application of the function f(x)=2^x to the argument x=3 then its inverse function (in the R+ domain) is g(x)=log2t(x).
scathiebaby Mês atrás
@InfluxDecline In Multiplication you have a * b = b * a so there is only one inverse operation. In exponentiation, a ^ b is not equal to b ^ a - we need two inverse operations which are roots and logarithms.
S Darby
S Darby Mês atrás
@refresh I suggest you never read Ayn Rand, or read her and then read Kierkegaard or Descartes, or Plato...any philosopher who will rinse the nasty idiocy of Rand from your mind forever.
Grant Hurlburt
Grant Hurlburt Mês atrás
Personally I dont understand that description at all. I have used logs a lot in my research. I found that just using them, and seeing how they straighten out a regression line was enough. Also, they're useful for the normal distribution, because no matter how far you go in terms of Standard deviations below the mean a negative log (e.g. log -1) is always a positive number, whereas with "raw" numbers, you rapidly get into negative numbers. We can be said to live in a logarthmic universe.
Zack S Mitchell
Zack S Mitchell Mês atrás
@rhombicuboctahedron You could say “What is the log to the base n of sqrt(n),” and the answer would be 1/2. The log here is the power 1/2.
Christian Pauchet
Christian Pauchet 3 meses atrás
Brilliant video, thank you so much for sharing. Maybe the person or machine that manages to solve this problem might have to think in a superior or different dimension.
Carsten Spräner
Carsten Spräner Mês atrás
Thank you so much! If I had these videos during my mathematics studies it would really be more fun. And surely result in more passion.
Hans Nelsen
Hans Nelsen Mês atrás
I love the way he says he'll guide you through this in plain language. Incomprehensible to me non math person.
Michael Koch
Michael Koch Mês atrás
I remember reading the first few pages of Prof. Dr. Kumar Eswaran almost a year ago and can still remember his shot being tremendously clear. I still hope he didnt provide the proof, but it seems it was genius.
Harshad Salunke
Harshad Salunke Anos atrás
Reimann, gauss, euler and all other guys did all this stuff without matplotlib😳 I can't even imagine the extent of their hardwork and dedication
Technolus Mês atrás
@imCurveee that's a myth, computers aren't making people dumb, it's just the generalized access to internet that simply brought a lot of dumb people into public forums.
tennisace Mês atrás
Back then it was art 🖼
John Rutledge
John Rutledge Anos atrás
Biswajit Pramanik
Biswajit Pramanik Anos atrás
they simply loved the numbers more than current generation love pokimane, sweet anita and so on.
ganondorfchampin Anos atrás
Yeah because they did actual math and not numerical BS. :P
REME 3 meses atrás
Very well produced and outstanding narration. Well done!
Pat Devlin
Pat Devlin Mês atrás
That was a great presentation. I saw it for the first time just moments ago. I would like some feedback if possible? Riemann asserted, in his paper/presentation, that whilst the real part of the roots of the Zeta Function, so far as he could tell, appeared to be equal to 1/2, that the validity of this unproven observation was inconsequential to his papers conclusion that the prime counting function tends to Li(x). If Riemann was correct, are we trying to prove or disprove an empty and meaningless hypothesis (1+1=2) or was Riemann unaware of the importance a critical (pardon the punn) point in his analysis? .
