Take a quick trip to the foundations of probability theory.
Need to find the least common multiple or greatest common divisor of two numbers? A billiard table of the right proportions holds the answers!
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?