Roger Penrose – Is Mathematics Invented or Discovered?

Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision.
So is mathematics invented by humans just like chisels and hammers and pieces of music? Or is mathematics discovered—always out there, somewhere, like mysterious islands waiting to be found?
Whatever mathematics is will help define reality itself.
Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects. These objects are either abstractions from nature (such as natural numbers or lines), or (in modern mathematics) abstract entities of which certain properties, called axioms, are stipulated.
There are 4 types of math, algebra, geometry, calculus, and statistics and probability. Those are the four main branches.