Higher K Group
Higher K Group Mês atrás
The Riemann Hypothesis and even the much weaker statement that there are no non-trivial roots of the Riemann Zeta Function with real part 1, imply that π(x) ~ Li(x), which is one of the equivalent forms of the so called Prime Number Theorem. So Riemann wouldn't be correct if he had stated that the Riemann Hypothesis was inconsequential to the Prime Number Theorem. However, he never did. In his epochal 1859 paper he stated that his hypothesis seemed secondary to him for his further investigations which he presented in this paper. As a main result he established the close and obscure connection between the roots of the Riemann Zeta Function and the prime counting function and his argumentation did indeed not depend on the Riemann Hypothesis. The ideas and techniques introduced by Riemann led to a proof of the Prime Number Theorem in 1896 and the crucial argument in this proof was that there are no zeros of the Riemann Zeta Function with real part 1. You asked if mathematicians are trying to prove a meaningless statement because the Prime Number Theorem can be deduced by a weaker statement. Well, it is very hard to understand the importance of the Riemann Hypothesis. I will try to give you a short answer. If you have further questions just write me an email. You can find the adress in my channel info. After Riemann published his 9 pages work on number theory and the zeta function, all gaps and inaccuracies appearing in his paper could be fixed within the following decades. The only (besides a related statement) open question from Riemanns highly influential work is the Riemann Hypothesis and it remains open for over 150 years. This shows that there is a huge lack of understanding in the fundamental theory of the Riemann Zeta Function. The ideas of Riemann inspired many mathematicians and generalizations of the Riemann Zeta Function were found (for example the Dedekind Zeta Functions for algebraic number fields). The generalization to function fields lead to the so called Weil Conjectures which involve an analogue of the Riemann Hypothesis over finite fields. The proof of the Weil Conjectures required a whole reformulation of algebraic geometry which in turn involves a lot of intricate and heavy abstract machinery (done in wide parts by Grothendieck) and the proof of the Riemann Hypothesis over finite fields was done by Grothendiecks student Deligne. This proof is one of the great mathematical achievements of the last century and laid the foundation for modern number theory. The impact of Riemanns work is in this sense still seen today in modern number theory for example in more recent works as the proof of the Modularity Theorem (Fermat's Last Theorem) or the Langlands Program. So there is a huge influence and impact of Riemanns work and the Riemann Hypothesis is by no means a meaningless statement.
Δаσ Αcid
Δаσ Αcid Mês atrás
University professors should be coerced to watch this and actually present this topic with sense of clarity seen here. Thank you for doing what literally a briefcase worth of tuition fees couldn't.
Roland Gerard
Roland Gerard 9 meses atrás
This is great content, very well presented.
Saumitra SenGupta
Saumitra SenGupta 21 dia atrás
Thank you for explaining it so clearly!
HELLios6 11 meses atrás
Riemann's hypothesis continues to amaze me. He sure found something amazing
MATHS WISDOM 11 meses atrás
Loved the presentation. You made it easier to understand. Thankyou sir
MrEpicTruth 3 meses atrás
These visualizations of the Complex Plane helped me understand complex numbers REALLY EASILY.
Enrico Migliore
Enrico Migliore 11 meses atrás
Top quality content. Extremely clear. Thanks.
Yo Soy Libre
Yo Soy Libre 7 meses atrás
Your explanation of the Riemann hypothesis is wonderful!
Khwaja Azamat Siddiqui
Absolutely loved it! Thanks professor.
Haneul Kim
Haneul Kim 8 meses atrás
Golden content and visual explanation. Thank you very much :)
Ivens Góes
Ivens Góes Mês atrás
Very didactic. Easily explained. Congratulations! I loved this curiosity.
Andrey Cheremskoy
Andrey Cheremskoy 7 meses atrás
It was an exceptional visualization of what is the Riemann Hypothesis.
Hitesh Pandharkar
Hitesh Pandharkar 6 meses atrás
This explained things very intuitively. Thanks for sharing.
unionsafetymatch 11 meses atrás
That shot of complex functions at ~ 9:40 was amazing
Greg Rodd
Greg Rodd Anos atrás
For those who saw Beautiful Mind, this was the puzzle Nash was working on at the end of the movie. There is a Dover book from Edwards, "Reimann's Zeta Function". 305 pp. The first 25 pages explain Reimann's original 8 page paper. The rest of the book tackles developments since 1859 (up to 1974). Edward's book is presented as a guide to the primary sources. If you saw "The Man Who Knew Infinity", Hardy and Ramanujan also did work related to the conjecture. Turing also worked on the problem, taking a computational approach. Just so you know the competition and how it relates to nerd culture. I get stuck just trying to draw a Greek Zeta.
