Thanks Curt! And you have really levelled up your game again and again over the past year. Loved your Penrose interview, and looking forward to the Harvard epics
"Nobody expects the Spanish Inquisition" But if God was a Mathematician or Theoretical Physicist and wanted to summarise the whole of human knowledge, from spinors and QFD, to Quasars, in the shortest possible sentence, what would his first words be? Fiat Lux - "Be light made." - Science in Action - Heb. 11.1-3
Indeed, I saw the series, but it suddenly was terminated, I wonder why. The series was very interesting and various zeta functions were representing various physical. Once I thought all these were fake. If not I would like to read the book where all the Reiman number theory are explained if true.
So glad to see you back with another episode. This series is easily the greatest piece of mathematical media I have ever been blessed with being able to watch. Please continue with it; you are making topics that I used to feel were gatekept behind extremely advanced mathematics, a lot more accessible!
I have a question concerning your proposal that L-functions form a Hilbert space. Since adding two of them corresponds to pointwise multiplication, would this not entail raising meromorphic functions to arbitrary exponents? I don't claim to have actually checked, but finding the square root of the Riemann zeta function would likely involve branch points and branch cuts; I shudder to contemplate what it would be like to raise it to the pi-th power. It seems much more plausible to me that they form a Z-module (with additional ring structure).
Totally agree! If you look back to E6, around minute 34, this is also exactly what we propose there, saying that the "scalars" are Z rather than R or C. You can still tensor a Z-module with R or C though, but the resulting scalar operations will be of a more formal nature, not involving any shuddering or raising things to the pi-th power.
@PeakMathLandscape Thank you. I'd missed that. I've been meaning to revisit the earlier episodes. I'm particularly intrigued by the proposed inner product as well as the ring product distributive over addition. For example, I've seen that the inner product is linear with respect to the addition of L-functions.
The more I study RH, the more cross-pollination I learn about between Number theory and QFT. I'm beginning to suspect that RH's eventual proof will be something similar to the Hilbert-Polya approach. Fascinating!
I would argue that the appearance of L function values in these computations is not a sign of their fundamental nature but more of the fact that they are a great computational tool. After all, also Feynman diagrams are just a computational tool.
My favorite series. Wonderfully well constructed overview for an idiot physicist like myself that never could make any sense of mathematicians' work on number theory and L-functions 🤩🤩😍
It's interesting how you mentioned Mellin transforms of theta functions. More generally, we could consider Mellin transforms of all modular forms, and something I found a while ago along this line is that the Mellin transform of some Eisenstein series can be represented in terms of the Riemann zeta function. I say some because I only looked at a few, but it's possible that I should say all.
I also found that you can combine the multiplicative relations between Eisenstein series with the convolution theorem for the Mellin transform but it got messy so I stopped (it didn't look like it was going anywhere interesting)
21:36 Does anybody know of a good reference for theta series related to mixed L-functions besides Francis Brown's A multivariable version of the completed RZF and other L-functions (2019)? Thanks in advance... [Btw, I recall a paper by Simard: Notes on theta series (2015) that seems a nice introduction to theta series]
@@PeakMathLandscapeI thought you got busy with other works and no more interested in RH saga. Thanks for coming back. Request you to make the longer videos with more data.
Hello, I’m working on the problem of mutually unbiased bases, and it is known finite fields can be used to generate said objects. I am currently trying to use methods from algebraic geometry to investigate the relationship between projective geometries and Riemann surfaces to see if there is a clue to the problem of MUBS, (as the field extensions over the finite fields can be used to construct Galois groups which are analogous to the fundamental groups of Riemann groups thru the geometric langlands correspondence.) I wanted to know if you think there may be some merit to F1 geometry being hinted at by the Riemann sphere, as it is simply the complex projection of the projective line.
The area of a circle = PI * r^2 - however Euler showed several centuries ago that PI can be expressed as the product of all primes (with appropriate denominators). How can circles know about the distribution of primes ? This is not how the world is supposed to work!
"Nobody expects the Spanish Inquisition" But if God was a Mathematician or Theoretical Physicist and wanted to summarise the whole of human knowledge, from spinors and QFD, to Quasars, in the shortest possible sentence, what would his first words be? Fiat Lux - "Be light made." - Science in Action - Heb. 11.1-3
I wonder if this series will explain 'design of experiment'? My grandfather named Q.M.Hossain developed 'Hossain's chain rule', but we seldom hear about this statistical theory, that seems to me to be the divine design n which the chain rule achieve life and consciousness at the end of the universal experiment.
