[Chris2048]

Isn't there a very small demand for actual, proof-writing mathematicians, versus "mathematicians" in the sense that they can use advanced math.

I'd say being able to use advanced math, even for engineering, is a suitable definition for "having studied advanced mathematics".

[ska]

   'versus "mathematicians" in the sense that they can use advanced math.'

Those people are not "mathematicians", they have other useful names (most physicists, bio-statisticians, some engineers, etc.)

Mathematicians are people who create new mathematics, not people who use mathematics.

[Chris2048]

Where does that definition come from?

I feel the term is often used more broadly.

http://c2.com/cgi/wiki?MathematicianDefinition

In any case, the point stands - The need for persons who can construct mathematical proofs, versus those who simply need to derive the correct numerical result, is very different.

As such, most classes that teach calculus are for practical, applied purposes - who don't need to "prove what they know" beyond demonstration procedural competence.

[ska]

I don't find that discussion particularly insightful. Yes, the term is used more broadly, but doing so invites confusion.

Compare perhaps "composer" to "musician", they are both involved in music but operating on different axis. Most people would agree that there isn't a strict relationship superset, and there is overlap. There are skilled composers who are lousy musicians, and vice versa. There are a few people who are top rate at both. However, it is very useful to have the distinction between creating and performing.

It's much the same with mathematicians.

[Chris2048]

Excuse me, but you're the one who went off on that tangent.

If we're relating to how people use words, it's not "much the same with mathematicians"