Randomness is surprisingly hard to define. Fortunately the mathematical language we use to describe it is beautifully well defined.
The second guiding principle in probability theory is more subtle – universality.
Symmetry is one of the two guiding principles in understanding probabilities – if different outcomes are equivalent they should have the same probability.
Here's a resolution for one of probability theory's most famous paradoxes.
Is nature using digital tools to deal with genetic information?
Learn about magical mathematical methods for fixing errors on the fly.
Double counting proves a neat result in graph theory.
Can physics do for maths what maths has done for physics?