Riemann Hypothesis

[@jcdavid1974]

This is the clearest outline of the Riemann hypothesis I've seen here. No tricks or quaint graphics...just facts and necessary backup info...THank you!

[@base12universe]

Best explanation of the Riemann hypothesis I have come across, thank you!

[@smoorej]

The best overview of the RH I’ve ever seen. I love number theory but just have an undergrad degree in math and I was able to follow everything. Well done.

[@kquat7899]

Excellent synopsis.

[@99bits46]

It's criminal Riemann's name doesn't pop up in top mathematicians list

[@stephendean2896]

Best explanation I have found Don’t take this statement lightly because I have watched over 10 videos so far on the zeta function. If I am able to stay interested, then when I either prove or disprove the Riemann Hypothesis I will give you all the credit Thanks

[@musicalBurr]

Thanks *SO* much for putting this video together Andrea - I have it as a goal in life (I'm a little late to be embarking on this particular chapter - at age 55 - mind you I've been poking at it off and on for years now) to fully grasp essentially what you have put together as the contents of this video. You've hit every point I'm interested in, now it's just time for me to dig in deeper and really learn about the details. Thanks again!!

[@metapix]

Your goal is more nobler than many other stupid things people aim at. Best of luck.

[@atulmod1]

Great effort

[@mcook10128]

There's a lot of information in this video. I think it's actually an excellent summary of some key points, especially concerning the flow of Riemann's thought.

[@MOHNAKHAN]

I like your style of polite pronounciation...

[@valor36az]

What an elegant explanation,

[@David-dvr]

Very nice treatment of Riemann Hypothesis.

[@tutordave]

Nice. A bit dry, but nice. Like a good red wine. I really like the way you defined the zeta function piecewise. I was originally under the impression that the continuation on to the left of s = 0 would also work in the critical strip. Thanks for the info.

[@blakff5373]

bravo

[@seraphik]

super underrated channel. please make more vids. i’m liking and subscribing in hopes of seeing more!

[@wertherquartett]

Lemma: For every KZbin exposition of the Riemann Hypothesis there exists at least one person for whom it’s the clearest such exposition.

[@williejohnson5172]

Solved it. Zeta(0)=-1/2=i=sqrt(-1)=critical line =non trivial zero.

[@ckmishn3664]

I don't see how the Riemann Hypothesis being proven true could represent any threat to public encryption. The value of the proof is in that it allows other things to be proved, but simply assuming it to be true is sufficient to use them for practical purposes (and that's what matters to someone trying to break encryption). The implied distribution of primes won't change just because we know for sure it's true. The proof itself could, of course, lead to new math the might tell us something about the primes but that's just speculation.

[@itsRAWRtime007]

But his point is assume it is correct and find such an algorithm, if it works you will know.

[@davidwilkie9551]

The layout of the information about series and sequences "on the face" of Cartesian coordinate math, is a good first principles approach to stating the conditions of the analysis to be done. A comparison of naturally occurring math and a micro equivalent, of something like the Babbage machine taken to the limits of possibilities, demonstrates the cause-effect /calculation of superposition/spin as spin-potential of QM-TIME, generating the structures of constants by irrational continuity convergence and reciprocals of exclusion. We look at resonance constants from an "outside" across a "band-level" wave connection to an eternal engagement with a rotating equal phase, all within the kind of compound spin, characteristic of the Babbage machine. So if the limits of calculation are the spin-potential shells of irrational resonance with the constant complex containment property of i, in completion of irrational series at the coordinated vanishing point of a complex i probability staement, then to prove this Conjecture, the series has to have the same characteristics as those used in Renormalization of infinities and zeros at 1-0 Discreteness/Dimensional prime/probability boundaries. (Math-Philosophy context) In the circumstances of the Riemann Hypothesis, the Gauss and Euler propositions "recognize" 1-0D mathematically in the form of a cause-effect limit of axial-tangential, Ln, e-Pi connection. It's the innate duality ratio, rationalizing of quantization. Excellent lecture.

