"Understanding" involves Networking Concepts and Theories, e.g. within a mathematics area and between areas (Algebra and Geometry: from Descartes and Galois to Klein and beyond, e.g. Noether & Langland). Such a higher level of understanding, is advocated (pioneered?) by Andre Weil’s "Power of Analogy", with contributions from Simone Weil, in connection with the "Number Field / Function Field Analogy". We use such analogies to substantiate the tower of theories: Geometry, Homotopy Theory and Dynamics, as a background for understanding Lagrangian Mechanics vs. metric geometry, towards grasping in a simpler way Noether Theorem relating groups of symmetry and conserved quantities in Physics. This is another use of Galois Principle, as explained in a previous talk on Programs in Mathematics and Physics. The presentation is at an undergraduate level, with pictures available YouTube’s author channel, part of the zoom recording of the talk.