"The more we ourselves are enraptured by the beauties of mathematics, the more we regret that we can bring so few people to share our pleasure. But at least those of us in the school of abstract mathematics have one consolation: as we make our presentations clearer and more transparent, they automatically become easier to understand. Bear in mind that four hundred years ago, arithmetic was a difficult art. So great an educator as Melancththon [a sixteenth century scholar who reformed German education] did not trust the average student to penetrate the secrets of fractions. Yet now every child in elementary school must master them. Perhaps eventually the beauties of higher mathematics... will be accessible to every educated person."
-- German mathematician Wolfgang Krull (1930), quoted in Ivars Peterson's "Islands of Truth: A Mathematical Mystery Cruise"