- Paul Anthony Jones

# Algebra

The penultimate entry in our series of extracts from the new HH book, * The Accidental Dictionary*, tells the surprisingly 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 *ax*2 + *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 Muḥammad ibn Mūsā al-Khwārizmī.

In AD 830, al-Khwārizmī 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-Khwārizmī 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-Khwārizmī’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...