Mathematical models predict how fast a rumour will spread and how many people it's likely to reach.
A model of the interaction between predators and prey explains why sometimes frogs appear to eat snakes.
What would happen if the Sun suddenly exploded? Einstein wondered the same thing, and completely changed our understanding of the Universe.
Can you move a knight on a chessboard so that it visits every square exactly once? Euler was one of the first to analyse this problem systematically, but some questions about it are still open today.
Can you find a path through on this city map that crosses every bridge exactly once? Euler's answer to this problem started off the filed of graph theory.
Euler may not have cracked this problem completely, but it led to a lot of important work, including on what we today know as sudoku.
This surprising result about 3D shapes tells us something deep about the nature of space.
This problem about an infinite sum has a surprising answer.