I read that homology, cohomology, and simplex emerged due to physical motivation on our country's blog. However, I cannot attach a link because my country is not an English-speaking country. For example, the author explains De Rham cohomology among cohomology.
Stokes' theorem and Gauss's divergence theorem came purely from the equations for magnetic field induction by current and magnetic flux due to charge, respectively. Extending this to higher dimensions is Stokes' theorem on generalized manifolds. This is where the concept of De Rham cohomology came from.
The author explains as above. And I especially want to know about simplex. I know that the basis of simplex appeared in Poincaré's Analysis Situs. And, motivated by this curiosity, I looked up simplex on Google, and it turned out that a person named Clifford contributed to the emergence of the concept of simplex before Poincaré.
The concept of a simplex was known to William Kingdon Clifford, who wrote about these shapes in 1886 but called them "prime confines". Henri Poincaré, writing about algebraic topology in 1900, called them "generalized tetrahedra". In 1902 Pieter Hendrik Schoute described the concept first with the Latin superlative simplicissimum ("simplest") and then with the same Latin adjective in the normal form simplex
And this person named Clifford also contributed to physics, and I wondered if this person was the person who contributed to the physical idea of simplex.
I would really appreciate it if you could answer about the physical motivation of the simplex.