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?

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.

Physics is all about observation, but how much can we actually see?

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?

Cosmology has an ambitious goal: to understand the Universe in its entirety. Find out more here.