Posts Tagged ‘Bakhshali Manuscript’

A Treasury of Ancient Mathematical Texts

February 4, 2017

Henrietta Midonick, The Treasure of Mathematics: 1 (Harmondsworth: Penguin 1968)


I realise that the history of mathematics is an arcane subject, that few people will have much interest in, having struggled enough with the subject at school. But with Black History Month, there is immense interest amongst scholars of Black and Asian history about restoring Black and Asian scientists and mathematicians to their rightful place in history.

I picked up this book in one of the secondhand bookshops in Cheltenham about a year or so ago. It’s a collection of ancient and medieval mathematical texts from Ancient Egypt, Babylon, China, India, Islam, the Jews and, of course, the ancient Greeks. The blurb for it runs

Mathematics is the only true international language. men can communicate more directly, precisely and logically in pure mathematics than in any other tongue. Moreover we have much to learn from the achievements of past civilizations in this field: even modern computers have not fathomed all the intricacies of Stonehenge. In this fascinating collection of original sources (many of them published in a popular edition for the first time) Henrietta Midonick shows individual mathematicians grappling with varied problems – some practical, such as architecture, money valuation, mechanics, astronomy and calendar calculation; others verging on philosophy, such as the existence of zero and the concept of infinity. Her arrangement also demonstrates the growth of key ideas in geometry, arithmetic, logic and calculus.

Volume 1 documents the growth of mathematical science in the civilizations of Babylon, Ancient Egypt, the Mayas, India and China, and assesses the revolutionary discoveries of Plato, Archimedes and Euclid in classical antiquity.

Among the various extracts are pieces on Babylonian mathematics; four geometrical problems from the Moscow Papyrus, which dates from Ancient Egypt, c. 1850 BC; the Rhind Mathematical Papyrus, again from Egypt, c. 1650 BC; the Bakhshali Manuscript, from 4th century AD India; the Mayas – discussing their system of numbers, the calendar, arithmetic and chronology, and the Quipu, the method of keeping statistical records using knots, used by the ancient Incas in South America.

Chinese mathematicians include Wan Wang, from the 12th century BC, Chou Kung, c. 1100 BC; Chang Tsang, died 152; Liu Hui, 3rd century AD; Sun-Tsu, from the same century; Hsia-Hou Yang, 6th century AD; Wang Hs’iao-T’ung, 7th century AD, Li Yeh, c. AD 1178-1265; Ch’in Chiu-Shao, c. AD 1250; Yang Hui, c. AD 1275; Chu Chi-Chieh, c. AD 1300.

The Indian scholars collected include Aryabhata the Elder, c. AD. 476; Brahmagupta, AD 598; and Bhascara Acharya, AD 1114-c. 1185.

It also includes the Algebra of Mohammed ben Musa al-Khowarismi, who founded much of modern algebra, including giving it its modern name.

The two Jewish mathematicians collected include the Mishnat ha-Middot of Rabbi Nehemiah, from c. AD 150; and the Method of Division of Immanuel Ben Jacob Bonfils, c. AD 1350.

The ancient Greeks include Hippocrates of Chios, 5th century BC; an extract from Plato’s Dialogues; the Elements of Euclid of Alexandria, c. 300 BC; Apollonius of Perga’s Conic Sections, from the same period; Archimedes’ On Spirals, Mechanical Problems, and Quadrature of the Parabola, Pappus, c. AD 300, and Proclus, AD 410-485.


Ancient Babylonian Multiplication Table for X 10.

For the non-mathematician like myself these texts aren’t easy reading. There are diagrams to help, but many of them, as the pioneering works of their time, are trying to express difficult mathematical ideas without the modern language of Maths, and so it can be difficult understanding what they are trying to describe. Nevertheless, this is an important collection of some of the classic texts of ancient mathematics on which the structure of modern maths has been built.