Symbolic Algebra

If you search Symbolic Algebra in major search engines, you’ll likely find a lot of articles about computer science — but that’s not what we mean here at Maths from the Past! Instead, we are talking about the symbolic algebra described by 19th Century Mathematician Agustus De Morgan.

What was Math Before Symbolic Algebra?

Before the mid-19th century, Mathematics was restricted to the idea that everything described had a real-world equivalent ((primarily through Euclidian geometry); however, this perception was gradually changed over time until De Morgan severed the connection between algebra and number of objects.

A Brief Overview of Symbolic Algebra

Simply put, Symbolic Algebra says that mathematics can be used as a language.  Since symbolic algebra severs the ties between symbols and numbers, now variables like x, y or a don’t need to represent numbers and rules of operation like + do not need to represent addition.

We’ve already discussed mathematical symbols on the site — as recently as 1921, the division symbol was used for subtraction! We would like to think of this as a mistake, but in advanced mathematics, every symbol (every item!) must be defined. For example, in a proof of a mathematical ring, mathematicians must write, “ + means addition and * means multiplication”, to ensure that the symbols are interpreted correctly. (This can be seen as the mathematical equivalent of semiotics in English!) Inside algebra, rules called axioms define how operations work within it.