It is foolish to answer a question that you do not understand. It is sad to work for an end that you do not desire. - George Pólya

It is generally useless to carry out details without having seen the main connection, or having made a sort of plan.

We wish to see... the typical attitude of the scientist who uses mathematics to understand the world around us. ...In the solution of a problem ...there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude.

Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.