In this post, I’m hoping to give a little insight into the way a mathematician thinks. This has been inspired by a conversation with the other teachers in my faculty.
(This may well apply to computer programmers too.)
The other thing that I’ve seen people do and just can’t understand is this: they get a mug and teaspoon out, get a tea bag and then put the kettle on. This is madness. It should be glaringly obvious that putting the kettle on first and doing those other things while it is boiling is far more time efficient. In fact, there’s a whole area of maths called discrete or decision maths dedicated to this sort of thing. Decision maths is what gets your Sat Nav to pick the best route. It’s what helps make sure your baggage ends up in the right place (and it’s not the maths fault when it goes wrong). The kettle is a classic example of something called Critical Path Analysis.
All these (possibly minor) things come about as a result of planning and thinking ahead. This is why mathematicians are often better at writing questionnaires because we think through what might happen before we’ve even done it. It is this planning ahead that is one of the signature features of mathematical thinking. When there was statistics coursework, there were marks available for planning ahead for potential problems and thinking about what you would do should they arise.
Some might say that thinking about how best to pack the dishwasher is in itself a waste of time. Well, there are two answers to that:1) It isn’t. It saves time, 2) I have more time to ‘waste’ thinking about these things because I think about these things. Finally, I’m aware that this may sound a little like I have OCD. I don’t think I do. It’s just that planning ahead and being logical about certain things has such obvious benefits. To me, and I think mathematicians in general, the ‘putting the kettle on first’ situation is clearly the right answer. The other way is glaringly wrong. Really, really wrong. Essentially, the way I do this is the correct way. I’m aware that this may well be exactly the way people with OCD reason about their behaviour too.
I hope you enjoyed this little insight into the mind of a mathematician.