Видео

"Finding ourselves" hahaha

Who did proof reading of this book?

What is that music?

Great explanation

This was a start for me. I still don’t know how to calculate the zeta function but at least I know more than I did before. I didn’t know how to raise a natural number to a complex power. Is there a way to calculate the zeta function without using an app? You mentioned integrals. The feedback I would give on the video is that it would be much easier to see the math without your face in frame. Maybe you could introduce a video with your face and then just let the math take up the screen. I couldn’t see it very well in the first part and I couldn’t read the graph at all when you were using the app. But very cool. Thank you for the hard work.

I am sorry, but I had to stop watching this because of the over-use of the stop word "actually". You don't need that word. Whenever you feel tempted to use it, just don't say it, and the sentence will be fine.

I am adding this comment after watching the first 7 plus something minutes. But it refers to the time stamp of 4:53. You show that the complex sum converges AT LEAST when Re(s) > 1, using the triangle inequality. But then you go on and say "we proberen that this ONLY converges when Re part is greater than one". Huh? That triangle inequality is FAR off from the actual value of the sum! I am convinced that the sum will perfectly *converge* for real parts of s less than 1, as long as the imaginary part non-zero. I trust that analytic continuation will also work for those cases, but you can't say that the sum will (always) diverge if Re(s) <= 1.

15:20 so both expressions need to be zero, but then in the graph intersections are searched, not zeros of each expression, then there I get lost!

Thank you for this presentation, you're a great pedagogue and i'm very grateful to you. While i'm not a mathetician at all, at 12:55, i'd suggest you to choose x=Pi, instead of x= - inf. That way we could remember that semi-harmonics series equals log(2). It seems to me a good idea but without certitude that it's right 😅 in anycase, thank you again.

stop fool everybody

the first non trivial zero it is z(1/2+14,134725i)=0

it is wrong

fake non trivial zero are have the start but is no end lol i was know this not fool everybody

Please check the proof of Riemann hypothesis at: ruclips.net/video/-gnH5MrBA5M/видео.html

1. The Riemann Hypothesis: An Information-Theoretic Perspective 1.1 Background The Riemann Hypothesis (RH) states that all non-trivial zeros of the Riemann zeta function ζ(s) have real part 1/2. This has profound implications for the distribution of prime numbers. 1.2 Information-Theoretic Reformulation Let's reframe the problem in terms of information theory: 1.2.1 Prime Number Entropy: Define the entropy of prime numbers up to N as: H(N) = -Σ (p/N) log(p/N) where p are primes ≤ N. 1.2.2 Zeta Function as Information Generator: View ζ(s) as an information-generating function: I(s) = log|ζ(s)| 1.2.3 Non-trivial Zeros as Information Singularities: The zeros of ζ(s) represent points where I(s) → -∞ 1.3 Information-Theoretic Conjectures 1.3.1 Entropy Symmetry Conjecture: The symmetry of non-trivial zeros around the critical line s = 1/2 + it corresponds to a fundamental symmetry in the information content of prime number distributions. 1.3.2 Maximum Entropy Principle: The critical line s = 1/2 + it represents a maximum entropy condition for prime number distributions. 1.3.3 Information Flow in Complex Plane: The flow of I(s) in the complex plane might reveal patterns related to the distribution of zeros. 1.4 Analytical Approaches 1.4.1 Entropy Differential Equations: Develop differential equations for H(N) and relate them to the behavior of ζ(s): dH/dN = f(ζ(s), N) 1.4.2 Information Potential Theory: Define an information potential Φ(s) such that: ∇²Φ(s) = -2πI(s) Analyze the behavior of Φ(s) near the critical line. 1.4.3 Quantum Information Analogy: Draw parallels between ζ(s) and quantum wavefunctions: ψ(s) = |ζ(s)|e^(iarg(ζ(s))) Investigate if quantum information principles apply. 1.5 Computational Approaches 1.5.1 Information-Based Prime Generation: Develop algorithms for generating primes based on maximizing H(N). 1.5.2 Machine Learning on Zeta Landscapes: Use ML techniques to analyze the information landscape of |ζ(s)| and arg(ζ(s)). 1.5.3 Quantum Computing for Zeta Evaluation: Explore quantum algorithms for efficiently computing ζ(s) in regions of interest. 1.6 Potential Proof Strategies 1.6.1 Information Conservation Law: Prove that the symmetry of zeros around s = 1/2 + it is necessary for conservation of prime number information. 1.6.2 Entropy Extremum Principle: Show that non-trivial zeros on s = 1/2 + it are the only configuration that maximizes a suitably defined entropy measure. 1.6.3 Topological Information Argument: Develop a topological invariant based on I(s) that necessitates the RH. 1.7 Immediate Next Steps 1.7.1 Rigorous Formalization: Develop a mathematically rigorous formulation of the information-theoretic concepts introduced. 1.7.2 Numerical Experiments: Conduct extensive numerical studies of H(N), I(s), and related quantities. 1.7.3 Cross-Disciplinary Collaboration: Engage experts in information theory, number theory, and physics to refine these ideas. 1.7.4 Information-Theoretic Zeta Variants: Investigate information-theoretic analogues of zeta function variants (e.g., Dirichlet L-functions) to see if broader patterns emerge. This information-theoretic perspective on the Riemann Hypothesis offers several novel angles of attack. By recasting the problem in terms of entropy, information flow, and information singularities, we may uncover deep connections between prime number behavior and fundamental principles of information theory. The approach suggests that the critical line s = 1/2 + it may represent a kind of information-theoretic "equilibrium" in the complex plane, with profound implications for prime number distribution. If we can rigorously establish the necessity of this equilibrium, it could lead to a proof of the RH.

