+ The mathematician (mathematicien) is like someone who composes music; doesn't have to perform, be good w/instruments. He/she just "invent" math.
+ The matheux is someone who plays an instrument; can be a virtuoso but doesn't compose music. I learned from a long career in math finance to never hire mathematicians (PhDs in math) to solve math problems or toy with actual equations. You get a better payoff with a "matheux" who studied (undergrad) electrical engineering in India, Russia, Lebanon, Brazil, etc.