...it is the greatest achievement of a teacher to enable his students to surpass him.

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.

...it is the greatest achievement of a teacher to enable his students to surpass him.

If you have a large number of unrelated ideas, you have to get quite a distance away from them to get a view of all of them, and this is the role of abstraction. If you look at each too closely you see too many details. If you get far away things may appear simpler because you can only see the large, broad outlines; you do not get lost in petty details.

A considreable portion of my high school trigonometry course was devoted to the solution of oblique triangles... I have still not had an excuse for using my talents for solving oblique triangles. If a professional mathematician never uses these dull techniques in a highly varied career, why must all high school students devote several weeks to the subject?

The only reason psychology students don't have to do more and harder mathematics than physics students is because the mathematicians haven't yet discovered ways of dealing with problems as hard as those in psychology.