Glenn Rossi
Glenn Rossi Mês atrás
Thanks, Greg! I just ordered this book on Amazon. :-)
MM Anos atrás
Surgeon - Cool. I was just going to recommend Derbyshire's "Prime Obsession" that I find the most helpful intro for laymen & serious investigators.
Jonny Bravo
Jonny Bravo Anos atrás
Surgeon MD
Surgeon MD Anos atrás
Trauma Surgeon There's another very good book, entitled "Prime Obsession" that alternates chapters on the theory with biographical chapters on Riemann. If you love math, it's a wonderful book. Highly recommended.
Riddhi Manna🇮🇪
Heyy thanks I didn't know this book existed!
savetheguineaworm 9 meses atrás
This was a beautiful presentation. Thank you.
Dimitrios Betsis
Dimitrios Betsis Mês atrás
Thank you Professor Kontorovich! Amazing! Mathematics can be so Beautiful!
Bernhard Riemann
Bernhard Riemann 2 meses atrás
A very nice Video, very good explained and real entertaining 🙂 I love cool science content, thank you very much 🙃😊
BOBSHIFIMODS 11 meses atrás
Riemann was a complete genius. It's good that this video correctly credit him and Gauss for laying the foundations for SR. I've only seen them credited once before. Most people seem to think that Einstein came up with it out of thin air and it's been stated we'd have had to wait 80 years if Einstein hadn't done it. Apart from Gauss and Rheimann disproving this, Hilbert was working on his own form of SR in parallel with Einstein.
Ian Paul Saligumba
Ian Paul Saligumba 11 meses atrás
Amazing video 😮😍👏👏👏 Very easy to understand! More videos like this please
Silh S
Silh S 4 meses atrás
This presentation is a real treat 🍰🍯🍹 I feel so grateful everytime I watch thisl 🙏
Bill Seidel
Bill Seidel 11 meses atrás
I've watched this video and don't distrust math as much. I appreciate how you talk about math as a tool and what makes this interesting, rather than make it a 'I know more than you' lecture 👍
Stephen Hicks
Stephen Hicks 7 meses atrás
Brilliantly explained, thank-you
Rick Sanchez D99
Rick Sanchez D99 Anos atrás
If this reaches to you, please create a video for each millennium problem with the clarity of this video. A great introductory video to dummies like us. I never knew Riemann hypothesis had a harmonic side.
COLD but FREE 29 dias atrás
@Ruinenlust P vs NP is by far the easiest to explain. "Is it faster to find the solution to a problem, or test a plausible answer to see if it's right?"
Empika Mês atrás
@GonnaEndYa wtf are you talking about
Loturzel Restaurant
Loturzel Restaurant 3 meses atrás
@Ruinenlust Question: Want scientific Recommendations? BRvidrs to check out?
GonnaEndYa 4 meses atrás
Ya no one told me there was harmonics...
GonnaEndYa 4 meses atrás
What's the friggin problem.. Is that life though? Like the inverter that makes the quantums into reality. Is the universe a taco bell cinnamon twist donut rolled into a croissant?
Adventure 11 meses atrás
GenieStream 6 meses atrás
especially when the importance of such equations or numbers is explained to the students very simple example: differentiation and integration are the first two "complicated" math you encounter in high school, but teachers fail to explain their importance and that never made them interesting (to me).
topquark22 10 meses atrás
I already knew this material. I enjoyed this video for the pedagogy, the way you explained it.
Glenn Hope
Glenn Hope 4 meses atrás
For anybody interested in learning more about the history of this search, I highly recommend the book The Music Of The Primes by Marcus du Sautoy!
Quark Sravitrino
Quark Sravitrino 8 meses atrás
Top notch quality content.... Thank you for this
Deepstaria Enigmatica
Keep pumping out content like this. Love the level of detail & creativity in these videos.