[@tariklahcen9928]

جزاك الله خيرا أستاذتنا الغالية شرح غاية في الروعة لقد استفدت كثيرا سيدتي الفاضلة

[@fmikael1]

Awesome video - you deserve way more subscribers

[@vector8310]

Thank you for your first - rate overview of the Riemann Hypothesis. I've just begun reaching Riemann's paper and this video provides helpful context. I'd like to share that so far my experience has been that reading the original German is a modicum more suggestive, which may make sense given that Riemann took notoriously great pains to precisely phrase his writings.

[@theedspage]

If the Riemann Hypothesis is proved, the zeta function could be the function of the 21st century because so much is riding on the hypothesis. Great video!

[@99bits46]

I am six years from the future, RH still hasn't been proven.

[@jessstuart7495]

Very nice video. Clear and informative. Thank you!

[@mattkerle81]

Great video! (Except for the bit about encryption at the end)

[@robharwood3538]

Really great summary and documentary. Thank you for making this! :-)

[@diarmuidkeane1]

Well put together presentation simple clear and without frills

[@TheNachoesuncapo]

Awesome!thank you so much,your explanation was delightful

[@ghiribizzi]

the analytic continuation of zeta function for analyticality of it in order to get the famous zeros

[@cadceedm.b6192]

The best explanation that i seen ever

[@rmarinov5770]

BEST OF THE BEST. THANK YOU!

[@elcrackkrack9559]

Bolivian Beimar Wilfredo López found FORMULA THAT HE WANTED TO FIND GAUSS and RIEMANN kzbin.info/www/bejne/g3OzkmOGdrNkqsk - Well, it would be good to verify the demonstration of the BEIMAR FORMULA to give APPROVED or REJECTED. - In CONCLUSION, when a demonstration of the beimar formula was approved, since BEIMAR WOULD GO INTO HISTORY AS ONE OF THE 21ST CENTURY MATHEMATICS.

[@ahmadtariq3960]

Thanks mam

[@RSLT]

Great Video !!!!!!!!!!!! Does anyone knows the reference and proof for zeta(s) timestamp 9:33?

[@ImaliveUSA]

Pls upload more videos 🙏🙏

[@DavidVonR]

Great video, please do more.

[@doubop]

thank you! beautiful video, i have vibration as if i was listening music!

[@messaoudifares808]

فيديو جميل ومذهل /// ساحاول حل هذه المعضلة عما قريب إن شاء الله 2031

[@MostlyIC]

Andrea this is awesome, none of the other RH videos I've watched explain Riemann's counting-primes-plus-powers-of-primes and how that gives and explicit formula for PI(x) based on zeros of zeta. However I would like to see an explanation for why pi/n(x^(1/n)) counts n'th powers of primes though. And I wonder what stroke of genius on Riemann's part lead him to think about it this way.

[@dreia2405]

Great video

[@chevasit]

Very good!

[@Nasirmah]

Isn’t period functions can’t also be expressed in closed form, even e^x since e is transdental, therefore series to the power of x

[@moudar981]

Thanks a lot. Very nice explanation

[@melese1988]

Many thanks!

[@Alcani3ca]

Really well explained! Loved how you explained so many details even the basic stuff from pre-calc. By the way when you say "using some tricks from analysis" at 9:28 are you talking about the class Real Analysis? I haven't taken the course yet but I'm really looking foward to it! Thanks for the video.

[@mattersofheart22]

great video! thanks

[@stillsayt6192]

Greath job, i will continue learning, thx.

[@nikola2024]

Nice video , thanks

[@keinKlarname]

8:57: the summation should start with j=0

[@stephankuerner315]

The problem of the Riemann hypothesis is solved and Quatch what you are talking about here

[@stephendean2896]

Sometimes I forget KZbin has a past

[@KingHim00]

I solved Riemann's hypothesis that every zero does end up on the line and I have proof to show you in a way for you to check and see if every zero ends up on a critical line

[@calvinjackson8110]

PUBLISH!!

[@jigsaw1063]

if "there is no eplicit formula for the non-trivial zeros" then how the hell did they calculate the non-trvial zeros so far? seems like a contradiction to me. And if we can´t use the function as described between 0 and 1then what is it for? I would like some one to describe the mechanism from point A to point whatever. How do we use the mentioned version of the zeta function to calculate non-trivial zeros?

