Why can some physical laws be generalized to mathematics? Because both physics and mathematics are mappings of the objective world onto two different domains.

I even feel that physics is the transition of the objective world's mapping into mathematics.

The Ricci flow was originally an evolution equation describing the deformation of curvature, carrying intuitive imagery akin to physical relaxation flows. Hamilton first applied it to the study of three-dimensional manifolds. Perelman further refined the argument; after stripping away its physicalized evolutionary interpretation, the Ricci flow became the core tool for proving the Poincaré conjecture, a purely topological proposition.

Similarly, the Principle of Least Action was initially born in classical mechanics and optics to characterize particle motion and light propagation. After stripping away physical concretizations such as kinetic energy, potential energy, and medium refractive index, the calculus of variations developed into a pure functional tool, widely used in mathematical branches such as differential equations and optimal control.

Fourier analysis originated from the study of heat conduction and vibrating sound waves. Setting aside physical meanings like temperature and vibration amplitude, it serves as an orthogonal expansion framework and has become a fundamental decomposition method in number theory and group representation theory.

Hamiltonian systems stem from classical celestial mechanics. Removing physical contents such as mass, force, and orbits, its underlying structure evolved into symplectic geometry and Poisson structures, becoming independent objects of geometric and topological study.

The Yang-Mills equations were originally field equations in particle physics describing gauge interactions. Detached from the physical interpretations of particles and charges, they gave birth to gauge theory. Leveraging the properties of moduli spaces, it is used to distinguish the topological differences of four-dimensional manifolds.

Brownian motion was first used to explain the random diffusion of suspended particles. Erasing physical conditions such as the medium and viscous drag, this stochastic process was abstracted into martingale theory, underpinning harmonic analysis and potential theory.

The concept of entropy began in thermodynamics, characterizing the degree of disorder in macroscopic systems. Detached from the constraints of heat and temperature, it was transplanted into information theory and further extended to ergodic theory and dynamical systems to measure the uncertainty of system evolution.

Witten’s introduction of spinors originating from relativistic quantum physics into the proof of the Positive Mass Theorem constitutes another classic illustration of this lineage. Spinors were originally devised to describe spin‑1/2 particles and carry a distinct physical background; Witten extracted the differential‑algebraic structure of the spinor formalism, discarded the physical interpretation of particles and quantum fields, and employed spinors as geometric constructs on Riemannian manifolds. This yielded an elegant proof of the Positive Mass Theorem, whereby a tool rooted in physical intuition resolved a long‑standing open problem in differential geometry.

They all follow the same trajectory: first emerging in physical scenarios; once the core structure is extracted and the exclusive physical carriers are stripped away, they are transformed into universal mathematical skeletons.