I don’t think math makes those kinds of predictions. There are certainly cases, though, where someone worked out certain kinds of mathematics as a theoretical exercise, and then we only later discovered real world applications that the math described.
Math is a structured “precise” terse way of thinking that allows models to be built of the physical world. The models are built using known physical facts and as well as assumptions (depends on the problem!). Its true you don’t need the physical world to build “models” (pure mathematics) but its often the motivator. Back to mathematics modeling the physical world, quite often in manipulating the equations (model) new possible “physical properties” which you can (hopefully) design an experiment to test, example neutrinos. Right now given our current level of knowledge & engineering capability we have situations particularly in cosmology where no experiment can be designed. So do we stop? Throw up our hands and say we give up! No because continued thinking building on past knowledge and “manipulation” as some put it will eventually (hopefully) to a way to do an experiment that might tie it all together. Even if the “manipulations” produce nothing in the near term except mathematics quite often that math finds uses in other fields. For example George Boole’s effort to model “thinking” produced Boolean Algebra, try doing a computer design without it!. Abstract algebra existed in many forms prior to computers but you need parts of it for compiler design. Consider Topology there’s a esoteric mathematics field - sub-discipline of it graph Theory useful for power engineering and anything where connecting things together subject to constraints is necessary. Even some String Theory ideas are finding useful application in theoretical materials science. I could go on!