A Century of Mathematics in America (History of Mathematics, by Peter Duren

By Peter Duren

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The art of 30,000 bc was probably somewhat similar to a BEGINNINGS25 child’s drawing, not because our ancestors were simple minded, but because drawing nameable things is such a basic, human skill. Indeed, we can say that children’s drawings are understandable precisely because we can talk our way about them. ). Just as a child might not need to draw ears and a nose before their marks become a face, so the caveman artist may have drawn some tusks and already seen a mammoth. Such stylized, intelligible drawings are not the same as writing, but there is a related logic of meaningful marks, and it is surely safe to assume that our ancestors talked about their drawings.

Indeed, the Babylonians were familiar with the empirical content of Pythagoras’ Theorem over a thousand years before Pythagoras himself was born. Our main sources of evidence concerning Babylonian matheÂ� matics are the many clay tablets that have survived, preserving the math homework of young scribes from BEGINNINGS33 over 3,500 years ago. Like the Egyptians, the Babylonians would sometimes phrase questions in terms of unknown quantities, and remarkably, they knew effective methods for finding positive solutions to quadratic equations.

Furthermore, at some point our ancestors must have made the vital step of imbuing those expressive gestures with an essentially matheÂ�matical meaning. This remarkable feat was not achieved by the discovery of abstract objects: it was achieved by developing rituals. Suppose, for example, that there was a pre-existing form of expression that conveyed the speaker’s irritation over missing a flint. Now imagine the earliest people running their hands over their treasured tool kit of flints. As a 22 MATHEMATICAL THOUGHT person checked their tools time and time again, they may have expressed their familiarity with these objects by reciting a sequence of names.

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