Thank you. I didn’t edit my post and have no idea where you saw “empirical math,” so I was as confused as you were. I did however realize that a way of exploring mathematical concepts can be scientific. Using existing rules of math like algebra or calculus has led to us discovering new ways to use math and even new mathematical concepts. The process of long dead mathematicians discovering things like geometry and calculus was scientific in that they had a hypothesis based on past details and measurements, tested it, and found it applied to the real world. Math itself is a construction that doesn’t constitute science, but science can be done in the field of mathematics. This is because science is fundamentally a process.