Jude The Man
Jude The Man Anos atrás
@Mikhail Fedorov That’s called passive learning
Mikhail Fedorov
Mikhail Fedorov Anos atrás
Me too. It makes me feel like I'm doing something with my life even though I'm slouching back and passively consuming someone else's hard work.
nidalapisme Mês atrás
To me, the modified prime counting function looks suspiciously similar to the "infinite product of infinite sums of primes power" that Euler proved to be the same as zeta function. I wonder if they represent the same thing.
vikineo 2 meses atrás
I was able to follow until 13:10, after that it was a difficult one for me to follow. An excellent video, perhaps I need to work more on understanding the building blocks of this problem a bit more
Megablademe 9 meses atrás
Now just imagine if they had the computing power we have today.
Really, I'd rather not.
Really good when it's explained very slowly, lost me as soon as it started glossed with the zeta function. Specifically 7:08 lost me completely.
Avasapphic Anos atrás
You just made mathematics fun, I understood only half of it but the video was great, glad I discovered your channel! :)
SardonicHarlequin Anos atrás
Math is fun tho. It's bad teachers that make it unfunny.
Gabriel La Rosa
Gabriel La Rosa Anos atrás
@ArghyaFromNE Imagine that has a proof...
ArghyaFromNE Anos atrás
@Gabriel La Rosa that's s good first step tho
Gabriel La Rosa
Gabriel La Rosa Anos atrás
Understanding only a half of the Riemman Hypothesis is not the way to demonstrate it...
CyberDeus Anos atrás
So true, people need more of videos like that, to explain complex issues in a simpler and more streamlined way, to get more brains on solving real problems
Mike Smith
Mike Smith Mês atrás
About 50years ago an abstract mathematician tried to explain this to me, now (finally) I can see what he was getting at! Thanks.
Alefen 8 meses atrás
1:54 For the buildings with multiple floors, are the colors of the numbers just random or did you have a certain way of coloring them based on stuff about the numbers?
Timmy Fangs
Timmy Fangs Mês atrás
I've always held the hypothesis that this would probably be solved with a proof by contradiction. Since it claims all lie on that one line, say there is a number off of that line and try to go from there. I've been out of school too long to mess with trying to tackle this.
Anirudh Sasank
Anirudh Sasank 11 meses atrás
Awesome explanation sir 🔥🔥👍
Κωνσταντίνος Καρβουνιάρης
I know very little about mathematics yet I was able to keep up with this video till the end. That's a rare talent you've got there, explaining such advanced concepts in plain English. Thank you!
Deadshot Anos atrás
Yeah it sounded nice
Jo Kah
Jo Kah Anos atrás
That is the talent only the TRUE professors posess. Feynman and sagan were like this.
D W 5 meses atrás
I've tried explaining to people that imaginary numbers are indeed real but no one ever understands. I'm glad to see some agreement out in the wild.
Niko Nyrhila
Niko Nyrhila Mês atrás
Great video, but it is very frustrating that most videos stop here. I'd like to learn how to evaluate the function within the critical strip, how was he able to prove this relationship etc.
Harshavardhan Ponnada
Harshavardhan Ponnada 9 meses atrás
"There is only one way to be sure of it and it's the same way the ancient Greeks did their math: rigorous, absolute mathematical proof" - chills!
John DoDo Doe
John DoDo Doe Mês atrás
There's one other way. Finding the one prime that breaks the hypothesis. Hence the computer search.
Nathan 'Nate' Whitehat
Nathan 'Nate' Whitehat 11 meses atrás
Wow. I sure wish I understood any of this. Eventually I will, has I've recently became fascinated with primes and this is too good to overlook.
az Anos atrás
I have discovered a truly marvellous proof of this, but it's much too large for this youtube comment to contain. Therefore it is left as an exercise to the reader.
