The difference is that an algorithms patent is a patent on a mathematics; a patent on a drug is not a patent on a law of nature. That is why software patents try to make clever end-runs around the restrictions on patents by saying things like, "...on a computer."

Could you patent the application of a law of physics/chemistry, where a new one discovered? Or could Feynman have patented using Feynman diagrams to visualize interactions between particles?

In principle, no. They are laws of nature and therefore not subject to patentability.