Keith Devlin > Quotes

“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.”
― Keith J. Devlin, Introduction to Mathematical Thinking

“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.”
― Keith J. Devlin

“For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to
convey just what the subject is about. Instead, the focus is on learning and applying various procedures
to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers
to get the ball into the goal. Both accurately describe various key features, but they miss the \what?"
and the \why?" of the big picture.”
― Keith Devlin, Introduction to Mathematical Thinking

“When he was about fourteen years of age, Leonardo would have left the fondaco and most likely traveled with an older merchant, a form of apprenticeship system common in those days. Around that time his father summoned him to Bugia. No one knows exactly when he made this voyage. In the introduction to Liber abbaci, he later wrote: “When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“Underlying all this activity—in the customhouses, on the wharves, in every place of business—were numbers. Merchants measured out their wares and negotiated prices; customs officers calculated taxes to be levied on imports; scribes and stewards prepared ships’ manifests, recording the values in long columns using Roman numerals. They would have put their writing implements to one side and used either their fingers or a physical abacus to perform the additions, then picked up pen and parchment once again to enter the subtotals from each page on a final page at the end. With no record of the computation itself, if anyone questioned the answer, the entire process would have to be repeated.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“a mathematician is someone for whom mathematics is a soap opera.”
― Keith J. Devlin, The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip

“European scholars had translated into Latin two important Arabic manuscripts, written by the ninth-century Persian mathematician Abū ‘Abdallāh Muammad ibn Mūsā al-Khwārizmī (ca. 780–ca. 850 CE).”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“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.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“In chapter 10, he explained how to use similar methods to manage investments and profits of companies and their members, and showed how to decide who should be paid what.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“The choice of ten basic number symbols—that is, the Hindus’ choice of the base 10 for counting and doing arithmetic—is presumably a direct consequence of using fingers to count. When we reach ten on our fingers we have to find some way of starting again, while retaining the calculation already made. The role played by finger counting in the development of early number systems would explain why we use the word “digit” for the basic numerals, deriving from the Latin word digitus for finger.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“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.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“By the latter part of the first millennium of the Current Era, the system we use today to write numbers and do arithmetic had been worked out—expressing any number using just the ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and adding, subtracting, multiplying, and dividing them by the procedures we are all taught in elementary school. (Units column, tens column, hundreds column, carries, etc.) This familiar way to write numbers and do arithmetic is known today as the Hindu-Arabic system, a name that reflects its history.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“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.”
― Keith J. Devlin, The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip

“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.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“Arithmetic and number theory study patterns of number and counting. Geometry studies patterns of shape. Calculus allows us to handle patterns of motion. Logic studies patterns of reasoning. Probability theory deals with patterns of chance. Topology studies patterns of closeness ans position.”
― Keith Devlin

“You cannot hold on to two things. If you use two hands to hold two things, the strength would be half. So it is best to let go of one and hold on tightly to the other.”
― Devlin

“I shall also have to look deeply into the nature of language. I will have to explain the difference between language, which appears to be unique to humans, and a system of communication, which many species possess in varying degrees of complexity.”
― Keith Devlin , The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip by Keith Devlin

“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.”
― Keith J. Devlin, Introduction to Mathematical Thinking

“At first, calculus was mainly directed toward the study of physics, and many of the great seventeenth- and eighteenth-century mathematicians were also physicists.”
― Keith Devlin , The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip by Keith Devlin