J.N. Richey
J.N. Richey 13 dias atrás
Fave BRvid comment ever
Cheloss321 14 dias atrás
@Macitron3000 kk
Cheloss321 14 dias atrás
Yeah it’s a lot like like 👍🏽 and m
chemistry world
chemistry world 16 dias atrás
Where is your proof?
Nataranja 3 meses atrás
It’s so crazy to know the distribution of prime numbers is dependent upon imaginary numbers, things that would ordinarily seem to be completely unrelated.
Nataranja Mês atrás
@A Name You Can't Remember agree
A Name You Can't Remember
If I know one thing about math, is that all of it is 100% related even if we don't know the relation yet.
Riki Newton
Riki Newton 8 meses atrás
Brilliant - totally fascinating - thanx for putting this together. Really appreciated. Cheers 🥂
kharnak crux
kharnak crux 3 meses atrás
as a math major... this still blows my mind regularly... the more i've dove into the subtle world of Zeta functions
b_hanock 11 meses atrás
Thank you for that, I sorta got lost at the harmonics part and had to rewatch a couple of times, but I think I understood it somewhat
InterstellarHD Anos atrás
I think you deserve $1 million just for explaining this hypothesis in a clear and understandable language. Well done!
Apuji 10 meses atrás
@MM wut
Robert hodgins
Robert hodgins Anos atrás
MM Anos atrás
@pxlqq > Hi. Thanks for noticing. Yet thats a bit cryptic. Care to expand your comment?
pxlqq Anos atrás
@MM among us
MM Anos atrás
Unfortunately, despite the rhetoric, most maths pros, like Riemann himself, really don't want know why R's zeta formula functions as it does, nor why RH remained unsolved for more than 157 years. Also, like Riemann, nor do they want to learn or do anything other than what they are doing inside The Box of the current paradigm of their fave maths niche. If that were untrue Riemann could have solved RH--IFF he could've gotten out of his tumnel-vision syndrome (& outa The Box). Also, if the culture of current maths was not allergic to superior theory & metatheory of maths & logic it would be easy to get my proofs reviewed, published & verified. As is, that's almost impossible. Sigh...seems a shame to let 21 years of good work and next-gen maths go to waste. Oh, well...humanity is clearly stuck with a culture of cowardice, conceit & corruption. So, i guess we're doomed. So, nothing matters. Rite?
Catman 321
Catman 321 5 meses atrás
I can imagine one way this problem may be solved but there is an issue What if there was a problem that you could prove works if and only if the reimann hypothesis is true, but then you prove it is true without relying on the reimann hypothesis, instead using a fact already proven, like e is transcendental or something (obviously something more complex than that but this is just an example) The thing is... what would this problem be? It is possible since Euler and Euclid both proved there are infinite prime numbers in different ways, with different logic behind it, but the issue is what would it be here?
Catman 321
Catman 321 29 dias atrás
@COLD but FREE because if the reimann hypothesis is false and has to be true in order for our arbitrary theorem, whatever it may be, to be true, but then we prove our theorem true by means other than the reimann hypothesis, then there's a contradiction and it must be true in the end.
COLD but FREE 29 dias atrás
How can something be "if and only if" and then be proven without that contingency? All you'd be doing is an attempt at 2 semi-related, unproven, axioms.
Marco Frey
Marco Frey 5 meses atrás
That was fantastic, even for a non-math nerd such as myself.
TheAtheist Mês atrás
What a beautiful presentation. Thank you. I've subscribed.
David Palmer
David Palmer 6 meses atrás
I love how they story journey we were taken on all came together at the end of the video in what was a light bulb moment for me. Thank you Professor.
D Shepherd
D Shepherd 5 meses atrás
Clearly we were on diff journeys, lol
s3cr3tpassword Anos atrás
This is literally the best video on BRvid explaining why the Rieman hypothesis is related to the prime numbers and why proving it is so important. Other videos only briefly mentions that it's important because the 'prime number distribution is encoded in the function', like bruh that doesnt explain it enough. This video also beautifully shows how anaylitcal continuation works.
