<ul><li>A mathematical exploration journey has led to the discovery of a new diagnostic toolset for deep open problems in mathematics, including the Birch and Swinnerton-Dyer Conjecture and the Navier-Stokes equations.</li><li>The study proposes a new summation function over rational points to extract structure and investigate the connection between the number of rational solutions on an elliptic curve and the behavior of an L-function.</li><li>The research also applied the same summation-divergence idea to synthetic scale-sensitive velocity fields related to the Navier-Stokes equations, revealing underlying structure in fluid flows, potentially even in turbulent systems.</li><li>This work, starting from curiosity and basic questions, led to the development of a versatile toolset that could offer insights into various mathematical and physical domains, emphasizing the importance of curiosity in exploring unsolved problems.</li></ul>

Have We Reshaped Our Approach to Some of Math’s Hardest Problems?

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