Mesopotamia & Egypt
The cradle of mathematics — where counting, measuring, and calculating began
1.1 Babylonian Mathematics
The oldest known mathematical texts come from Mesopotamia, written on clay tablets in cuneiform script around 1800 BCE. The Babylonians used a base-60 (sexagesimal) number system — a legacy that survives in our 60-minute hours and 360-degree circles.
Babylonian scribes could solve quadratic equations, compute square roots with impressive accuracy, and had extensive tables of reciprocals, squares, and cubes. Their methods were algorithmic — step-by-step procedures rather than proofs — but remarkably effective.
Plimpton 322 (c. 1800 BCE)
This famous clay tablet from the Yale Babylonian Collection contains a table of Pythagorean triples — sets of integers (a, b, c) satisfying a² + b² = c² — compiled more than a thousand years before Pythagoras. Whether it was used for teaching, surveying, or pure mathematical investigation remains debated among historians.
1.2 Egyptian Mathematics
Egyptian mathematics, preserved primarily in the Rhind Mathematical Papyrus (c. 1650 BCE) and the Moscow Mathematical Papyrus, served practical needs: land surveying after the annual Nile flood, construction of pyramids, and distribution of rations.
Egyptians used a decimal system but represented fractions exclusively as sums of unit fractions (fractions with numerator 1). They had methods for computing areas of triangles, trapezoids, and even an approximation of the area of a circle — effectively using π ≈ 256/81 ≈ 3.16.
The Method of False Position
Egyptian scribes solved linear equations using a technique called "false position": guess a convenient value, compute the result, then scale to get the correct answer. This algorithm survived through the Middle Ages and was still taught in European schools in the 18th century.
1.3 Mathematics as Administrative Tool
In both civilizations, mathematics was fundamentally practical. Scribes were trained in computational techniques to serve the bureaucratic needs of temple and palace — measuring fields, calculating taxes, distributing grain, and planning construction projects.
The concept of mathematical proof, as the Greeks would later develop it, was entirely absent. Instead, both Babylonian and Egyptian mathematics were procedural: they demonstrated methods through worked examples. This approach was extremely effective for the problems they needed to solve, and many of their algorithms are essentially identical to methods still taught today.
1.4 Key Contributions
Mesopotamia
- • Base-60 positional number system
- • Quadratic equation solutions
- • Pythagorean triples (Plimpton 322)
- • Extensive numerical tables
- • Algorithmic problem-solving
Egypt
- • Decimal number system
- • Unit fraction arithmetic
- • Area and volume calculations
- • Approximation of π ≈ 3.16
- • Method of false position