Intro Riemann hypothesis

A simple graphical explanation of arguably the most important unresolved conjecture in all of mathematics. See my other videos

[charlesqin]

I stumbled across this while doing some random youtubing on a few science topics. Great to see that you have compiled a whole series of "mathematics made easy" videos. Keep up the awesome work, mate! And hope things are well! :-)

[capjus]

Ok now i understand at least one thing that i couldnt from other videos!!!
The one graph is the input complex graph and the other is the output complex graph!!
Omg why never someone made that so clear!!

[ruffifuffler]

The 1/2 line, is the only line in the whole coordinate system that would rent the Zeta function a spot for a zero, and that rent, is the distance between the new zero, and the old zero, which changes with the new unexplored territory, keeping itself consistent with the rule of the old territory already displaced, as the Zeta function has memory, but no foresight.

[conradgarcia]

I just discovered your channel today. Your explanation of Riemann's hypothesis is the best explanation I've seen on the web. You are an incredibly good math communicator. Math is really a lot of fun when done with visuals. Please make more videos of RH and other conjectures. Galois theory and nth degree polynomials would be awesome. by the way, do you do consultations on email? I've a few findings regarding prime numbers.

[sanferrera]

Congratulations! I just finished the book "the prime obsession". It is really well written, and explains these zeroes very thoroughly... although I must say that some of the last chapters were beyond my reach.

[moutunlay]

factoring is based on the fact of writing a number C like : C=BQ+R and process like
C=BQ+R=(B-x)(Q+x)+R-Bx+Qx+x²

and make the reason like :

C=BQ+R=(B-x)(Q+x )+ (R-Bx+Qx+x²)

(R-Bx+Qx+x²)/(B-x)> or = i can t give the value

[kbecgr]

Thanks for the answer for my previous first query 6 months ago. My next 2nd queries are: How will someone begins solving the Riemann hypothesis? in other words. Where should he starts?; What computer softwares or programs should be used? What mathematics knowledge, topic, or subject should be applied (Example: Taylor series, Calculus, Integrals)? What is your recommendation? Do these questions make sense? THANKS again! God bless.

[ytang]

Why can't we make a polar graph of limaçon-looking-shapes at Re=1/2? Looks doable....

[williejohnson]

I solved the Riemann Hypothesis. In short: s=negative one half=zero.

[cameronspalding]

Here’s an idea:
If n(s) = 1-1/2^s+1/3^s-1/4^s+...
(1-2^(1-s))*zeta(s)=n(s)
The formula for n(s) converges for re(s)=0, zeta(s)=0 iff n(s)=0

[musabbafridi]

Hi

Can you please elaborate on analytic continuation as you mentioned in the video.

Otherwise please feel free to point me to a source. I don’t understand mathematics symbols yet and have struggled to find a source.

Lastly, really appreciate your videos and comments as well!

[ralphjaymagsalay]

Hi. I like the way you explain and illustrate. But I am hoping that you're gonna make a video for the poincare conjecture's proof.

[osmanimourad]

Hi Dr Randall thank you for this amazing video, I wander where I can find some of the value of the critical strip like those 0.4, 0.6 along with some other value of the critical line where the zero of zeta function are
I mean is there any paper where someone compute those point and list their value plz help .

[AlexanderDeTrano]

learned something new today. great video.

[Tadesan]

Lol what if you analytically continued all the roads in your state beyond it's border... Road crew chief holding up his thumb and going "yeah that looks right!"

[sunkhirous]

Randell have a news for you ! Zeta zeros are not on 1/2 line, cheers .

[funinvegas]

At about 5:50 where you start plotting values other than 0.5, how are you evaluating these points or how are you creating these charts? I found various online tools to evaluate points along 1/2, but nothing that lets me plot non-1/2 charts. I tried coding something myself, but floating point precision or cos/sin approximations made all my results useless.

[misternewoutlook]

The thing I never hear is what is the main hurdle that makes a proof so elusive. Why do the greatest minds in mathematics put the question to the public? If they can't find a solid confirming reason for zeroes on the critical line in 150 years, then what chance has the layman? Isn't that sort of getting people to chase rainbows or are they very serious of the real possibility of some diamond in the rough figuring it out? I mean, it doesn't seem like the kind of thing you just stumble upon.
A million dollar question obviously requires a million dollar answer that works. And what about the primes? What does the zeta function tell me about their distribution? What would a proof be likely to look like anyway? Could it fit on a t-shirt?
A great video though and I'm glad I could finally see what the first zero calculation looks like on a graph.

[rositaledesmamataromenorca]

What will be the impact in the world of finance and cyber security if someone like Perelman or Wiles presented a valid proof or counterproof of the RH?

[discountbrains]

This must be a very general overview of this. It must mean that these series converge to 0. How do u calculate any of them =0 unless you've determined a formula expressing
(= to) these infinite sums? I suppose the conjecture is they equal 0 for all 1/2-ε <re(s)<1/2+ε for some ε.