A PhD in Mathematics is three years of guessing it wrong, plus one week of getting it right and writing a dissertation.
Keith DevlinI certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need.
Keith DevlinGiven the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.
Keith DevlinWhat makes it possible to learn advanced math fairly quickly is that the human brain is capable of learning to follow a given set of rules without understanding them, and apply them in an intelligent and useful fashion. Given sufficient practice, the brain eventually discovers (or creates) meaning in what began as a meaningless game.
Keith DevlinThe human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.
Keith Devlin