[@Tadesan]

A quiet reserved German Jew...

[@GintoGeorge2007]

BEST

[@ZbigniewStebel]

Thenk you

[@RSLT]

Does anyone know the reference and proof for zeta(s) timestamp 9:33?

[@mariyammapapabathiniratnam7862]

1+2+3+4=10 -01=00 00 = 20 as 1=1,2=3,3=6,4=10 that is it is as 1+3+6+10=20 as called two zeeros as 00

[@manofculture8666]

Can someone please tell me, or give me a link that shows how the zeta function at 9:26 was derived? I've seen the zeta function for Re(s)>0 and how it was derived. But I've never seen this.

[@neeraj399]

Max Echendu I just tried to simplify it, and it just yields the original zeta function. Even I need some details now.

[@calvinjackson8110]

The hypothesis of Riemann is that ALL NON TRIVIAL ZEROS ARE ON THE CRITICAL LINE. If only one non trivial zero of the zeta function fails to be on the critical line, the Riemann conjecture is false. So i dont get what being "close" to the line is about.

[@LifeIsBeautiful-ki9ky]

Why, you don't do no more videos ?

[@magicfigures]

The new finds in the field of prime numbers. The prime numbers form so-called nests of the prime numbers in the fourth dimensions. Please see the homepage www.number-galaxy.eu in the directory "news" and positions: 01.01.2020 3D bordered prime magic squares in world and antiworld configuration 03.02.2021 Projection 3D bordered prime magic squares on critical linie of Riemann zeta-function. This is completely new in the field of the Riemann hypothesis.

[@marlonsoto648]

A table of prime numbers from the RH? Never heard of it. Riemann mentioned that he believed all the non trivial roots of zeta lie on the line Re(s)=1/2, in passing. His "prime" concern was finding a better approximation to The Number of Primes Less Than a Given Magnitude...He did find it, as all empirical data available today have indicated, data which, by the way, was out of his reach at the time he made his seminal contributions (hats off to the man!). So, we are talking about an analytic formula for an approximation here, not an exact one. How can we then "exactly" count the number of primes? Some things just don't add up here. And by the way, when discussing the functional equation the word "terms" are used to refer to what are really "factors". As far as I know those definitions haven't changed.

[@zoozolplexOne]

wow, i like the explanation

[@manofculture8666]

I MUST prove this.

[@HocineFerradj]

Good luck!

[@brendawilliams8062]

No

[@seraphik]

please make more videos!

[@gurmeet0108]

Really good video, but there is a small mistake at 16:38, you mistakenly swapped zeta and psi functions, it should be "express psi in terms of the zeros and poles of zeta"

[@orenkrimchansky]

Great video. Thanks!! What is the smallest imaginary number on the 1/2 real number strip ever found?

[@DeanNiemi-r1m]

The 2 points you refer to (directly across the real number line from each other) are the start and end of the Riemann Zeta function from -time infinity to +time infinity.

[@obsidaisy7776]

I don't see how proving the hypothesis would influence cryptanalysis, unless you made a major breakthrough in order to do so. You couldn't just reverse engineer the hypothesis with some dummy variables and let statements, as most mathematical proofs do nowadays; you'd actually have to come up with some kind of historically unprecedented algorithm or formula that relates to the hypothesis on a basic level. Even then, knowing about the distribution of primes is a long way off from being able to factor primes.

[@jimmpingwhosthat1747]

What are non-trivial zeros

[@calvinjackson8110]

Zeros that lie in the strip with vertical lines x=0 to x=2. The trivial zeros are the negative even integers.

[@kamalbouarfa3732]

Dont worry i found thé finaly Formula of primes nimbés wich descripe them pattern

[@جحخخحج-ل1ض]

الترجمه العربيه

[@ksmyth999]

This is a good introduction to the subject. Unfortunately, the last comment concerning public key systems is rubbish. Without going into the details it can easily be inferred that if the truth of the Riemann Hypothesis means factorization becomes much easier, this would have been tried long ago by hackers. Since the concensus and computer evidence to date gives a strong indication the hypothesis is true, why would a hacker wait for the absolute proof? Actually looking at the comments I see that Patrick Wise had already pointed this rather glaring error out about 2 years ago. To put this into perspective. You would really need to do an undergraduate course in number theory to understand how the analytical continuation really works.