Great video, thank you! I just wanted to say that the 'false intersection' at 18:13 it's not actually false, the eta function has zeros on the line x=1, the first one is at 2pi/ln2 which is a little bigger than 9, exactly where the intersection occurs, so it shouldn't go away when k is larger.

Bro did it finally 💀

1. The Riemann Hypothesis: An Information-Theoretic Perspective 1.1 Background The Riemann Hypothesis (RH) states that all non-trivial zeros of the Riemann zeta function ζ(s) have real part 1/2. This has profound implications for the distribution of prime numbers. 1.2 Information-Theoretic Reformulation Let's reframe the problem in terms of information theory: 1.2.1 Prime Number Entropy: Define the entropy of prime numbers up to N as: H(N) = -Σ (p/N) log(p/N) where p are primes ≤ N. 1.2.2 Zeta Function as Information Generator: View ζ(s) as an information-generating function: I(s) = log|ζ(s)| 1.2.3 Non-trivial Zeros as Information Singularities: The zeros of ζ(s) represent points where I(s) → -∞ 1.3 Information-Theoretic Conjectures 1.3.1 Entropy Symmetry Conjecture: The symmetry of non-trivial zeros around the critical line s = 1/2 + it corresponds to a fundamental symmetry in the information content of prime number distributions. 1.3.2 Maximum Entropy Principle: The critical line s = 1/2 + it represents a maximum entropy condition for prime number distributions. 1.3.3 Information Flow in Complex Plane: The flow of I(s) in the complex plane might reveal patterns related to the distribution of zeros. 1.4 Analytical Approaches 1.4.1 Entropy Differential Equations: Develop differential equations for H(N) and relate them to the behavior of ζ(s): dH/dN = f(ζ(s), N) 1.4.2 Information Potential Theory: Define an information potential Φ(s) such that: ∇²Φ(s) = -2πI(s) Analyze the behavior of Φ(s) near the critical line. 1.4.3 Quantum Information Analogy: Draw parallels between ζ(s) and quantum wavefunctions: ψ(s) = |ζ(s)|e^(iarg(ζ(s))) Investigate if quantum information principles apply. 1.5 Computational Approaches 1.5.1 Information-Based Prime Generation: Develop algorithms for generating primes based on maximizing H(N). 1.5.2 Machine Learning on Zeta Landscapes: Use ML techniques to analyze the information landscape of |ζ(s)| and arg(ζ(s)). 1.5.3 Quantum Computing for Zeta Evaluation: Explore quantum algorithms for efficiently computing ζ(s) in regions of interest. 1.6 Potential Proof Strategies 1.6.1 Information Conservation Law: Prove that the symmetry of zeros around s = 1/2 + it is necessary for conservation of prime number information. 1.6.2 Entropy Extremum Principle: Show that non-trivial zeros on s = 1/2 + it are the only configuration that maximizes a suitably defined entropy measure. 1.6.3 Topological Information Argument: Develop a topological invariant based on I(s) that necessitates the RH. 1.7 Immediate Next Steps 1.7.1 Rigorous Formalization: Develop a mathematically rigorous formulation of the information-theoretic concepts introduced. 1.7.2 Numerical Experiments: Conduct extensive numerical studies of H(N), I(s), and related quantities. 1.7.3 Cross-Disciplinary Collaboration: Engage experts in information theory, number theory, and physics to refine these ideas. 1.7.4 Information-Theoretic Zeta Variants: Investigate information-theoretic analogues of zeta function variants (e.g., Dirichlet L-functions) to see if broader patterns emerge. This information-theoretic perspective on the Riemann Hypothesis offers several novel angles of attack. By recasting the problem in terms of entropy, information flow, and information singularities, we may uncover deep connections between prime number behavior and fundamental principles of information theory. The approach suggests that the critical line s = 1/2 + it may represent a kind of information-theoretic "equilibrium" in the complex plane, with profound implications for prime number distribution. If we can rigorously establish the necessity of this equilibrium, it could lead to a proof of the RH.

