Is Math Invented or Discovered?
The answer, as usual, is both, and the answer, as usual depends on how we define the terms of the question. Mathematics is a formal structure, or more accurately it is several formal structures - a tremendous number, in fact. An infinite number? Some of these formal structures are very closely related and resemble each other closely. Others are more distant. Some formal structures are close enough to each other that it can be very difficult to distinguish between them. The progress of human mathematics can be understood as humans getting better at distinguishing between formal structures. Indeed, that is what is meant by "formal": informally, we may use concepts in a loose way, which may change from one meaningful context to another, and people will still generally be able to understand each other about a great variety of topics. Indeed, a poet might borrow terms from different areas of life and use them freely and creatively, in combinations that have ne...