The previous post, *Halt! (or not)*, described the Turing Halting Problem, a fundamental limit on what computers can do, on what can be *calculated* by a program. Kurt Gödel showed that a very similar limit exists for any (sufficiently powerful) mathematical system.

This raises some obvious questions: What is *calculation*, exactly? What do we mean when we talk about a *program* or *algorithm*? (And how does all of this connect with the world of mathematics?)

Today we’re going to start exploring that.