Harvey Friedman tells us about a mathematical movement called constructivism and why we need it.

We explore non-constructive proofs and what happens if you try and avoid them.

Can a mathematical object be said to exist if you can't construct it?

We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy.

If you like mathematics because things are either true or false, then you'll be worried to hear that in some quarters this basic concept is hotly disputed. In this article Phil Wilson looks at constructivist mathematics, which holds that some things are neither true, nor false, nor anything in between.