If you thought that science was certain - well, that is just an error on your part.

To not know math is a severe limitation to understanding the world.

If an apple was magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.

If it disagrees with experiment, it's wrong.

We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on.

Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.