The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

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

My method to overcome a difficulty is to go round it.

I am too good for philosophy and not good enough for physics. Mathematics is in between.

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

In order to solve this differential equation you look at it until a solution occurs to you.

If you cannot solve the proposed problem try to solve first some related problem.