Euclid's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checki… - George Pólya

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.

People tell you that wishful thinking is bad. Do not believe it, this is just one of those generally accepted errors.

Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean [to be] doing mathematics? In the first place, it means to be able to solve mathematical problems.