Algebra

(n.) a mathematical system in which letters are used to express variables and often unknown quantities

The penultimate entry in our series of extracts from the new HH book, The Accidental Dictionary, tells the surprising medical history of a branch of mathematics.

If you didn’t much care for mathematics at school, it might come as little surprise to learn that algebra started out as another word for the agonizing bone-setting surgery used to heal fractures—which frankly might sound like a more enjoyable way to spend your time than pondering the likes of ax2 + bx + c = 0.

Algebra is a Latin corruption of the Arabic al-jabr, literally meaning ‘the reunion’ or ‘the restoration’ of something lost or broken—it just so happens that the things being ‘reunited’ or ‘restored’ were originally broken bones, not unknown quantities.

It was in this sense—as a medical term referring to the healing and treatment of fractures—that the word algebra was first imported into English in the early Middle Ages, via translations of European and Arabic medical textbooks: as one English translation of La Grande Chirurgerie or ‘The Grand Surgery’ (c. 1425) put it, algebra was originally the “stretching out and or restoring of broken bones and bones out of joint”. That would have been that too, were it not for the arrival of a ninth-century Persian mathematician called Muhammad ibn Musa al-Khwarizmi.

In AD 830, al-Khwarizmi wrote a mathematical treatise called The Concise Book on Calculation by Restoration and Completion, in which the things being ‘restored’ by al-jabr were no longer broken bones, but the unknown quantities in quadratic equations. By figuratively referring to these kinds of calculations as al-jabr, al-Khwarizmi laid the foundations not only for the word algebra, but the entire discipline of algebra itself (as well as countless hours of bewildering mathematics lessons).

This arithmetical meaning of algebra arrived in English in the mid 1500s, and the subject’s widespread popularity soon helped to consign the older medical use of algebra to the history books. Al-Khwarizmi’s work, however, wasn’t done.

With a little linguistic twisting and turning, his surname eventually morphed into the title of another branch of mathematics that his work helped to introduce: algorithms. So if you really don’t like maths, you really only have one person to blame...