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A leading figure among the early Greek mathematicians is Pythagoras.
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.
The fame of Archimedes in history and legend derives largely from his practical inventions and discoveries, but he himself regards these as trivial compared to his work in pure geometry.
He is most proud of his calculations of surface area and of volume in spheres and cylinders.
Of the two Babylon is far more advanced, with quite complex algebraic problems featuring on cuneiform tablets.
A typical Babylonian maths question will be expressed in geometrical terms, but the nature of its solution is essentially algebraic (see a Babylonian maths question).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.This is a late arrival in the story of mathematics, requiring both the concept of place value and the idea of zero.As a result, the early history of mathematics is that of geometry and algebra.Equally 2 cubed is the volume of a cube with 2 as the length of each dimension.The first surviving examples of geometrical and algebraic calculations derive from Babylon and Egypt in about 1750 BC.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.Many of the theorems derive from Euclid's predecessors (in particular Eudoxus), but Euclid presents them with a clarity which ensures the success of his work.It becomes Europe's standard textbook in geometry, retaining that position until the 19th century.