TITLE: Is "mixed math" a useful way to learn math?
QUESTION [7 upvotes]: I was reading a book about how mathematics was taught in Cambridge in the 19th century, and it struck me how much physics was included in the syllabus, and it wasn't optional but everyone had to learn it. For example, there were things like planetary theory, hydrostatics, mechanics, astronomy, optics, electricity & magnetism, elasticity. Is there really any point for a student who wants to major in strictly pure math to go through the ordeal (and it was an ordeal back then, especially with those terrifying olden tripos papers) of learning mathematical physics alongside pure math? What about a student now, would it be useful to learn physics given the relations between e.g. quantum physics and the Riemann Hypothesis? If so, what benefits can such a student hope to derive from dabbling in physical topics?
Another question: Is it likely that someone like Andrew Wiles has a thorough grasp of physics, metaphysics, etc., or is it possible to prove great problems in math merely by learning pure mathematics deeply enough.
Thanks

REPLY [2 votes]: Only in the twentieth century did a substantial amount of mathematics come into being that was not connected with physics. 

mathematical logic / proof theory;
(some) abstract algebra;
computability;
type theory; 
...

Thus it is now possible to have a mathematical career untouched by physics. There is at least one substantial body of such people. We call them (theoretical) computer scientists. 
At the other end of the spectrum, there are many concerned with the analytic and numerical solution of essentially physical problems, not so concerned with shaking the logical tree of theory. We call them applied mathematicians. 
May all prosper and do good work.