The article gives tons of good reasons to believe and there are many more.

1. Numbers work completely reliably. They let us build bicycles and canals and the Internet and picture frames and...

2. There is a broad and deep philosophical foundation to numbers that dates back thousands of years and has withstood several storms and come back even stronger.

3. Even non-human creatures are governed by numbers. You never for example see three adult swans together without conflict. Crows can count as high as seven.

When I got to the bit about "the difference between mass and volume", well, to be honest I believe you're being deliberately difficult.

Every grown up understands that some "big" things "weigh less". I can carry three big bags of paper to recycling, or two smaller bags of glass.

And what's your theory aside from "numbers don't exist"? You don't say.

Mathematics is a beautiful and elegant thing that humans have worked on since the dawn of time. To say, "It doesn't exist, and my argument is I don't understand it," is insulting to those of us who love it.