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Mathematics and all sciences existed before man and without man.
People discover only what has already existed and still exists.
A human is a part of Nature and a biorobot.
Mathematical theories are fantasies. Fairy tales.
Any mathematical theory implicitly begins with the words ” Imagine a world in which such and such laws apply and we will understand what is possible and what is not possible in such a world.” Mathematicians have invented many such worlds, and in each one you can endlessly build new statements and try to test them.
Sometimes made-up worlds are exactly the same as parts of the real world. Then they become a tool of the natural sciences.
No one can definitely answer this question correctly. There are many different points of view on the ontological status of mathematical objects and mathematical laws. Some people think that mathematics is a tool, a language invented by humans, which is well suited for describing certain processes and phenomena in nature. Others, starting with Plato, believe that mathematical objects actually exist in a certain “world of ideas”, and mathematicians only discover it with the help of their minds. There is also a radical point of view (Max Tegmark, the mathematical Universe hypothesis) – there is nothing but mathematics, and all consistent mathematical structures exist physically. Some of the mathematical structures are so complex that they subjectively perceive themselves as existing in the real world. We are just such a complex mathematical structure. There is also a religious point of view (which was held, for example, by Galileo) – God wrote the “Book of Nature” in the language of mathematics (he created the world with its help), which is why all the fundamental physical laws are so well described with the help of mathematics. How it really is – no one knows, there are only different points of view on this matter
Mathematics does not make discoveries, it only theorizes (assumes). Some physical, biological, chemical, or mechanical regularities. Naturally, there are lots of regularities in mathematics itself, but they usually don't go any further than paper. Therefore, theorists are scientists in so far as their entire significance is only on a piece of paper.
I apologize for the short answer.
It is probably more accurate to call mathematics not a science, but a language for describing the natural sciences.
I also highly recommend Wigner's short essay ” On the Incredible Effectiveness of Mathematics in the Natural Sciences.” Read it, you won't regret it.
Mathematics is the same science as the rest. Of course, there are still unsolved problems and unknown methods of solving them. It doesn't surprise you that there are discoveries in physics, does it? Why can't they be found in mathematics?