You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply ….

Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination..

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to m….

In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fac….

When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touch….

The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what….

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying 'No, that's wrong.' Rather, h….

The present syllabus in our high schools corresponds almost exactly to what was known in 1640..