Maths in a minute

Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words. From symmetry to Euclid's axioms, and from binary numbers to the prosecutor's fallacy, learn some maths without too much effort.

An infinite set is called countable if you can count it. In other words, it's called countable if you can put its members into one-to-one correspondence with the natural numbers 1, 2, 3, ... .

How would you go about adding up all the integers from 1 to 100? Tap them into a calculator? Write a little computer code? Or look up the general formula for summing integers?

Sometimes you just can't argue with the evidence. If a large sample of
very ill people got better after dancing naked at full moon, then surely
the dance works. But hang on a second. Before you jump to conclusions, you need to rule
out a statistical phenomenon called regression to the mean.

The dome of St Paul's, rising elegantly above London since the cathedral was rebuilt late in the seventeenth century, hides an intriguing early example of the interplay between maths and architecture.

Sometimes people are nasty when it would have been better to be nice.

Kneeling in the mud by a country road on a cold drizzly day, I finally appreciated the wonder that is a lever. I was trying to change a flat tyre and even jumping on the end of the wheel wrench wouldn't budge the wheel nuts. But when the AA arrived they undid them with ease, thanks to a wheel wrench that was three times the size of mine. There you have it ... size really does matter!