I have a weird problem with hearing that may be the reason why I understand barely anything in this series. I often hear something different from what's actually said, and that's often consistent. According to my co-creator's theory, it's because I don't want to do what they ask me to do/etc. However, if this theory is true, it's weird that my host system chose this method that would be easily circumventable if others actually wanted to convey their message. So far, I've identified the following ways this happens: - I hear non-questions as questions and vice versa; - I hear /s/ as /ts/; - I hear one sentence as multiple. I've identified the last one from this video's ending, where it completely explained the difference between what I hear and what I see. Now, I've added some rules to merge sentences, but they're not perfect. In particular, sentences with a clause put in the beginning would be merged with the previous one, and there's a case near the very beginning of this saga where this resulted in an attempt to merge on the boundary of parts
Great video, but plaese, PLEASE, stop using the AI audiotrack feature. It cannot be deactivated on mobile browwer and it is just not good enough. I imagine you care that your message comes across correctly, which is not at all guaranteed with this feature.
When I see a video from you, it's going to be a good day.
Thanks Curt! And you have really levelled up your game again and again over the past year. Loved your Penrose interview, and looking forward to the Harvard epics
Two channels that have caused my brain to activate in ways it never does anywhere else! Thank you for being awesome
"Nobody expects the Spanish Inquisition"
But if God was a Mathematician or Theoretical Physicist and wanted to summarise the whole of human knowledge, from spinors and QFD, to Quasars, in the shortest possible sentence, what would his first words be?
Fiat Lux - "Be light made." - Science in Action - Heb. 11.1-3
babe wake up! new RH Saga episode is out!
OH my god, you guys are back, good news!!!!
Indeed, I saw the series, but it suddenly was terminated, I wonder why. The series was very interesting and various zeta functions were representing various physical. Once I thought all these were fake. If not I would like to read the book where all the Reiman number theory are explained if true.
holy I just stumbled upon this about two weeks ago and now you suddenly started doing videos again? I thought christmas was last month
So glad to see you back with another episode. This series is easily the greatest piece of mathematical media I have ever been blessed with being able to watch. Please continue with it; you are making topics that I used to feel were gatekept behind extremely advanced mathematics, a lot more accessible!
I am SO THRILLED these are back and I really hope you work out a way to continue this AMAZING work. These videos are in a class of their own.
Is it me, or is every episode way more thrilling than anything on TV right now?
I adored this episode, it's one of topics which skypes my curiosity to learn more arithmetic geometry and hopefully motivic stuff as well
Thanks for another wonderful video
I second that - Thanks.
Tusen takk for videoene du lager! Fantastisk å få innsikt i disse tingene.
Takk! Det er et team bak :-)
This is peak
I have a question concerning your proposal that L-functions form a Hilbert space. Since adding two of them corresponds to pointwise multiplication, would this not entail raising meromorphic functions to arbitrary exponents? I don't claim to have actually checked, but finding the square root of the Riemann zeta function would likely involve branch points and branch cuts; I shudder to contemplate what it would be like to raise it to the pi-th power. It seems much more plausible to me that they form a Z-module (with additional ring structure).
Totally agree! If you look back to E6, around minute 34, this is also exactly what we propose there, saying that the "scalars" are Z rather than R or C. You can still tensor a Z-module with R or C though, but the resulting scalar operations will be of a more formal nature, not involving any shuddering or raising things to the pi-th power.
@PeakMathLandscape Thank you. I'd missed that. I've been meaning to revisit the earlier episodes. I'm particularly intrigued by the proposed inner product as well as the ring product distributive over addition. For example, I've seen that the inner product is linear with respect to the addition of L-functions.
great to hear about you guys!
Just found this channel. Very glad I did.
Hello and thanks for the video! What drawing app are you using on the tablet?
Notability
Very good approach to re-unite mathematics and physics. Thank you
Like Cornelius Fudge said - He's Back!
😂😂😂
The more I study RH, the more cross-pollination I learn about between Number theory and QFT. I'm beginning to suspect that RH's eventual proof will be something similar to the Hilbert-Polya approach. Fascinating!
excited to watch!
I've been waiting for you for so long...
Thanks for the video!
It's like second Christmas.
I would argue that the appearance of L function values in these computations is not a sign of their fundamental nature but more of the fact that they are a great computational tool. After all, also Feynman diagrams are just a computational tool.
To attribute antropomorphic qualities like knowledge to electrons is to perpetrate mystification and metaphysics.
This is both wonderful and crazy!
Woooo let’s go!!! 🎉🎉🎉 this one is gonna be a banger
So happy ur back
"Somehow the Riemann zeta function knows about the electron. That is not how the world is supposed to work!"
