Origins

Mathematics is a beast. It is now a few hundred years since anyone could be said to have had a a thorough knowledge of the entire discipline. This is simply because of its scope. As a result it seems to be becoming harder to define what mathematics is and what it isn’t.

Let’s begin with the stock definition from the Oxford English Dictionary. My physical copy of the tome was printed in 1999. In brief it says:

“the abstract deductive science of number, quantity, arrangement, and space… customarily divided into:

pure (including arithmetic, algebra, analysis, geometry and logic) and

applied (mechanics, statistics, computing, economics, biological sciences)“

Moving forward a quarter century another source, this time Britannica, (https://www.britannica.com/science/mathematics) we have:

“the science of structure, order, and relation that has evolved from elemental practices of counting, measuring and describing the shapes of objects.“

I could go on but that would labour the point. I do, however want to delve briefly into the linguistic roots of mathematics and geometry. Mathematics can be traced back to the ancient Greeks, and specifically to Pythagoras and his Mathematikoi. These were one of two groups of his followers, the other being the Akousmatikoi. Mathematikoi itself comes from mathema which is ancient Greek for “to learn” and so the Mathematakoi translates closely to “those who learn“. Similarly Akousmatikoi translates to “those who listen“.

I’m sure many of you are familiar with the root of Geometry, in that it is Earth (geo) Measurement (metry). Something I discovered when reading Kitty Ferguson’s Pythagoras His lives and the Legacy of a Rational Universe was that this came as a result of how a group of people, the Geomoroi, divided up the land in Greece.

Why do I find this important? Both mathematics and geometry as words, and hence concepts, come from the actions of groups of people. The actions came before the names for them.

I am going to take another turn now, and sketch out what classical and medieval education looked like. There were seven “Liberal Arts” or skills which were deemed necessary for thinking. They were divided into two smaller sections:

The Trivium: Grammar (the mechanics of language), Logic (the mechanics of thought and analysis) and Rhetoric (use of language to instruct or persuade).

The Quadrivium: Arithmetic (the discrete at rest), Geometry (the continuous at rest), Music (the continuous in motion) and Astronomy (the discrete in motion).

The short descriptors in brackets ore one set of descriptions. What is discrete is that which is countable. What is continuous is that which is measurable. Classical and Medieval education was highly mathematical as we now understand the term.

The question I wish to pose in this post is whether we have lost something of the meaning of learning by disconnecting our current curricula from these beginnings. Note, I am not advocating a “back to basics” crusade. I simply want to remind those who are interested of the origins of what education was for.