Why Negative Numbers Were Once Taboo

You probably take integers—whole numbers that can be positive, negative or zero—for granted. They’re the building blocks of everything from your phone’s battery level to your bank account balance. But for a long time, mathematicians weren’t so sure about negative numbers. In this post, we’ll explore why these “forbidden” numbers were once taboo, how they eventually earned their place in math, and where they pop up in your everyday world.

Where did this come from?

As early as the 2nd century CE, Chinese mathematicians used red rods to represent positive numbers and black rods for negative ones. But in Europe, negative solutions to equations were often called “absurd” or “fictitious.” It wasn’t until the 17th century that English mathematician John Wallis and French philosopher René Descartes began treating negatives as legitimate. Even then, some still argued you couldn’t have “less than nothing.” Over time, their power to solve real problems won the day, and negative numbers became part of standard arithmetic.

Where you’ll see this in real life

1. Personal finance: Your bank balance can dip below zero, showing a negative amount when you’ve overdrawn your account. 2. Temperature scales: In many places, winter temperatures drop below 0 °C, so negative numbers are essential on the thermometer. 3. Elevation: Topographic maps use negative values for depths below sea level (like Death Valley in the U.S. at –86 m). 4. Gaming scores and health bars: Video games often use negative points or “debuffs” to track status effects that weaken your character.

A common misconception

Many students think that subtracting a negative number is a mysterious fourth operation, but it’s really just addition in disguise. For example, 7 – (–3) becomes 7 + 3. The two minus signs cancel out, so you move three steps to the right on the number line. Likewise, multiplying two negatives (–4 × –5) gives a positive 20 because reversing direction twice lands you back on the positive side.