# Articles

Heisenberg's uncertainty principle

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

The real numbers and Cauchy sequences

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

Citizen science: Schumann resonances

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.

Maths in a minute: Chomp

A game involving biscuits and maths — what could be better?

Maths in a minute: The axioms of probability theory

Take a quick trip to the foundations of probability theory.

Arithmetic billiards

Need to find the least common multiple or greatest common divisor of two numbers? A billiard table of the right proportions holds the answers!

The maths of randomness

Randomness is surprisingly hard to define. Fortunately the mathematical language we use to describe it is beautifully well defined.

The maths of randomness: universality

The second guiding principle in probability theory is more subtle – universality.

The maths of randomness: symmetry

Symmetry is one of the two guiding principles in understanding probabilities – if different outcomes are equivalent they should have the same probability.

The two envelopes problem solved

Here's a resolution for one of probability theory's most famous paradoxes.

Error correcting codes

Learn about magical mathematical methods for fixing errors on the fly.

Genetics: Nature's digital code

Is nature using digital tools to deal with genetic information?

• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.