Proof by intimidation
Mathematical proofs can be established by various means, including induction, contradiction, construction, and exhaustion. My favourite is proof by intimidation.
Bet your (after)life
If you’re a gambling man, you better believe in God. So suggested Pascal’s wager, one of the first applications of decision theory to philosophy.
Boring numbers
What is the smallest boring number? There’s no such thing, because the title of smallest boring number automatically makes that number interesting.
Kidney stone paradox
Statistics are tricky. Consider this: of two treatments for kidney stones, Treatment A is better on average for large stones and small stones. But consider all stones together and Treatment B is better. This is Simpson’s paradox.
Gamblers’ downfall
The gambler’s fallacy is the belief that random independent events “even out” over time. In Monaco in August 1913, this belief cost casino gamblers millions because of an extraordinary streak at a roulette table.
World computer
What are the practical limits of computation? Hans-Joachim Bremermann theorized a computer the size of the world, as old as the world. It could process 10^93 bits.
Mathematical beauty
Can mathematics be beautiful? Mathematicians often describe proofs in aesthetic terms – they are elegant, sublime, ineffable; in a word, they are beautiful.
Wurundjeri counting
The Aboriginal languages of southeast Australia have an ingenious counting system – there’s a physical mnemonic built directly into the language.
Build your own magic square
A magic square is a grid of numbers in which any row, column, or diagonal adds up to the same total. They look complex, but it’s actually easy to design your own using the Siamese method.
0.9 recurring is 1
0.999… is the same number as 1. It’s counterintuitive, but mathematics says that it’s true. Whether you believe it or not is another matter.
