How do they study the mathematics of nature ? Apparently there is mathematic of oceans and waves? How and what do they study mathematically?
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Any time you have a pattern, or any time you can identify some force that acts on a system, you have math. The math part is just relating that math to the math you already know. All math is is the idea that the same patterns show up in lots of different systems, and that it’s useful to study those patterns in their own right. Then, when you can find patterns in one system, you can use everything you’ve learned about the patterns to immediately tell you a lot about that system.
To address your specific example: a mathematical pattern called the [wave equation](https://en.wikipedia.org/wiki/Wave_equation) turns out to describe lots of different things: waves in water, vibrations in a drum, the behavior of light, and the behavior of an electron in an atom. We know a lot about the wave equation, so any time we can show that a system seems to be described by the wave equation, we can instantly apply everything we know about the wave equation to that system.
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