I don't have a lot of experience with physics beyond minimal potential energy and forces. I recently saw cool proofs in geometry using physics, such as Fermat-Torricelli point. The proof appears here in pages 4,5 http://www.cmi.ac.in/~vipul/olymp_resources/olympiadarticles/geometricoptimization.pdf
Is there a way to make those proofs mathematically formal?