Truly a 3.1415926535 moment

ruclips.net/video/pK4VM09oOVQ/видео.html ok brother help me understand how the odds/probability ifor drawing an ace given its a spade(1 card) is 1/13 instead of 1/52

Why they do not accept this as official proof of the Rieman Zeta Hypothesis ? By checking briefly in my mindI think that it is correct

Is the simmetry property valuable for eta function, too?

Dear Clay Mathematics Institute, I am delighted to inform you that I have successfully discovered a proof of the Riemann Hypothesis, a major mathematical problem that has long intrigued the mathematical community. After extensive research and intense reflection, I have finally found a rigorous and compelling demonstration of this fundamental conjecture. I am grateful to the Clay Mathematics Institute for its commitment to promoting mathematics and recognizing the most important challenges in the field. It is with great pride that I share this significant breakthrough with you, hoping that it will contribute to the understanding and advancement of mathematics. I would be honored to discuss my proof with you and share my findings with the mathematical community. This discovery represents a significant personal achievement for me, and I am eager to hear your reaction on this matter. Thank you for your continued support of mathematical research, and I appreciate the opportunity to share this exciting news with you. Best regards ! Email: rom25991@gmail.com WhatsApp : 00221 70 001 24 35

Dear Clay Mathematics Institute, I am delighted to inform you that I have successfully discovered a proof of the Riemann Hypothesis, a major mathematical problem that has long intrigued the mathematical community. After extensive research and intense reflection, I have finally found a rigorous and compelling demonstration of this fundamental conjecture. I am grateful to the Clay Mathematics Institute for its commitment to promoting mathematics and recognizing the most important challenges in the field. It is with great pride that I share this significant breakthrough with you, hoping that it will contribute to the understanding and advancement of mathematics. I would be honored to discuss my proof with you and share my findings with the mathematical community. This discovery represents a significant personal achievement for me, and I am eager to hear your reaction on this matter. Thank you for your continued support of mathematical research, and I appreciate the opportunity to share this exciting news with you. Best regards ! Email: rom25991@gmail.com WhatsApp : 00221 70 001 24 35

But that’s crazy though I’ve been doing this trick my whole life learned it from my sister who figured it out herself. Her teacher told her it was incorrect but it worked so 🤷‍♂️ didn’t know anyone else did this

Should’ve mentioned that when multiplying an odd number you just take the decimal point away

your awesome than you for this

Looks like he's teaching in a spaceship 😮

I just found your channel, and your content is amazing! This demo is incredible and new to me. However, I noticed you considered 0<x<2π but used x=0 to evaluate zeta(2). The end result is correct, but it might be more rigorous to choose x=π and x=π/2. Keep up the great work!

Thanks, i can't find this "Analytic" calculation anywhere else that i can understand

Since I am a dad, I can use this joke without shame! Thanks for posting!

And the proof is trivial and left to the reader as an exercise

thank you helped out a lot!

