Mathematics is not the study of numbers, but the relationships between them
- Henry Poincaré
I want to stress this because I think you have too rigid of a definition of math. Your talk about optimization sounds odd to me as someone who starts with math first. Optimization is done with a profiler. Sure, I'll also use math to find that solution but I don't start with optimization nor do I optimize by big O.
Elegance is not first. First is rough. Solving by math sounds much like what you describe. I find my structures, put them together, and find the interactions. Elegance comes after cleaning things up. It's towards the end of the process, not the beginning. We don't divine math just as you don't divine code. I'm just not sure how you get elegance from the get go.
So I find it weird that you criticize a math first approach because your description of a math approach doesn't feel all that accurate to me.
Edit: I do also want to mention that there's a correspondence between math and code. They aren't completely isomorphic because math can do a lot more and can be much more arbitrarily constructed, but the correspondence is key to understanding how these techniques are not so different.
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Elegance is not first. First is rough. Solving by math sounds much like what you describe. I find my structures, put them together, and find the interactions. Elegance comes after cleaning things up. It's towards the end of the process, not the beginning. We don't divine math just as you don't divine code. I'm just not sure how you get elegance from the get go.
So I find it weird that you criticize a math first approach because your description of a math approach doesn't feel all that accurate to me.
Edit: I do also want to mention that there's a correspondence between math and code. They aren't completely isomorphic because math can do a lot more and can be much more arbitrarily constructed, but the correspondence is key to understanding how these techniques are not so different.