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What the Ancients did for Us
Egyptian Mathematics page 1 2

For many centuries the indecipherability of Egyptian hieroglyphs helped to perpetuate the Greek belief in Egypt as the source of higher knowledge and wisdom, in mathematics as well as other matters. However, with the decipherment of the trilingual Rosetta Stone (hieroglyphic, demotic and Greek) by Jean Champollion in the 1820s, the picture changed to reveal a civilisation much more pragmatic and down to earth. Although the pyramids and other monumental constructions provide us with substantial evidence that the Egyptians had a good knowledge of mechanics and astronomy, when it comes to mathematics the story is rather different. Despite the fact that the classical Greeks believed mathematics to have been invented in Egypt, there is disappointingly little evidence of the Egyptians’ mathematical attainments. This is because most Egyptian documents were written on papyrus which is extremely fragile and deteriorates over time. Of the few papyri that survive only a tiny number (about a dozen) are concerned with mathematical calculation, of which the earliest dates from 1850 BCE and the most recent from 750 AD.

It is generally agreed that these mathematical texts were used to teach apprentice scribes basic numerical accounting and other techniques that they would need in their later professional life. They are written in a script called hieratic, a semi-cursive derivative of hieroglyphs. (Hieratic came into use for writing on papyri from about 2000 BCE, although hieroglyphic was retained for monumental stone-carving and more formal inscriptions.) Most of our knowledge of Egyptian mathematics is derived from two papyri, the Rhind papyrus (1650 BCE), the largest and the best preserved, and the Moscow papyrus (1850 BCE). The other mathematical papyri are mostly fragmentary in nature.

The Rhind papyrus, which (according to its scribe) is a copy of a text from 200 years earlier, was allegedly discovered in the ruins of a small building close to the temple of Ramesses II at Thebes. It is named after the man who bought it while on holiday in Luxor in 1858 and is now in the British Museum. It is approximately 18 feet long and 13 inches high, and contains extensive lists of divisions on one side and 87 mathematical problems on the other. The Moscow papyrus, now in the Pushkin Museum of Fine Arts, Moscow, is 15 feet long but only about 3 inches high. It contains 25 mathematical problems.

There are also a few Eygptian mathematical texts not on papyrus, the most significant of which are the Leather Roll (1650 BCE), which was so brittle that it remained unopened for 60 years, and the Two Thebes Wooden Tablets (2000 BCE). The Leather Roll contains an addition table, in duplicate, and is now in the British Museum, whilst the Thebes Wooden Tablets contain calculations relating measures of capacity and are now in the Cairo Museum.

The texts can be divided into two different types—problem texts and table texts. The problem texts pose mathematical problems and give their solution in the form of a step-by-step procedure, with each step representing a single mathematical command such as ‘add’ or ‘multiply’. These texts use plain language, not symbolism (apart from actual numbers themselves, of course) and the problems always involve particular numbers, not general formulae. The table texts are tables of numbers that are used in solving mathematical problems, e.g. tables of addition, tables used in fraction reckoning, and tables for conversions of measures.

Egyptian hieroglyphics
About Our Expert
Dr June Barrow-Green is a lecturer in the history of mathematics at the Open University and is involved with the Topics in the History of Mathematics (MA290) course.

Her interest in the history of mathematics originates from her undergraduate days at King’s College London when she wanted to find out more about the mathematicians responsible for the mathematics she was studying.

She is the author of the book Poincaré and the Three Body Problem which derives from her OU PhD thesis and which tells the story of the mathematical beginnings of chaos theory. Her current research interests include the history of dynamical systems, the role of British mathematicians in the First World War, and the use of history in mathematics education.
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