QED

Back when I was at high school (the late 19xx’s!!) we learnt something of the art of geometric proof, which had not yet started to go the way of the Tasmanian Tiger. Despite the fact that the learning of Latin HAD just about gone the way of the Tasmanian Tiger we signed off our proofs with the traditional “QED”, for quod erat demonstrandum, or “which has been demonstrated”.

I like proof, for its rigour, order and structure, for the way the pieces fit together, and for the brilliant little (and big) leaps of ingenuity needed to make things work. I also liked the erudite traditionalism of completing a proof with the notation “QED”, even though when it came time to type up my mathematics PhD I used the late 20th century electronic language-free equivalent of an empty square tombstone symbol at the end of my proofs.

Unfortunately, the presence of proof in contemporary mathematics schooling is rare. Nevertheless I insist on showing my pre-service primary teachers a proof of the famous Pythagorean Theorem. Worse than that, I expect them to learn it and reproduce it in the exam (I’m a mean old anachronism … although I DO tell them that they’ll need to know it).

So, it warmed the cockles of my mathematical heart tonight when, as I marked exams, I came across the work of a student who not only reproduced the proof of Pythagoras’ Theorem but wrote QED at the end of it!

Theorem: Someone else out there likes erudite traditionalism as well.

Proof: See example above. (This is an existence proof.)

QED