432 words

Today I heard a talk in which everything that was written on the blackboard were formulae. Well,

I hear people say, that's what maths are all about. I was never good at formulas, so I didn't do maths.

. And of course they're *expletive deleted* wrong. Such talks are very bad and trying to follow them is a royal pain.

Sure, formulae are a very convenient method of writing down formalised statements and manipulating them. But that's not – or at least not the main – point of mathematics. It's not about formulae at all – they're just means to an end.

So why exactly are formulae bad? The explanation I'd give is that a formula means nothing. It's just a bunch of letters and symbols along with some fancy typography. To actually make sense of it you need massive amounts of context. Let's just consider a well-known example. What's this?

a^{2} + b^{2} = c^{2}

Pythagoras' theorem,

I hear you cry. And you're wrong again. Even Three letters, three numbers and four lines,

might have been a better answer than that. Of course, Pythagoras' theorem *can* be stated in a way that contains the formula above – but that statement also, vitally I may add, includes saying what *a*, *b* and *c* mean (and, on a more nitpicky level, making sure you know you're dealing with mathematics and interpret the layout of the glyphs accordingly). Furthermore, the choice of letters is not relevant and the theorem can easily be stated without having to use a formula at all.

Another example would be the wildly popular

E = mc^{2}

And exactly the same main point can be made here. Until you explain what the all the letters mean, it's not worth much (except making people shout Einstein

and Everything's relative!

, I guess). Just showing the formula to someone will not make them understand anything about energy, say. They'll have to bring a lot of theoretical knowledge to appreciate it – or you'll have to do a lot of explaining.

I hope this illustrates why blackboards full of formulae aren't very helpful if you're trying to explain something. To communicate what's going on you also need to say what they mean and how they're related.

To finish consider, the question whether the equation

a^{3} + b^{3} = c^{3}

has any solutions. And of course it has: triples of the form , for any *a* and *b*.

Uh, all numbers were supposed to be integer? Well, nobody told me that. No solutions then, I guess.

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