Mathematicians use the universe to think about math; physicists use math to think about the universe. Most physicists don't "understand math" in a way that a m

Mathematicians use the universe to think about math; physicists use math to think about the universe. Most physicists don't "understand math" in a way that a mathematician would recognize, but rather use math as a natural language (with all the dialectical oddities that implies) to help us think about physical reality. When we get too enamoured of the math, we go off the rails, because the universe isn't very good at math and doesn't obey most equations very well (thus the reason most wave equations require us to throw away half the mathematically allowed but physically forbidden solutions from of the off, for example.) This is why the search for "naturalness" has been such a loser. Elegance and naturalness are attributes of our descriptions, not attributes of the universe we describe. Newton's laws aren't in any sense "natural": they are counter-intuitive and weird. Einstein's equations even moreso. Mathematically-minded physicists convince themselves of the "naturalness" of these descriptions and go out seeking the same quality, but they fail to realize that it is something that is bolted on afterwards. Using it is a guide will very rarely work (the Dirac equation is arguably the one time it ever has, which is an equation that actually seems to describe the universe without any extra bits left over.)