## I wish I had been taught mathematics by Socrates

February 24, 2015 by Matthew R. Malcolm

I hated maths at school – both in primary school and high school. I just couldn’t understand it. It seemed pointless and impenetrable – just a bunch of numbers. So I quit maths as soon as I was able to do so in high school – I went out of my way to do extra science, just so I could get out of maths.

But maybe if my teacher had been Plato’s Socrates, my experience would have been different. I was just listening to him talk about geometry to a slave in the dialogue *Meno*. I’ve heard the passage before, but this time I decided to work through the geometrical issue with Socrates as he talked it through. It turned out to be interesting and elegant (even if basic): he didn’t just give me a formula or use jargon; he allowed me (and the slave) to try to work out a concrete issue – how to make a square that’s twice the volume of another square… here’s what I drew:

Isn’t that elegant? I know people probably do this in primary school, but due to my utter hatred for numbers, I’ve never taken it in.

But there are a number of other points at which Socrates puts things more interestingly and elegantly than maths teachers – like when he points out that four thirds is one third of one more than one, and it’s also two thirds of two less than two. See? Elegant and interesting. My favourite bit is when (in the Phaedo) he problematizes 1+1=2: Which of the 1s became 2? Or did both disappear and become replaced with the 2? And how is it that if you split one of those 1s in half, you would also get 2? Intriguing! If only mathematics had been approached philosophically, I might have become interested!

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