Please keep continuing this. There are so many of us who yearn for such quality content

Guess I've found a series to watch this summer

We don’t often see this unique approach to a mathematics problem. I hope this series continues.

I thought this was about to be the greatest collaboration between formula 1 racing and advanced mathematics

I’ve seen lots of content on the RH, but have never seen someone explain ACTUALLY how the zeros on the critical strip related to the primes! That’s amazing!

From a mathematician, thank you very much for the video and the references!

This is very high quality content. I am a first year mathematics undergraduate and appreciate that I can understand concepts of such advanced level because of the way you dissect each and every part. Please continue these videos!

Premium epic math content for free is the greatest achievement of the internet

Best math video on KZfaq this year. I've always marvelled at how productive Archimedes was with such a limited notion of number that I decided maybe my notion of number was the problem. We treat transcendentals like integers all day long and never bat an eyelid. Have you ever done a calculation with pi? No you haven't.

I'm super excited!

I have NEVER been so enthralled by a topic in mathematics. Eagerly awaiting the next installment!

Good lord I'm excited for this series lol

Awesome video! I'm very happy KZfaq recommended this to me. I always wanted to understand how the Riemann Zeta function is related to prime numbers and you explained it so clearly and easy to understand. Keep up the great work!! I'm really looking forward for the next episodes of this series :D

going into my 3rd year of mechanical engineering, I have almost zero idea whats going on but still super interesting to watch

You explained it so simply and clearly. I like how you highlight the clues to tie many concepts together.

Here's a comment on Random Matrices. The coincidences between the asymptotic statistics of eigenvalues of random matrices and zeros of the zeta function are striking. But they are only probabilistic in nature, referring to averages over large sets of random matrices, not to any particular linear operator. At first sight, this only implies that these may somehow belong to the same "universality class", when properly scaled. The use of a spectral approach to proving the RH would have required showing the existence of a specific linear operator, whose discrete spectrum coincides with the zeta function zeros, and which is invariant under an involution whose fixed points are the critical line. Nothing like this has ever been done (for the genuine zeta function) - although analogs for prime number fields have been used to prove the RH in those cases. So the resemblance to the statistics of the eigenvalues of large random matrices is perhaps helpful in suggesting such asymptotic properties for the zeta function zeros, but it does not mean that a spectral approach provides the key to proving the RH. However, it is an appealing idea that, especially for physicists familiar with scattering theory, is very natural, and perhaps should be further pursued. It is just that the class of linear operators used in proving the RH over mod p finite fields, which were discrete analogs of the Laplacian, need not be the same as the one required to prove it for the usual zeta function.

i dont know anything about math but the sum of negative cosines feels almost like a transcendental number like e, getting closer and closer with each continuation of a function, never reaching its full value. its like one step forward from a number. this comment is just for the perspective of what people with only basic math knowledge might think of this video.

I'm a math's student. and you are the teacher like god. I salute you for introducing this pure Knowlege us. I wish, someday I will go deep down this L-function world and make out something. thank you .

So wonderful and well executed, I can’t wait for the rest.

Strong start! I hope future videos, once we've gotten through the big-picture overview, dive deeper into the details and rigor of the problem. In the meantime, I appreciate the links to the papers youve cited!

Very interesting, please continue the series. 😊 A short personal anecdote, because I thought you were going here when connecting the primes to the Riemann zeta function: Some 38 years ago, with only freshman physics education, and never having heard of Basel problem or Riemann ζ, I was fiddling about with factorisations and found that the product Π 1/(1-p^(-k)) over all primes had to be equal to the sum Σ 1/n^k over all integers (for some fixed k>1). My dad saw my notes and wanted to show it to a mathematician friend of his. I protested a bit, because It was only a few scribbles showing the idea to myself, but he persisted. A few weeks later, I got it back full of red stripes, because my 'proof' was wrong. My dad then lost faith and thought that all of my scribbles were nonsense. Later I found out that Euler had found the same result. Probably the mathematician had thought that I wanted to show a proof for Euler's result, or even trying something with ζ(k), whereas I, naive as I was, just thought to have found an interesting new connection between primes and powers of natural numbers, and had not focused on (and probably could not provide) a watertight proof.

Thank you for starting this series. I sincerely hope it continues.

Love it. Commenting for reach.

Absolutely beautiful video.

I just began watching this series and am already enthralled! Thank you so much.

I love the way you've framed this, a mystery and an adventure!

Sublime video, I think we are all looking forward to the next chapter. Thank you!

The way you deliver is mesmerising. I could listen to this for hours

I very much hope this continues, great work!

Absolutely loved this introductory video! You're a great storyteller and have me really excited for the future episodes! As a math student, I love seeing stuff like this

This series looks like it's gonna absolutely amazing, please please please give us more!! 🙏

Excited to see future episodes!

The algorithm suggested this to me and this is exactly the kind of content I love. Subscribed, and hope to see more videos like this!

Great work! Looking forward to seeing more!

A lot of interesting points in one video. Great job! 👍 I love to see more videos on this topic. I hope this series continues!

Amazing content. Very clear and brilliantly explained. Thank you!

Thanks for all your hard work. Great introduction. Looking forward to next episodes.

Can't tell you how excited I am for the series. Please do continue !

Excellent review of the RH, the best I've seen. I can't wait for the next episode.

Absolutely wonderful start. I'm looking forward to the continuation

Fascinating video with great explanations. I look forward to continuing our journey through this subject.

