Quotes from Keith J. Devlin

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence.

Give a man a fish, he'll eat for a day. Teach a man to fish, he'll eat for a lifetime."? It's the same for mathematics education for twenty-first century life.

a baby's failure to reach for an object hidden under a blanket does not support the rather dramatic conclusion that the baby thinks the object has ceased to exist. Perhaps he simply does not yet have sufficient hand-arm coordination to reach for a hidden object. In fact, we now know that this explanation is correct. Recent experiments, more sophisticated than Piaget's, indicate that even very young babies have a well-developed sense of object permanency.

a mathematician is someone for whom mathematics is a soap opera.

A significant difference between Pacioli's book and Treviso Arithmetic is that Pacioli dealt with negative numbers. The concept of negative numbers was new in Europe, and Pacioli is believed to have provided the first printed explanation.

Having described the basic methods of Hindu-Arabic arithmetic in the first seven chapters, Leonardo devoted most of the remainder of the book to practical problems. Chapters 8 and 9 provide dozens of worked examples on buying, selling, and pricing merchandise, using what we would today call reasoning by proportions—the math we use to check the best deal in the supermarket.

The number system we use today—the Hindu-Arabic system—was developed in India and seems to have been completed by around 700 CE. Indian mathematicians made advances in what would today be described as arithmetic, algebra, and geometry, much of their work being motivated by an interest in astronomy. The system is based on three key ideas: notations for the numerals, place value, and zero.

European scholars had translated into Latin two important Arabic manuscripts, written by the ninth-century Persian mathematician Ab? 'Abdall?h Muammad ibn M?s? al-Khw?rizm? (ca. 780–ca. 850 CE).

How do we educate such individuals? We concentrate on the conceptual thinking that lies behind all the specific techniques of mathematics. Remember that old adage, "Give a man a fish, he'll eat for a day. Teach a man to fish, he'll eat for a lifetime."? It's the same for mathematics education for twenty-first century life.