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

It is better to solve one problem five different ways, than to solve five problems one way.

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

It may be more important in the mathematics class how you teach than what you teach.

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.