Love to see more such videos. Fantastic introduction and inputs.

This was awesome!! Hope to see more episodes and season this was so inspiring and fun to watch :)

Physicist chipping in here. You are putting the bar high up there, love it! I look forward to all the next episodes. Hope you will extensively cover random matrix theory as well.

Accessible yet not too dumbed-down, simply AMAZING!

From the beginning to end everything was perfect. Waiting for the next part. Thank you!

I am glad that youtube recommended this video for me. Very excited to watch it and eagerly waiting for the next ones.

An excellent introduction and overview of the topic. Thank-you so much for taking the time to make such an accessible, well-paced, clear video on the search for proofs of the RH. My hope is that this stimulates young & old mathematicians to embark on this journey of discovery.

Can’t wait to see this channel grow🎉

Nice work! This was the first explanation I've seen of how Riemann actually relates to the primes, via the Riemann spectrum and the cos(K ln(x)) sums... I love when I see new material like this when I know it's been out there all this time. I'll be waiting for your next episodes!

Just stumbled across this series and I am excited to watch it all.

I am very thankful for this series and so glad I found it!

I'm watching for the second time and love what you are doing. Thanks!

What an amazing introducton. Superb.

Looking forward to your next video!!!

this is so well made. looking forward to see the up-coming episodes ouob

I'm a mathematics graduate student right now working in non-commutative geometry, operator theory, and field theories. I'm not particularly interested in working on the Riemann hypothesis myself, but (while not necessarily frequent) I do recurringly hear and read about how the the stuff I work with has various sorts of connections with the Riemann hypothesis, and I do find that rather fascinating I hope this series continues! Though I don't plan on ever working on the Riemann hypothesis myself, I'm excited at the prospect of hearing an extended pressntation which elabourates on some of those connections I've heard about!

It's beyond amazing to see the mathematics of reality. It's incredible to see the very building blocks of our existence, far beyond the quantum level - in number form. Wow.

Such high quality! Your channel will definitely succeed if you continue. Keep it up!

Awesome video! Looking forward to the next one and this series

Love the content, love the format!

I'm impressed by the effort to look at numbers and RH at a different perspective, given RH has been around for more than 160 years and yet to be proven!

Looking forward to the rest of the serie !

It's fascinating. Please carry on.

That's so exciting and well presented. Can't wait for the next episode. It might feel a bit like the lecture of Wiles, where he casually proved Fermats last theorem without explicitly telling in the Titel... Greatfully, Alex

Can't wait to hear more about it.

This is so beautiful ❤

Now you've got me excited for the next episode :D

Absolute respect for using Ravel's g minor concerto as the background music

I haven’t started this video yet and somehow already know I am going to love it!

Thank you so much!!! This is exceptional content.

Amazing... అద్భుతం...

this video is amazing, plz keep continuing

I wait with baited breath. Truly an excellent video

This is insane!

Please don't stop. Can't wait for S2.

Wow! I didnt get everything at all but i loved the way you went through the hipothesis and the structure of the video. Thank you!

Really interesting ideas, I've downloaded the pdf and I'm looking forward to the next episodes!!

Fantastic!

I haven‘t been dealing with L-Functions since my days at university… :-) Interesting lecture series - keep up your great work!

You managed to catch me, very nice approach! please continue

Superb!

Looking forward to the next episode!

I can see some sort of deep connection between quantum mechanics and number theory from this presentation. Never realized this before.

Nice, awaiting for next videos! Good editing also :)

Will be waiting for part 2 and so forth. Cheers.

This video is a thing of beauty. The presenter's approach was just right and I even loved his long pauses. The tablet was a perfect choice, while the hand drawn notes humanised it. I was drawn in to the subject matter and felt engaged from the outset, as if I was part of the adventure. The only thing I didn't like was that this was the only video on the channel. Please can we have more like this.

This is amazing! I stand subscribe :) please keep them coming!

Thanks, fascinating 😃

Now this is some high-end KZfaq content. I am here for it!

Instant subscription

Great presentation

I like your way of presentation.

Very enjoyable, please continue this series. Regards from India

One of the best introductions I've seen to prime numbers and RH. Thank you! As a lay person I'd like to ask something. To me, there clearly is some sort of geometry to numbers, they are a geometry. One we seem able to just see, as far as we look at numbers and what they do. All it takes is looking. How do numbers stand and behave relative to eachother. Now, one thing is to look at that and describe it, while another is being able to predict things. Why should we be able to predict everything, meaning anything in particular, without computing? We may find a proof of something, some day, or not, but does it imply anything at all about certainty, or rather lack of it, whether we haven't managed yet or it is impossible to prove that? My point is: we might sometimes actually see clearly that which isn't proven or even provable. For instance, the twin primes conjecture. To me it is by definition a conjecture, but at the same time, it seems obviously true, "visually" obvious, to be true, we KNOW it to be true. We can look and see how there will always be twin primes. It is something purely mechanical. We cannot compute all numbers in practice, but we can see how, computing them, necessarily leads to infinite twin primes. It simply is part of their "geometry". My question is: this which I am saying, does it make sense to any mathematician here? Would any of you agree that you can see it (how this conjecture is true) and be just as certain, without a proof? Thank you!

This is exciting

Excelent! I love it.

I'm stoked!!! 🌞👍🏻

This is amazing.

I just subscribed to see how this plays out. The suspense is killing me.