Ambiguity and its cousins, contradiction and paradox, are everywhere in mathematics, both in content and thinking. Strangely, the subject that appears to be the very paradigm of reason, and that is ...

Draw a diagonal line across a unit square. Its length is √2, roughly 1.414. Now approximate that diagonal with a staircase of tiny horizontal and vertical steps. Each staircase has a length of 2 - one ...

Sometimes your gut feelings lead you astray—particularly in mathematics, in which one constantly comes across results that seem impossible. For example, infinity does not always equal infinity, and ...

Have you played the puzzle game Tangram? I remember, as a child, being fascinated by how just seven simple wooden triangles and other shapes could offer endless entertainment. Unlike LEGO, the Tangram ...

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...