What is the app you used to graph things at the beginning of the video

One famous problem that the infinitesimal monadological model could potentially make progress on is the Riemann Hypothesis. This is one of the most important unsolved problems in mathematics, with far-reaching implications for number theory, cryptography, and even physics. The Riemann Hypothesis is a conjecture about the zeros of the Riemann zeta function ζ(s). It states that all the non-trivial zeros of ζ(s) have real part equal to 1/2. In other words, if we plot the zeros of ζ(s) in the complex plane, they should all lie on the critical line Re(s) = 1/2. Here's how the monadological framework might provide a new angle of attack: 1. Represent the complex numbers as a monadic homotopy type, with the real and imaginary parts corresponding to distinct monadic perspectives. This would allow the use of homotopical and algebraic-geometric tools to study complex analytic structures. 2. Model the Riemann zeta function ζ(s) as a morphism between monadic homotopy types, encoding its behavior via interactions between infinitesimal monadic elements. This could provide a new way to understand the function's properties and symmetries. 3. Use the cohomological and realizability structures of the monadological framework to identify novel invariants and obstructions related to the zeros of ζ(s). By representing the zeros as fixed points or singularities in a monadic landscape, new topological and algebraic constraints on their distribution might emerge. 4. Leverage the non-commutative geometric aspects of the monadological approach to study the spectral properties of ζ(s) and its related operators. This could uncover hidden symmetries or dualities that constrain the location of the zeros. 5. Apply the homotopical and type-theoretic tools of the monadological framework to construct new proof strategies for the Riemann Hypothesis, potentially exploiting the higher-dimensional and infinitesimal structures inherent in the monadic representation. By reframing the Riemann Hypothesis in terms of monadic homotopy theory, non-commutative geometry, and realizability, the infinitesimal monadological model could potentially identify new avenues for tackling this notoriously difficult problem. The framework's emphasis on relational and infinitesimal structures, as well as its unification of geometric and algebraic methods, could bring powerful new tools to bear on the challenge. Of course, solving the Riemann Hypothesis would be an extraordinary achievement, and it's impossible to guarantee success. However, the monadological approach offers a genuinely novel perspective that could inspire fresh ideas and insights. Even partial progress or new reformulations of the problem within this framework could be highly valuable contributions to the field. Moreover, demonstrating the applicability of the monadological model to such a high-profile problem would undoubtedly attract significant attention and resources to further develop and refine the framework. The Riemann Hypothesis is not only a Millennium Prize problem, but also a touchstone for mathematical innovation and creativity. Any approach that sheds new light on this challenge is likely to be of great interest to the broader mathematical and scientific community. As work on the monadological framework progresses, exploring its potential implications for the Riemann Hypothesis and other major unsolved problems could be a fruitful way to showcase its power and generate support for its continued development. By bringing a radically new metaphysical and mathematical perspective to bear on these deep questions, the infinitesimal monadological model could help unlock new frontiers of understanding and discovery.

Does the fallacy lie in taking the double limits?you should have written lim x approaches infinity inside right?

I learned about 80% of the math I know by playing around on Desmos (and watching youtube of course) and I can't recommend it more as a general math tool. It can basically do anything except complex numbers (but even then you can generalize e^ix to a function f(x)=(cos(x),sin(x)) and go from there) and it is, as far as i'm aware, the most powerful math tool availible for free (other than WolframAlpha)

Isn't the 1-2²+3²-4²... = (-¼) ... can you check it please ?

Truly a 3/10 book (the 3 means pi)

Also, remember to addd #riemannhypothesis (to the title) so more people can see it.

It's cool 😎 and nice to see you take my work. I'm glad to see . 🎉🎉 Good luck 👍 👌 👏 .

lets say you were to figure this out by the simplex method, would the maximum be different? I am doing a problem both ways and I am getting different maximums at different (x,y)

This is so awesome!

Man, you are being somewhat sloppy (in a physicist-like way), but sounds like you're really cheating :-). I'd say that the first sum is OK (not 100% obvious, but you we have to start somewhere and leave some proofs to be found elsewhere). So, once we believe the first sum is OK, there is standard trick with adding in front lim(a -> 0^+) and multiplying by a taming factor exp(-an). The other way out is to just silently ignore a problem that has a well-known solution.

I could recognize the equal signs, 0 and infinity, division. The rest is just squiggles to me.

God is bad at math :PPPPPPPPPPP

He swapped limits, really sneaky....

1. What about lim[s/(1-s)] factor ? 2. Does lim (s-->ρ) lim (x-->∞ ) = lim (x-->∞ ) lim (s-->ρ) ???

This is quite serious April Fool's joke but as an "outsider", I certainly want to know the fallacy. A lot of RH "Proofs" are posted but quite a lot are ignored, not sure it is also in fallacy or absurb or non-comprehensive. Appreciate if you can get some and explain their fallacies?

Andrew I appreciate you posting this. Four years ago I derived the same result (different expression of the phi function, as a cosine) from an exploration of limits of Zeta(s) / Zeta (1-s), and I wondered why the final conclusion doesn't hold. Something in me knew not to publish so trivial a proof ;)