How to read a theorem
The first precept was never to accept a thing as true until I knew it as such without a single doubt.
René Descartes, Le Discours de la Méthode, 1637
Theorems and proofs are central to mathematics. In this chapter I will explain how to deal with a new theorem; consideration of proofs will come later.
As explained earlier, students often conceive of mathematics as being about processes applied to solve set problems, such as using a certain rule to differentiate a product or quotient, or solving a differential equation ...