Ancient Science · Part 23 · Late Alexandria · B1
Diophantus and Pappus: Equations, a Riddle of a Lifetime and the Bees’ Geometry
Part 23 of Ancient Science: Diophantus will write the oldest surviving Greek book of problems with an unknown number, and a riddle will claim to tell us how long he lived; a note in its margin will puzzle mathematicians for three hundred years. Pappus will save the work of earlier geometers and explain why bees build hexagons. How many…? How much…? Do you know how old he was?, with Philo, Sophia, Marcos and Demetria.
Tonight I look two or three hundred years ahead, to two mathematicians of Alexandria. The first, Diophantus, will write the oldest book of problems with an unknown number in them.
An unknown number? How can you count with a number you don’t know?
That is exactly what Diophantus will teach. How old was he when he died? Nobody knows, except through a riddle. And the second, Pappus, will ask why bees build their honeycombs in hexagons.
Diophantus lived in Alexandria, probably in the third century CE, though his dates are uncertain. His great work, the Arithmetica, had thirteen books of problems. Six survive in Greek. Four more were found in an Arabic translation in 1968.
In the Arithmetica, Diophantus uses a special sign for the unknown number, and short signs for its square and its cube, and for “minus”. He was not the first to solve problems with unknown numbers: Babylonian students did it on clay tablets nearly two thousand years earlier. But he was the first Greek we know of to use signs like these, a step towards the algebra we write today.
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