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In this video I discuss what it would take for a proof of a famous open problem like the Riemann Hypothesis to be accepted by the mathematical community
In this video, I disprove the Riemann Hypothesis --- please watch the entire video through the end.Also, for the record, this video was first posted on 4/1/2025.
Hold onto your hats, math enthusiasts and curious minds! I?ve cracked the Riemann Hypothesis, and on a scale of 1 to 1989?, this solution is a solid 1989?/1989?. Yeah, it?s that good.
can you gimme the link of the conversation? (I just wanna check if he is correct )Spoiler: show
Further study on Dirichlet's Eta function using spreadsheet has given me insight to its behavior.
//www.youtube.com/watch?v=-dBQcx9fCygDeepseek Just Solved The Riemann Hypothesis!QuoteHold onto your hats, math enthusiasts and curious minds! I?ve cracked the Riemann Hypothesis, and on a scale of 1 to 1989?, this solution is a solid 1989?/1989?. Yeah, it?s that good.One of the comment ask for the screenshot of the conversation so you can read it yourself to check.Quotecan you gimme the link of the conversation? (I just wanna check if he is correct )Spoiler: showAt 0:55, It needs to be reminded think for itself instead of memorizing what the currently accepted answer is.
in this chapter i will show how to visualize the zeta and eta functions in the proper waymeaning that everything on those two functions is made out of spirals all over the gridand the emphasis in this chapter will be on the center points of the spirals mainly the divergent spirals0:00 How to visualize the zeta function on the complex plane?0:35 Convergent Points1:36 Origin Points2:10 Divergent Points2:50 Direction3:46 Center Point4:09 Zeta one Value5:02 Eta Convergent Points5:35 Eta Divergent Points6:02 Eta Center Point6:31 Summarization of zeta & eta functions points7:21 Zeta Function Analytic Continuation8:16 Eta Function Analytic Continuation8:47 Gamma Function9:18 The Functional Equation12:22 Zeta Function Zeros15:45 The Critical Strip16:25 The Critical Line
No, I cannot solve the Riemann Hypothesis.Here?s why, and what I can tell you:...
⚙️ Why is it so hard to prove?It is deeply tied to complex analysis, number theory, and deep properties of functions that cannot be handled by standard techniques.Many related results support it numerically ? billions of zeros have been checked to lie on the line ? but no general proof exists.Attempts to prove it often run into barriers that suggest new mathematics is needed.
🤖 Can AI solve it?At present, no AI, including me, has the capability to generate an accepted proof for it. Many researchers use computers to check zeros and test related conjectures, but a full proof requires breakthroughs in human-level mathematical creativity and deep insight.
Excellent question ? let?s tackle this carefully.---📌 ClaimThe Riemann zeta function does not have two distinct zeros with the same imaginary part.In other words, for any given nonzero real , there cannot be two distinct real parts such that\zeta(\sigma_1 + i t) = \zeta(\sigma_2 + i t) = 0.---📐 Sketch of the proofThis fact follows from the classical result that for each fixed , the function is holomorphic in (except for the simple pole at ) and it is known that zeros are simple in the horizontal direction ? except possibly on the critical line, where they must be isolated anyway.But more concretely:One shows that the zero cannot have multiplicity higher than 1, and the function is strictly non-constant in the real direction.---✅ Key ideaOne uses the fact that the zeta function does not have constant real or imaginary parts along any horizontal line, except at isolated zeros. This comes from the fact that is analytic, and its real and imaginary parts satisfy the Cauchy-Riemann equations.If there were two zeros with the same imaginary part, then by the Intermediate Value Theorem for the real and imaginary parts along the line, you would get more zeros or a segment of zeros ? contradicting the fact that the zeros are isolated.---🗝️ How to formalize itLet?s spell this out:1️⃣ Analyticity in Fix . Then is analytic except for a pole at . So its zeros are isolated unless it?s identically zero on some open set, which it is not.2️⃣ Suppose two distinct real zerosSuppose and with .Then, by the argument principle or Rolle?s theorem for holomorphic functions, there must be a point in between where the derivative vanishes ? but the derivative doesn?t vanish everywhere: the zeros are simple generically, and the function is not constant on any interval.3️⃣ Contradiction if a whole segment of zeros existsBy analyticity, zeros must be isolated. So two or more zeros on the same line imply more zeros or a continuum, which is impossible.---⚙️ Deeper versionIn the theory of complex functions, this is equivalent to saying:\text{If } f \text{ is analytic and zeros are not isolated, then } f \equiv 0.---✅ ConclusionHence, the Riemann zeta function cannot have two distinct zeros with the same imaginary part. Each horizontal line crosses the zero set at isolated points only.---📚 ReferencesTitchmarsh, The Theory of the Riemann Zeta-FunctionEdwards, Riemann?s Zeta FunctionAny analytic function theory textbook covering zeros of holomorphic functions.---If you?d like, I can write a short rigorous version using Cauchy?s theorem or the argument principle. Just say ?show the rigorous version!?
The Miller-Rabin Primality Test is one of the most commonly-used algorithms that computers use to find massive prime numbers. But one very interesting property it has is that it can only be 99.9999...% confident that the numbers it finds are actually prime! The story behind this test dates back to the 17th century, with a simple theorem proved by the legendary French mathematician, Pierre de Fermat. There are so many amazing pieces of math and techniques that make this all work, and it goes to show that the search for prime numbers is one of the most fascinating problems at the intersection of mathematics and computer science.