[FOM] Mathematics ***is*** formalising of our thought and intuition

[Kreinovich, Vladik]

I think part of this discussion is caused by the fact that there are two different meaning of the word "mathematics": 

* to a professional mathematician, anything absolutely rigorous, with proofs, is mathematics; one can proof a theorem about abstract mathematical objects, about algorithms, about physical fields (defined as solutions of a specific partial differential equation) -- to a professional mathematician, this is mathematics

* on the other hand, for many people who are not professional trained as mathematicians -- to many engineers, to many physicists, to philosophers sometimes -- any reasoning about numbers, solutions of differential equations etc. is called mathematics -- as long as it is not about a specific equation from a specific theory; in this case, a level of rigor does not matter; heuristic ideas about infinities and numbers are, to such people, called mathematics