Long before writing, before the wheel, people needed to know how many — how many sheep, how many days, how many mouths to feed. Arithmetic was humanity's very first technology: a tiny set of ideas that let us count, share, trade, and plan. Master it and you hold the keys to everything else in this tree.

It starts impossibly simply — pointing at things and saying one, two, three — and then it just keeps giving:

• Adding and subtracting — putting amounts together and taking them apart.
• Multiplying and dividing — shortcuts for adding the same thing over and over, and for splitting things fairly.
• Fractions, decimals, and negatives — numbers for the in-between, the tiny, and the "less than nothing".

And hiding inside these everyday operations are genuine surprises — prime numbers that can't be split, patterns that repeat forever, secret rules that make giant sums easy. Every more advanced idea in mathematics, all the way up to calculus, is built from these few moves.

There's one place to begin, the root of the whole tree: learning to count.

Start with Counting →