Anurag Chakraborty
Anurag Chakraborty Anos atrás
@Joh Embrey So let me ask you this: even if someone were to prove Riemann’s hypothesis what will it actually accomplish? In terms of tangible benefits for mankind??
TheMedia-Hacker Anos atrás
A Solution for the RIEMANN ZETA FUNCTION is extremely valuable because It also point to Solutions for enhancing the Poincare conjecture, Hodge Invariance conjecture as it relates to PRIME NUMBERS 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
Studley De Muffin
Studley De Muffin Anos atrás
@Titus Wong Keep in mind that this is one of the only attempts you can find on the internet at explaining the connection between the Riemann Hypothesis and prime numbers. I wrote a paper on the Riemann Hypothesis last month and when researching I could not find any explanation like the one at 12:40, even in books that were entirely about the Riemann Hypothesis.
Shobhit Sharma
Shobhit Sharma Anos atrás
Amazing Tarot Card Reading. Is Anandi Dhawan Dead/Alive ??
Shobhit Sharma
Shobhit Sharma Anos atrás
Amazing Tarot Card Reading. Is Anandi Dhawan Dead/Alive ??
The inscrutable scrooge
I love how in daily life one piece of evidence is enough to form conclusions but in math a computer can check the non-trivial zetas trillllllllllions of times and they're still like, "ahhhhh idk it's still too early to tell"
Neutri no
Neutri no 6 meses atrás
Solid explanation! 😍👍
Z Y 15 dias atrás
What would happen to the harmonics that approximate Gauss log prime counting (GLPC) function if it is found that a non trivial zero lies outside the critical line? Would that zero would distort the approximation badly? or you would need infinite non trivial zeros outside the critical line for the approximation of the GPLC to break down
A C 12 horas atrás
Long before Euclid of Alexandria, about him we know very little or his works, Indian mathematicians stated what is attributed to him and others like Pythagoras.
Will H
Will H Anos atrás
cool man, I think I'll solve this over my lunch break
COLD but FREE 29 dias atrás
@Mohd. Bailey The prize is a token. If somebody were to actually solve the problem and patent part of the solution, they would end up getting royalties from essentially all fields of complex work.
Doraemon Mês atrás
@Code with Doge i have solved this 'unsolvable' equation; x=2, y=1.
Matthew Landry
Matthew Landry 2 meses atrás
MrSimmies 3 meses atrás
You need THAT much time???
Cobalt Bar
Cobalt Bar 5 meses atrás
@Catman 321 or still im your lunch break
Math has never really been my thing, but this was fascinating.
579enact 3 meses atrás
What about the non-trivial 1s, or 0.5s, or 0.0001s? In other words, do any OTHER solutions of the function also lie on specific parts of the graph? What about the furthest values between each two zeroes? Is there a pattern to them? How about instead of using (i^2 = -1) for the imaginary plane, try i^2 = -pi, or -e. Has all this sort of stuff been tried?
Alan Grayson
Alan Grayson 14 horas atrás
Can you give one example where a finding or theory of physics depends upon Riemann's hypothesis being true?
Brenden Parker
Brenden Parker Mês atrás
Thanks, that is the best explanation of this I have heard.
Tanavat555 Anos atrás
I don't usually comment but holy crap, the quality of this video is insane. it's nice to see more easy to understand science/math content popping up. thanks for the hard work.
Franz F.
Franz F. 11 meses atrás
That was quite beautiful. Far better explained that my complex analysis professor. The traditional way we teach and learn is obsolete. And no, I don't mean to disrespect teachers, I'm a high school maths teacher myself.
Akhmad SW
Akhmad SW 9 meses atrás
What a good video! Watched it on a single breath!
Scarface190D Anos atrás
Fascinating! At 11:15 I was thinking a fractal appeared. Is there a link with the subject?
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