The Origins of Algebra Are Not What You Think

The Origins of Algebra: Hindu-Arabic Arithmetic

In this course, Dr Piers Bursill-Hall (University of Cambridge) explores the origins of algebra: Hindu-Arabic arithmetic. In the first mini-lecture, we consider types of arithmetic used by ancient peoples, including Egyptians, Mesopotamians, and Romans. In the second mini-lecture, we discuss the development of Abbasid-Muslim culture that gave rise to the Hindu-Arabic arithmetic we use today (and which technically should be called Hindu-Muslim arithmetic). In the third mini-lecture, we think about the transmission of Muslim ideas and technology to Christian Europe via Al-Andalus, the Muslim-ruled area of the Iberian Peninsula (modern-day Spain). In the fourth mini-lecture, we discuss how Hindu-Muslim arithmetic entered the European world thanks to the treatise, Liber Abaci, written by Leonardo Fibonacci. In the fifth mini-lecture, we explore the impacts of the Liber Abaci in Europe and see how it transformed not only European mathematics, but also the European economy. In the sixth mini-lecture, we think about how printing the Liber Abaci helped improve and modernise mathematical notation. In the seventh mini-lecture, we see how arithmetic and algebra merged at the end of the 16th century and paved the path for the revolutionary mathematics of the 17th century.

The Origins of Algebra Are Not What You Think

In this mini-lecture, we consider types of arithmetic used by ancient peoples, focusing in particular on: (i) ancient Egyptian arithmetic, including multiplying by successive addition; (ii) ancient Mesopotamian arithmetic, which used different notation and methods for operations, powers, and fractions than we use today; (iii) how the Hindu-Arabic numerals and methods we use today, actually originate from Muslims in the 8th century BC (the correct name should be Hindu-Muslim arithmetic); (iv) early Greek arithmetic, which we have minimal records on; (v) the ancient Roman abacus (2nd century BC to 5th century AD) and the Chinese abacus; and (vi) how the Romans were not great at arithmetic, which is evident in their Roman numerals which are not conveniently compatible with arithmetic operations.