Watching Robin Williams talk about poetry in Dead Poets Society reminded me of A Mathematician’s Lament by Paul Lockhart — yes, I have already linked to this once before. I want to make all pure maths students watch it, and replace “poetry” with “mathematics” throughout.

Rigour and structure are extremely important in mathematics, particularly so in pure mathematics. This however, does not mean that one should learn these things first; you need to have an appreciation for it. Schools all over the world teach students trigonometry; the sine of any angle in a right-angled triangle is equal to the length of the opposite side divided by the length of the hypotenuse. Are the people in charge of the curriculum under some deluded idea that this is what mathematics is all about? Or do they think that this is somehow “useful math” for the real world?

Instead of teaching students how to compute angles and lengths by plugging it into the same formula over and over again, we only need to teach them that it’s possible. We should start students with the old “compass and straight edge” problems; something akin to a puzzle. These kinds of problems are more in line with what mathematics is really all about, and then learning basic trigonometry afterwards wouldn’t just feel like rote. Or am I being too optimistic here?

From XKCD (Obviously)

Last week, I went to the State Library of Victoria for the first time. There I found a ~500 year old copy of a book, which is second only to the Bible in the number of editions published. Euclid’s Elements is almost certainly the most influential mathematical text ever, so it’s only fitting that Euclid be our first dead mathematician. Thankfully copyright ran out 2 millennia ago — because copyright was a thing then, right? You can read it for free from Google here. Go forth and learn the basic building blocks of geometry as it should be taught!

Update: There is a great online version of the Elements here, with some awesome interactive java applets. Thanks to Mat for linking it in the comments!

From → Education

1. Euclid is one of our heroes over at Socratica – we just made a video about him to start our “Great Thinkers” series on YouTube: http://goo.gl/4mF3Zi

We also started a series about geometric construction, check them out: http://goo.gl/mm0tVA
I never had to do geometric construction in school except as a diversion for rainy days. It would have been interesting to have it as a real basic part of my curriculum!

• Nobody got to do the kind of maths that is fun to think about as part of the curriculum; we learnt how to crunch numbers. I only discovered pure mathematics was a “thing” after briefly studying two different branches of engineering and completing a physics major.

Nice work on the videos too!

Lol, I’m not sure we should teach geometry from Euclids books. The whole thing looks to be entirely “verbal” arguments, which is tough going :p. Fun to see, but I think modern notation is worth keeping around :p.

• No, I’m not saying to actually teach from the books. But getting students to think about compass and straight edge problems seems like far better preparation for mathematical thinking than how we currently teach “mathematics”.