Early counting systems relied on tallies or counting with fingers and toes. But when you have more things to count than you have body parts, it’s hard to keep track.
The Greeks used 27 letters to devise a counting system that got them to 99,999,999. These 27 letters were split into three groups of nine, with each group of nine assigned to a place value. The first nine letters were used for the ones, then next nine for the tens and the last group for the hundreds. Additional notations expanded those initial 999 possibilities to cover bigger numbers. Oddly, the most famous Greek mathematician, Pythagoras, rarely used numbers in his explorations of the relationships between geometric figures.
When the Romans conquered the Greeks, they brought their own numbering system, which was more suited to counting than calculating. Roman numerals spread with their empire, and were the dominant numbering system in Europe until about 1500 AD.
Our system of nine numerals plus zero originated about 500 AD with Hindu scholars. The concept of zero was hard for many early people to grasp: how can you count zero animals killed, or zero days since a rain storm? And how can nothing be something?
But, with zero, a numbering system using positions rather than specific symbols for larger numbers could be developed. A positional system makes it possible to write any number in a relatively compact form, and makes mathematical manipulation easier. Try adding XLIX plus XXIV, or dividing CCIV by XVI.
The Hindu system spread via Arab traders across Europe, and came to be known as Arabic numerals. It was taught in the Moorish universities in Spain around 1000 AD. Fibonacci’s popular book, Liber Abaci, written in 1202, described the Arabic numbering system and demonstrated useful applications, including calculation of profit margins and compound interest.
However, a 1299 edict in Florence forbade bankers from using the “infidel” numerals. This was perhaps because several handwritten Arabic numerals could be easily altered with a pen stroke, so that a zero could become a nine or a six. However, fraud protections aside, centuries of familiarity with Roman numerals likely contributed to the resistance to change.
For a time, both Roman and Arabic numerals were used in parallel. Arabic numerals were favored by scientists while Roman numbers were used for administrative purposes and by the Catholic Church. Calculations were performed using an abacus or a counting board with final results recorded with Roman numerals.
The invention of movable type in the mid-1400s standardized the appearance of Arabic numerals and made the fraud protection argument largely moot. Ultimately, merchants and bookkeepers recognized that working with Arabic numerals was faster than with the cumbersome Roman versions.
In 1494, Luca Paccioli published his book, Summa de arithmetic, geometria et proportionalità, which, in addition to describing the principles of double-entry bookkeeping, adopted Arabic numerals to explain principles of algebra and geometry. Helpfully, it also included multiplication tables up to 60, which further spread the adoption of Arabic numerals.
Today, it’s hard to imagine life without the sense of numbers or a numbering system that doesn’t fit neatly into the cells in a spreadsheet. Without the concept of zero and a flexible numbering system, precise calculations in science, engineering and accounting would be much harder, if not impossible. And while it is possible to use Roman numerals for bookkeeping, as the medieval clerks demonstrated, we certainly wouldn’t have ten-keys!