Mathematical proofs can be established by various means, including induction, contradiction, construction, and exhaustion. My favourite is proof by intimidation.

The National Police Gazette: New York, dec 1898 [Public domain], via Wikimedia Commons

Proof by induction, for example, has two steps. First, you prove a single case – for example, involving just one number. Second, you prove a rule that shows how it’s also true for that number plus one. Now that the second case is proved, the rule automatically proves the third, the third proves the fourth, the fourth proves the fifth, and so on. Now, technically that’s deduction and not induction, but they’re mathematicians not grammarians.

Proof by contradiction is a nice one: you demonstrate that, if something were true, it would result in a contradiction. You can prove that the square root of 2 is irrational – i.e. it cannot be represented as the ratio of two integers – by imagining that hypothetical ratio and then demonstrating that it’s mathematically impossible for it to exist. A persistent myth holds that the Greek philosopher Hippasus was drowned in the sea by the Pythagoreans for proving that, by the way.

Proof by intimidation is mathematician humour. It posits a proof that is so full of technical jargon and overwhelming complexity that you have to accept it, or you would effectively be admitting that you’re not good enough to follow its intricacies.

Okay, I’ll admit it, to me most proofs are intimidating.

• Mathematical proof
• Hippasus
• Proof by intimidation

Categories: Mathematics & statistics Sciences

The Generalist

I live in Auckland, New Zealand, and am curious about most things.