Arithmetic & Number

Arithmetic and number is the study of counting, measuring, and combining quantities using operations like adding, subtracting, multiplying, and dividing.

Where Numbers Began

Long before anyone wrote equations, people needed to keep track of things — sheep, sacks of grain, days until harvest. Around 20,000 years ago in Africa, someone carved rows of notches into a baboon's leg bone, now called the Ishango bone. Those tally marks are among the oldest known signs of counting.

As villages grew into cities, counting on fingers wasn't enough. In ancient Sumer (modern Iraq), around 3400 BCE, merchants pressed marks into clay tablets to record trades. This was the birth of both writing and arithmetic — the two grew up together.

The Ishango bone (c. 20,000 years old), an early tally stick with carved notches — source

The Four Operations

Arithmetic rests on four basic moves:

• Addition ($+$) — putting groups together.
• Subtraction ($-$) — taking away.
• Multiplication ($\times$) — fast repeated adding.
• Division ($\div$) — sharing into equal parts.

Think of multiplication as a shortcut: instead of adding $4 + 4 + 4$, you write $3 \times 4 = 12$. It's like using a wheelbarrow instead of carrying bricks one by one.

The Power of Zero

For a long time, the world had no symbol for "nothing." How do you write the number 205 without a placeholder in the middle? Indian mathematicians solved this. Around 628 CE, the scholar Brahmagupta wrote rules for using zero as a real number, not just an empty space. He explained that a quantity minus itself equals zero:

$$a - a = 0$$

This idea travelled through the Islamic world — the Persian scholar al-Khwārizmī (whose name gave us the word "algorithm") spread it around 820 CE — and finally reached Europe, where it powered banking and trade.

Why It Still Matters

Every price tag, phone number, recipe, and computer chip depends on arithmetic. The system you learned in school — ten digits, place value, zero — is a shared human invention, polished over thousands of years across many cultures.

Further exploration

• Georges Ifrah, The Universal History of Numbers (2000) — a sweeping, readable tour of how humans invented counting worldwide.
• Charles Seife, Zero: The Biography of a Dangerous Idea (2000) — the surprising story of nothing and the fights it caused.
• Brahmagupta, Brāhmasphuṭasiddhānta (628 CE) — the ancient text that first set down the rules of zero.