How can mathematics be “theoretical?”
In: Mathematics
Mathematics doesn’t depend on the physical limitations of the real world. All that matters is that it’s consistent with itself. Think of it like a game: you make the rules, and then you discover what you can do with them. Sure, math can be used to describe and model real world phenomena, but by itself math is an abstract world separate from the real world.
A lot of mathematics describes things that don’t actually exist. In fact, most mathematics do. For example, the way a mathematician describes a line is impossible. A mathematical line has 0 width, yet any physical representation of a line has at least some width, even if it’s pretty small.
Some approximations (like the line one) are pretty realistic and don’t effect things much, so a lot of the reasoning about mathematical lines applies just as well to real lines, so it’s harder to see where the theoretical comes in. But there are also branches of math that have absolutely no relation to “real” objects or phenomena. It’s hard to give examples of such things at an eli5 level, since they are very far outside what a nonmathematician would ever think about.
Simplistically put (like you’re five) theoretical math consists of “what if” things that can’t exist in the real world. One of the most famous examples of theoretical math is probably Einstein’s theory of special relativity. This describes how objects traveling at the speed of light would behave, in a universe with no mass.
Theoretical Math can become applied math as scientific advances make equipment available. One example would be the theory of gravity as waves, which (I believe) was another of Enistein’s theories.) was eventually put to the test by Robert L.Forward who used the theoretical math to design the rotating cruciform gravity gradiometer or ‘Forward Mass Detector’.
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