From Pebbles to Commutators

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Donald W. Robinson describes the origin of mathematics in a metaphor everyone can understand: A shepherd keeps track of his flock by placing one pebble in a bag for each sheep. His matching in a one-to-one way leads him to the process of counting and eventually to the concept of number. Then he and his son split the work and hold two bags. The combination of two piles of pebbles introduces the notion of an operation—addition. The shepherd observes that it does not matter which pile comes first, which suggests a principle: commutativity. Next, Robinson details some of his current research on commutativity. His equations are advanced, but his message is basic. He emphasizes that “mathematics is an alive and growing subject,” that we have never discovered all that there is to know.

 

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