Computing the Uncomputable

I love the more mind-blowing results of mathematical logic:

• Surprises in logic.

Here’s a new one:

• Joel David Hamkins, Any function can be computable.

Let me try to explain it without assuming you’re an expert on mathematical logic. That may be hard, but I’ll give it a try. We need to start with some background.

First, you need to know that there are many different ‘models’ of arithmetic. If you write down the usual axioms for the natural numbers, the Peano axioms (or ‘PA’ for short), you...