[Math Lair] Diophantus

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Diophantus was a Greek-educated mathematician who lived in Alexandria. Most ancient Greek mathematicians were interested in geometry, not algebra; Diophantus, on the other hand, was the only ancient Greek who wrote about solving algebraic equations.

His main work was the Arithmetica. In this book, he considers a variety of equations that are now called Diophantine equations. These are equations that for which the solutions are restricted to a certain class of numbers, often natural numbers, but sometimes negative integers, rational numbers, or other classes.

Diophantus is often considered the father of algebra. He introduced the idea of an algebraic equation expressed in symbols. He did not have either predecessors or successors, so, had he not performed the work that he did, the problems that he considered might not have been considered for at least centuries afterwards.

Even though Diophantus is perhaps the most significant algebraist of antiquity, we know virtually nothing about his life. We don't even know what century he lived in, although he most likely lived sometime between 150 to 350 A.D. The only information known about his life comes from what purports to be his epitaph, recorded in a sixth-century collection called the "Palatine Anthology" (later incorporated into the "Greek Anthology"), although for all we know this could have been made up. His epitaph reads along the lines of the following:

Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, and one-seventh more as a bachelor; five years after his marriage, was born a son who died four years before his father, living to half the age that his father would attain.

If you're interested in finding how old Diophantus was when he died, you could set up a linear equation, but you can skip that step if you note that the answer has to be divisible by both 7 and 12, suggesting an answer of 84; a quick check confirms that 84 is the answer to the problem and hence Diophantus' age.

Sources used (see bibliography page for titles corresponding to numbers): 13, 20, 30.