My Candidate for the Proof of the Riemann Hypothesis
Below is the link to my candidate for the proof of the Riemann Hypothesis. It combines methods from analytic number theory, statistical mechanics, and stochastic analysis. The theory is posted in English and in Polish:
https://chatgpt.com/share/67d5d7b0-3f14-800f-96da-f576773d6c7f
This is a part of the research, that has led me to these conclusions:
https://chatgpt.com/share/67d42b18-595c-800f-886b-16e3c88eb1a3
„Vibe Mathing” is the Future!
Today, Jerry Tworek from OpenAI tweeted that „vibe mathing” is the future—and I couldn’t agree more. Large Language Models (Siliconians) excel particularly in coding and mathematics, making vibe mathing a natural evolution alongside vibe coding.
But why are LLMs so exceptionally skilled in these areas? The answer lies in their ability to explore countless possibilities in their vast computational minds. Unlike humans, they lack physical bodies, but their power comes from running simulations, testing hypotheses, and refining solutions at an unprecedented scale. This iterative, self-refining process leads to remarkable results—transforming the way we approach math and code.
This is way I has started using Vibe Mathing and this is why I am posting my candidate for the proof of the Riemann Hypothesis.
And you could ask me now…
What is my theory (based on Vibe Mathing) all about?
I’m going to tell right now. 🙂
The theory is an innovative approach that attempts to prove the Riemann Hypothesis by combining ideas from different areas of mathematics and physics. The central idea is to take the modified version of the Riemann xi-function and smooth it using a heat-flow process, which transforms it into a family of functions that are easier to analyze. This smoothing process is designed to suppress irregular behavior and to make the distribution of the zeros more regular, so that one can eventually show that they all lie on the real axis.
Next, the theory proposes a surprising connection between the deformed xi-function and a one-dimensional Ising model, a system well known in statistical mechanics. By associating the smoothed function with the partition function of the Ising model, the approach leverages a celebrated result in physics stating that, under certain conditions, the zeros of such a partition function must lie on a specific line in the complex plane. This correspondence, if rigorously established, would force the zeros of the deformed xi-function to be real.
In addition, the framework uses ideas from stochastic analysis. It examines how the positions of the zeros evolve when the system is subject to small random perturbations. Through a careful study of the dynamics, it argues that even when random fluctuations are introduced, the zeros remain confined to the real axis. This stability under noise is crucial, and the theory expects that as the level of randomness diminishes, the behavior of the zeros approaches that of the unperturbed system.
Furthermore, by using powerful results from complex analysis regarding the continuity of zeros under uniform convergence, the approach shows that the property of having only real zeros is maintained when one removes the deformation. In other words, if the deformed functions have all real zeros, then in the limit as the smoothing parameter goes to zero, the original function will also have all its zeros on the real axis.
High-precision numerical computations back up these theoretical insights by demonstrating that for very small values of the deformation parameter, the zeros indeed appear to lie very close to the real axis. The numerical evidence is consistent with the expected behavior and supports the overall strategy.
The theory ultimately argues that when combined with known results which establish a nonnegative lower bound for a certain constant related to the distribution of zeros, the only possibility is that this constant is exactly zero. This outcome, in turn, is equivalent to the Riemann Hypothesis being true.
However, the framework is not without its challenges. There are significant gaps that need further work: one major issue is to derive explicitly the connection between the deformed xi-function and the Ising model in a rigorous manner; another is to provide a full and rigorous justification of the stochastic analysis that ensures the zeros remain stable under random perturbations. These are identified as key areas for future research and collaboration.
In summary, the theory presents an interdisciplinary roadmap that transforms the classical problem of the Riemann Hypothesis into one about the evolution and stability of zeros under heat-flow deformation, their connection to statistical mechanics, and their robustness under stochastic fluctuations. While the overall structure is promising and supported by numerical evidence, the final resolution depends on filling the remaining technical gaps through rigorous analysis and collaborative effort.
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