Our Commitment to the 7 Millennium Problems

1. P ≠ NP?

SynaptikOne explores computational and AI-based methods to clarify the boundary between problems that can be verified and those that can be solved. Goal: move closer to a proof and strengthen global cybersecurity through advances in cryptography.

2. The Riemann Hypothesis

We develop numerical tools to analyze the zeros of the zeta function and approach an experimental resolution, with implications for number theory and cybersecurity.

3. Navier–Stokes Equations

Through numerical simulations and deep learning, we study turbulence and fluid stability in order to contribute to the existence of global solutions.

4. The Birch and Swinnerton-Dyer Conjecture

SynaptikOne investigates elliptic curves and post-quantum cryptography to uncover hidden structures behind this conjecture and strengthen future security systems.

5. The Hodge Conjecture

Our research combines geometry, topology, and neural networks to develop new approaches and move toward a solution to this fundamental problem in modern mathematics.

6. The Poincaré Conjecture (Solved ✅)

Solved by Grigori Perelman in 2002 (officially confirmed in 2003). Our role: popularize this breakthrough, integrate it into our educational tools, and use it as a source of inspiration for future generations of researchers.

7. Yang–Mills Theory and Mass Gap

SynaptikOne develops mathematical and physical models to bring innovative contributions to this key question of modern physics, essential for understanding fundamental particles.

To learn more about our research on the 7 Millennium Problems and follow their development, check out our research packages or contact us via the Contact page.