You are observing the evaluation map ev_p: C(M, R) -> R, ev_p(f) = f(p), is a ring homomorphism. In that spirit, you might find this Terry Tao article on the Yo

You are observing the evaluation map ev_p: C(M, R) -> R, ev_p(f) = f(p), is a ring homomorphism. In that spirit, you might find this Terry Tao article on the Yondea lemma interesting: https://terrytao.wordpress.com/2023/08/25/yonedas-lemma-as-an-identification-of-form-and-function-the-case-study-of-polynomials/ https://terrytao.wordpress.com/2023/08/25/yonedas-lemma-as-a...