How Were Numbers Invented and When?

Imagine a world without numbers: you wouldn’t know how much money you had and when you spent it you’d have no idea how much anything cost. On the other hand, you wouldn’t have to do quadratic equations.

The earliest evidence of numbers ever found, tally marks scored into stone, dates from more than 30,000 years ago. Making marks on stone or wood is all very well if you just want to keep a note of small numbers, but if you want to use bigger numbers, you need a system. For example, without a system the number 23 would look something like this:

/////////////////////// (i.e. not very useful).

But because we’re working on the decimal system, we put a 2 in the left-hand column to signify two lots of ten, and a 3 in the right-hand column to signify three lots of one.

The first people to use a number system were the ancient Mesopotamians, around 3400 BC. Unlike our decimal system (base ten), the Mesopotamians had a sexagesimal system (base 60). They probably liked the number 60 because so many other numbers divide evenly into it. The number 23 in the decimal system means two lots of ten and three lots of one, but for an ancient Mesopotamian the number would mean two lots of sixty and three lots of one, 123 in the decimal system.

We have the ancient Egyptians to thank for the earliest example of the decimal system, which dates to about 3100 BC and which means we don’t have to multiply by 60 all the time.

Zero tolerance: The 1 to 9 digits we use today were developed in India by Aryabhata I about AD 500. In the 800s Persian mathematician Muhammad ibn Musa al-Khwarizmi was among the first to establish the idea of using a 0 to show powers of ten (10, 100, 1,000 etc.)