[@williejohnson5172]

A General Solution to the Riemann Hypothesis Zeta(0) = negative one half = non trivial zero. Proof. 1. Superimpose two unit circles. 2. Designate the vertical diameters as 2i and the horizontal diameters as 2x. 3. Starting at zero degrees and rotating counterclockwise, the points of axes along the circumference then assume the values (1, 0); (0, i); (-1, 0) and (0,-i). 4. Pin the common point of the two unit circles at (1; 0) such that this point is restricted from moving. 5. Reduce the diameter of one of the unit circles by half. This creates an inner circle of diameter i vertically and diameter x horizontally, which is pegged/pinned to the larger unit circle at point (1; 0): 6. This pegged inner circle is identical in every respect to the larger parent unit circle except it has been scaled to half the size of the larger unit circle. 7. The origin of the parent unit circle assumes various equivalent values Cartesian: zero, plus or minus 1 Fermatian: zero, limit, derivative, maxima, minima, plus and minus 1, one half, i Newtonian: zero, shrinking the 2i secant to zero= i = limit = derivative = maxima = minima: Inner Circle shift: The (-1; 0) point of the reduced circle now occupies the origin of the larger parent circle. 8. The origin of the reduced/inner circle is identical to the origin of the larger parent circle. They differ only in location. 9. Thus since i = 0 then the entirety of the i diameter of the reduced /inner circle is, and must be, zero. 10. The same result may be obtained by shrinking the 2i diameter/secant of the parent circle to the length of the i = zero diameter/secant of the inner circle. 11. Thus the i diameter comprises the critical line and since its entirety is composed of zeroes then these zeroes are, obligatorily, non trivial zeroes. 12. Given step 7 and Figure 2.0.1, i is equivalent to the tangent = m = slope. 13. Vis a vis the parent circle, given Figure 16.3.2 this slope is manifest as the hypotenuse (tangent line) of a right triangle of height i and base .5x or one half x. 14. This results in the formation of a negative .5 slope or negative one half slope or a positive 2 precessional rate where slope = m = negative one half. 15. Therefore m = i = 0 = nontrivial zero = negative one half. 16. Therefore critical line equals i = 0 = non trivial zero= negative one half = Zeta(0). 17. Thus is it proven that Zeta(0) =negative one half=non trivial zero. QED

[@RtZt-jx2uo]

L ensemble des zéros est une famille génératrice est reliée couramment avec Fp(ns) ' telle que F(s)=hn×Fp(ns)^d tell que l ensemble As possède un sous ensemble Ap ' 1/27^s=1/3^3s ' Ap un sous ensemble de As l image de Ap =o pour s=1/n+ikπ/lnp le de la courbe de Fs il y a une relations ordonné à Fp

[@jeffreyluciana8711]

Reimann didn't have the benefit of my sixes or cancellations. All primes are twins next to the 6. And prime times prime cancels prime. Why waste your time on something that is described in base 10 when it is better understood in base 6?

[@arpcs]

Proving or disproving really wouldn't have any impact on cryptography. Calculating exact number of primes would be still as hard, and creating tables of primes is just a silly idea.

[@williejohnson1669]

Solved it. Read the Sagitta Key by Willie Johnson Jr or Gyro-Electrodynamics by the same author.

[@chrisbarlow6335]

Why do you introduce i, complex numbers, roots of an equation, prime numbers etc in this video? Its about the Riemann Hypothesis and its safe to say that people watching this know something about maths. If they have never heard of i or a prime number do you think your video will mean anything to them at all?

[@calvinjackson8110]

She was just trying to provide a little background to some who may be interested but who might need a little brush up. Trying to be helpful. If you found it boring, just skip ahead!

[@taresy6789pp]

Find a contradiction between heisenberg uncertainty principle disproved riemann hypothesis

[@diktakt1187]

10 36 Cos eq fonct

[@mikevaldez7684]

interesting

[@mikevaldez7684]

hey mike

[@mikevaldez7684]

+Mike Valdez, Yeah? What's up?