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Electoral impossibilities

One advantage of the UK voting system is that nobody could possibly fail to understand how it works. However, the disadvantages are well-known. Differently sized constituencies mean that the party in government doesn't necessarily have the largest share of the vote. The first-past-the-post system turns the election into a two-horse race, which leaves swathes of the population un-represented, forces tactical voting, and turns election campaigns into mud-slinging contests. There are many alternative voting systems, but is there a perfect one? The answer, in a mathematical sense, is no.
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Intriguing integrals

Intriguing integrals: Part I

What's the integral of xk? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it? Chris Sangwin introduces an ingenious method for deriving the integral from first principles.

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Understanding uncertainty: Infinite monkey business

 

David Spiegelhalter explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.

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mouse

Of pancakes, mice and men

Genes normally evolve by tiny mutations, but every now and then something more radical occurs and entire genes along a chromosome get flipped. Understanding gene flipping boils down to solving a problem from pure maths. Colva Roney-Dougal and Vincent Vatter explain, taking us on a journey from waiters sorting pancakes, via one of the richest men in the world, to the genetic similarities of mice and humans.

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five candles

On what day of the week were you born?

Want to impress an audience? Then why not become a lightning calculator by learning Burkard Polster and Marty Ross' method for working out the day on which someone was born from their birthday really fast.