On Epiphanies

I had a fascinating conversation on Twitter the other day about, I suppose, different modes of solving a problem. Here’s where it started:

I intended it as a throwaway comment, but it got some interesting responses.

@colinthemathmo (Colin Wright) pointed out:

… which, as Colin’s messages are wont to do, gets straight to the heart of things: is maths about getting the answer, or about getting the insight?

Of course, it’s both - but it’s a rare answer that makes me go ‘oo!’

@ajk44 (Alison Kiddle) suffers from the same difficulty as I often do:

@DavidB52s (David Bedford) took it on from a more pedagogical point of view:

And @RobJLow (Robert Low) followed up with this:

As the man said, you shouldn’t let other people get your kicks for you. Having someone else’s epiphanies for them is just impossible.

So what are your thoughts about epiphanies and elegance? Is there a good way to teach them? I’d love to hear your comments.

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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• Barney Maunder-Taylor

To illustrate: “a stick is snapped randomly into three pieces. What is the probability that those three pieces could be rearranged to make a triangle?”. This puzzle took me two days to solve, and only after getting two incorrect answers, some integration, and performing a simulation to check which of my answers was correct. Two pals then independently came up with the correct answer after barely more than a moment’s thought and no integration. What’s the point? Not sure to be honest, except that I did have enormous fun working through the problem and eventually cracking it successfuly – by whatever means, and the fact that I’d gone a needlessly long way has, peversely enough, only added to my enjoyment of it.

• Colin

That’s exactly it – I find that realising there’s a quick way *after* doing it the long way makes me appreciate the quick way more.

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