Algebraic geometry offers a powerful framework for approximating complex structures in the sciences. This manifests itself in the study of dynamical systems, statistics, and optimization, often in collaboration with physics. On one hand, algebro‐geometric invariants of (semi)‐algebraic sets quantify intrinsic complexity; on the other hand, computational methods from tropical and numerical algebraic geometry provide effective tools for analysis. In this talk, we explore the interplay between algebraic geometry and its applications by developing novel algorithms that not only compute these invariants more efficiently but also connect classical theory with cutting‐edge computational techniques. Our work aims to open new pathways for applications through interdisciplinary investigation while deepening our theoretical understanding. We target fostering synergies that bridge abstract mathematics with real‐world scientific problems.