How mathematics supports science principles?

Answer 1

This is a very broad question, so I'll try to cover all bases.

Scientists rely on math when they see patterns. For example, if I drop my pen, it always falls in the same manner with the same acceleration. By using math scientists have found a way to give concrete numbers that they can analyze and use to make further conjectures.

In and of itself, math does not support scientific principles. Math is just a way for scientists to express what happens. If some event shows a mathematical relationship between two or more variables, then scientists will tend to use whatever equations they find to fit what has happened. Sometimes these equations are completely wrong, or only work for a certain set of circumstances. (For example, Newton proposed some ideas about gravity that work fine on earth but break down in large scale.)

Basically, math is just a tool for scientists to show consistancy and patterns.