What kind of science is in mathematics?

Math is not science. Math is a system of logic applied to numbers. Science is a system of logic applied to observed phenomena, sometimes using math to describe what is observed.

It is important to remember that math is valid only when it describes reality. Many scientists forget that principle. For example, it is possible to prove the Earth is at the center of the universe using math. The math got so complicated that they eventually adopted the sun-centered model, especially after Isaac Newton used math to explain gravity. But Mr. Newton's math does not perfectly describe reality. For one thing, any analysis of a three body system always leads to one of the bodies being thrown out, but in reality that does not happen. So astronomers are still looking for a better way to describe the universe. Here is one alternate theory: www.thunderbolts.info/wp/daily-tpod/