As an applied mathematician, I disagree. Proofs are often useful in applied maths, and most applied maths is much more closely related to pure maths than to engineering. Infinities show up in practical applied maths, but there are more abstract things that don't (yet).
Though just like libraries in programming mean that you don't have to worry about how to implement a hash table when using Python's dicts, advances in math mean that you don't have to worry about infinities and infinitesimals when you are constructing a bridge using differential equations.
