there is nothing to learn about reasoning and invention if the motive and purpose of the most conspicuous step remain incomprehensible. - George Pólya

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

The volume of the cone was discovered by Democritus... He did not prove it, he guessed it... not a blind guess, rather it was reasoned conjecture. As Archimedes has remarked, great credit is due to Democritus for his conjecture since this made proof much easier. Eudoxes... a pupil of Plato, subsequently gave a rigorous proof. Surely the labor or writing limited his manuscript to a few copies; none has survived. In those days editions did not run to thousands or hundreds of thousands of copies as modern books—especially, bad books—do. However, the substance of what he wrote is nevertheless available to us. ...Euclid's great achievement was the systematization of the works of his predecessors. The Elements preserve several of Eudoxes' proofs.

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself.