Place value means a digit position changes its worth, which is why three means different things in thirteen and thirty.

The longer version

A digit carries two pieces of information: its shape and its column. The same mark three sits in the ones column of thirteen and the tens column of thirty, and the column multiplies it by ten each step leftward, so one symbol does duty for three and for thirty depending purely on where it stands.

That trick is why a handful of symbols can express any quantity, and why long multiplication reduces to shifts and adds. It also explains the need for a zero, since an empty column has to be declared empty. Non positional systems must invent fresh symbols for larger amounts, which is exactly where they run out of room.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.