Proofs Demystified!

Via James Cook, I find out that Timothy Gowers is blogging. Amongst other things, he has explanations of two mathematical theorems that proceed by analogy from a lower-dimensional case. The first is on how to discover the formula for solutions to cubic equations by analogy with the formula for quadratic equations. The second is on how to get to the essentially two-dimensional Cauchy integral theorem from the one-dimensional theorem that if and is everywhere 0, then is constant. Clear, intuitive explanations in fluent prose — a refreshing change from the usual math-textbook style.