Ethan veers into reductionism when talking about “the scientific method” in general, but is surprisingly anti-reductionist when talking about the math. Interesting.
No, The Universe Is Not Purely Mathematical In Nature, by Ethan Siegel:
In some ways, it’s a lesson that every physics student learns the first time they calculate the trajectory of an object thrown into the air. How far does it go? Where does it land? How long does it spend in the air? When you solve the mathematical equations — Newton’s equations of motion — that govern these objects, you don’t get “the answer.” You get two answers; that’s what the mathematics gives you.
But in reality, there’s only one object. It only follows one trajectory, landing in one location at one specific time. Which answer corresponds to reality? Mathematics won’t tell you. For that, you need to understand the particulars of the physics problem in question, as only that will tell you which answer has a physical meaning behind it. Mathematics will get you very far in this world, but it won’t get you everything. Without a confrontating reality, you cannot hope to understand the physical Universe.