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

Spider solitaire is a popular online game. But are users right in their suspicion that some programs are rigged?

How can we get a grip on the uncertainties in mathematical models?

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

Physics is all about observation. But how much can we actually see with the naked eye?

The limits to what we can observe are not only a matter of science, but also of politics and economics.

Observing the smallest building blocks of matter doesn't involve seeing in the ordinary sense.

Introducing an indispensable tool of mathematical logic.

If you can prove that a statement can't possibly be false, does this mean it's true?

There are limits to how much you can simultaneously squeeze the quantum fuzziness of an electron's position and momentum

We take the real numbers for granted, but what are they really?

Resonant electromagnetic waves, created by lightning flashes, circle the Earth. Wim Hordijk explores the maths and shows how you can keep track with these phenomena.