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Emotions are far harder things to understand than algebra and geometry, yet we spend hours in elucidating mathematics and expect such a problem as that of human relationships to solve itself.
We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free , but when the chips are down we close the office door and compute with matrices like fury.
A child in the 4th grade who's just learning algebra is not imperfect. While there may be a child in the 12th grade who's much better, the child who's learning is not imperfect.
The teaching of the ten thousand states of mind, particularly as one advances further, is done through transmission. This is where we differ from teaching algebra or calculus.
In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster.
When I was in school, my favorite subject was math. I took algebra and calculus. At an early age I grasped it and understood it quickly. I just enjoyed breaking the codes and solving problems.