*Since the numerical system is unwieldy, with a base of 60, calculation depends largely on tables (sums already worked out, with the answer given for future use), and many such tables survive on the tablets.Egyptian mathematics is less sophisticated than that of Babylon; but an entire papyrus on the subject survives.*

Euclid teaches in Alexandria during the reign of Ptolemy.

No details of his life are known, but his brilliance as a teacher is demonstrated in the Elements, his thirteen books of geometrical theorems.

Archimedes is a student at Alexandria, possibly within the lifetime of Euclid.

He returns to his native Syracuse, in Sicily, where he far exceeds the teacher in the originality of his geometrical researches.

Eratosthenes, the librarian of the museum at Alexandria, has more on his mind than just looking after the scrolls.

He is making a map of the stars (he will eventually catalogue nearly 700), and he is busy with his search for prime numbers; he does this by an infinitely laborious process now known as the Sieve of Eratosthenes.

But the theorem is typical of the achievements of Greek mathematicians, with their primary interest in geometry.

This interest reaches its peak in the work compiled by Euclid in about 300 BC.

He leaves the wish that his tomb be marked by a device of a sphere within a cylinder.

A selection of titles from his surviving treatises suggests well his range of interests: On the Sphere and the Cylinder; On Conoids and Spheroids; On Spirals; The Quadrature of the Parabola; or, closer to one of his practical discoveries, On Floating Bodies.

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