The word ‘theory’ has a couple of different meanings. You might say ‘In theory, if I leave right now I’ll still catch the bus!’ Alternatively, you might have heard of ‘Einstein’s theory of relativity.’

The first is a throw away statement that you’re making up on the spot.

The second is a rigorously tested idea, with a vast body of evidence to support it. It hasn’t been proved (it is impossible to prove anything in science), but still, there’s clearly a big difference between making up an idea, versus really testing it out.

Whenever we just make up what we usually call a ‘theory’, for example: “I reckon that in theory, it always rains after three days of sunshine,” it’s not *really* a theory, it’s a hypothesis. In everyday speech, this difference doesn’t matter that much. When we’re acting as trained, thoughtful mathematicians and scientists, it’s essential we can spot the difference.

In the rain example, I’ve stated a hypothesis. For it to become anything more, I need to test it, so I could make a record of the weather over a month. If I found that on one occasion we had four days of sunshine in a row, my hypothesis would be disproved. If I found that I was right, though, and it always rained after three days of sunshine, we might start to think about upgrading my hypothesis to a theory. It’s still not proved, and never will be – who knows, maybe next month we’ll get four of more days of sun, but at least we have some evidence for it now.

In maths, I might state a hypothesis: “I reckon that whenever you multiply two even numbers together, you’ll always get another even number.” I can then test the hypothesis, by multiplying a bunch of even numbers together and seeing what I get. If they always come out even, I have ‘demonstrated’ my hypothesis, gaining evidence to support it.

In maths, we rarely bother with mere theories, because we have something better. Unlike science, it *is* possible to prove a hypothesis. Often it involves using algebra (but not always), and when we prove that a hypothesis is certainly, definitely, always true, we call it a theorem.

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AQA Unit 1 November 2010 (F) - Page 8 Question 5(c)

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