My favorite series. Wonderfully well constructed overview for an idiot physicist like myself that never could make any sense of mathematicians' work on number theory and L-functions 🤩🤩😍
FINALLY!!!!!!!!!!!!!!!!!!
It's interesting how you mentioned Mellin transforms of theta functions. More generally, we could consider Mellin transforms of all modular forms, and something I found a while ago along this line is that the Mellin transform of some Eisenstein series can be represented in terms of the Riemann zeta function. I say some because I only looked at a few, but it's possible that I should say all.
I also found that you can combine the multiplicative relations between Eisenstein series with the convolution theorem for the Mellin transform but it got messy so I stopped (it didn't look like it was going anywhere interesting)
21:36 Does anybody know of a good reference for theta series related to mixed L-functions besides Francis Brown's A multivariable version of the completed RZF and other L-functions (2019)? Thanks in advance...
[Btw, I recall a paper by Simard: Notes on theta series (2015) that seems a nice introduction to theta series]
I too am very interested in this. Thanks for the Simard reference!
@@PeakMathLandscape You're welcome...and thank you very much for this saga! Have a great 2025...and keep them coming!
I'd love to know what is the outro music and if it can be found anywhere
If you don't solve it by the end of the saga im gonna need a refund
Finally!!!!
It continues!!
why PeakMath Community has closed down?
Hi Nikolay - it's a long story. The brief version is that we couldn't get enough paying members to reach financial sustainability.
@@PeakMathLandscapeI thought you got busy with other works and no more interested in RH saga. Thanks for coming back. Request you to make the longer videos with more data.
@@PeakMathLandscape I wonder if it might be worth it if you build up a good YT follow first? I started an MSc after watching your series!
Subscribed.
your websoite is down please fix it
bro you are back
voila voila voila
Every time I watch one of your videos I regret going to medical school and not study mathematics formally
Hello, I’m working on the problem of mutually unbiased bases, and it is known finite fields can be used to generate said objects. I am currently trying to use methods from algebraic geometry to investigate the relationship between projective geometries and Riemann surfaces to see if there is a clue to the problem of MUBS, (as the field extensions over the finite fields can be used to construct Galois groups which are analogous to the fundamental groups of Riemann groups thru the geometric langlands correspondence.) I wanted to know if you think there may be some merit to F1 geometry being hinted at by the Riemann sphere, as it is simply the complex projection of the projective line.
I was there when it was written.
Prepare by watching Fermilab’s videos on magnets.
yes yes yes
Please enable UA-cam Supers.
Good idea, and thanks! Right now we only have a Ko-fi page: ko-fi.com/peakmath
The area of a circle = PI * r^2 - however Euler showed several centuries ago that PI can be expressed as the product of all primes (with appropriate denominators). How can circles know about the distribution of primes ? This is not how the world is supposed to work!
Correlation between physics and number theory does not imply causation of either by the other.
"Nobody expects the Spanish Inquisition"
But if God was a Mathematician or Theoretical Physicist and wanted to summarise the whole of human knowledge, from spinors and QFD, to Quasars, in the shortest possible sentence, what would his first words be? Fiat Lux - "Be light made." - Science in Action - Heb. 11.1-3
I wonder if this series will explain 'design of experiment'? My grandfather named Q.M.Hossain developed 'Hossain's chain rule', but we seldom hear about this statistical theory, that seems to me to be the divine design n which the chain rule achieve life and consciousness at the end of the universal experiment.
I have a weird problem with hearing that may be the reason why I understand barely anything in this series. I often hear something different from what's actually said, and that's often consistent. According to my co-creator's theory, it's because I don't want to do what they ask me to do/etc. However, if this theory is true, it's weird that my host system chose this method that would be easily circumventable if others actually wanted to convey their message. So far, I've identified the following ways this happens:
- I hear non-questions as questions and vice versa;
- I hear /s/ as /ts/;
- I hear one sentence as multiple.
I've identified the last one from this video's ending, where it completely explained the difference between what I hear and what I see. Now, I've added some rules to merge sentences, but they're not perfect. In particular, sentences with a clause put in the beginning would be merged with the previous one, and there's a case near the very beginning of this saga where this resulted in an attempt to merge on the boundary of parts
Great video, but plaese, PLEASE, stop using the AI audiotrack feature. It cannot be deactivated on mobile browwer and it is just not good enough. I imagine you care that your message comes across correctly, which is not at all guaranteed with this feature.
Thanks for the headsup! It seems UA-cam pushed this new functionality without us asking for it, and I have now tried turning it off.
How does this help humanity,?? Nothing
Subscribed!