The central task of education is to implant a will and facility for learning; it should produce not learned but learning people. The truly human society is a learning society, where grandparents, parents, and children are students together.
Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.
