A degree in math or physics requires much more math than that which engineers study. Likewise a degree in physics requires much more physics than engineers study.
Nearly every engineering class I had was really a math class in disguise. Granted, it was often a very specialized, applied math class. Although in my experience at least by grad school, math students are usually in a very specialized field of mathematics as well...just a different one from engineers.
I think the difference might be this, in undergraduate degrees:
* Mathematics is entirely about proving arguments and solving problems within logical systems.
* The 'hard sciences' (esp. physics) are about working within a theoretical (often mathematical) framework and testing it with experimentation.
Contrast this to engineering disciplines, or even medicine, where the focus is on gaining knowledge which you can use to solve problems. It's problem-solving, but doesn't have much of the scientific method about it.
