The Decimal Point Is 150 Years Older

A Venetian merchant used the mathematical symbol while calculating the positions of planets between 1441 and 1450

published : 04 April 2024

For years, historians thought decimal points emerged when German mathematician Christopher Clavius began using them while writing about astronomy in 1593.

But new evidence suggests the decimal point may be 150 years older than previously thought: A 15th-century Venetian merchant named Giovanni Bianchini appears to have used the mathematical symbol in documents that date to between 1441 and 1450, according to a paper published this month in the journal Historia Mathematica.

Study author Glen Van Brummelen, a math historian at Trinity Western University in Canada, was teaching at a middle-school math camp when he noticed something intriguing: The number 10.4 was written in one of Bianchini’s Latin manuscripts, Tabulae primi mobilis B. Bianchini was explaining how to multiply 10.4 by 8.

“I realized that he’s using [the decimal point] just as we do, and he knows how to do calculations with it,” Van Brummelen tells Nature’s Jo Marchant. “I remember running up and down the hallways of the dorm with my computer trying to find anybody who was awake, shouting, ‘Look at this, this guy is doing decimal points in the 1440s!’”

Tabulae was a document that explained how to calculate the coordinates of planets. At the time, Bianchini was working for the d’Estes, the ruling family of Venice. As a merchant-turned-administrator, he helped guide the family’s investments—but he was also responsible for making horoscopes, which meant he had to study the night sky using trigonometry. Without computers, medieval astronomers relied on mathematical tables for these calculations.

“Suppose you’re using this table: It tells you what the sine of 43 degrees is. It tells you what the sine of 44 degrees is,” says Van Brummelen to NPR’s Scott Simon. “But planets don’t just hop from one degree number to the next. They travel continuously between them. So [there are] going to be moments when you’re going to have to work out the sine of a number that’s between 43 and 44 degrees. And that’s where we find the dots in his tables.”

This discovery “reveals the richness of medieval scientific activity, dispelling the popular notion that the medieval era was a time of intellectual stagnation,” per a statement from Trinity Western University.

Even so, Bianchini’s decimal point didn’t catch on right away. But 150 years later, Clavius may have read Bianchini’s work and adopted the symbol.

Previously, Clavius’ limited use of the decimal point—he didn’t use it in his later writings—had puzzled historians. “Why invent a powerful new system of arithmetic, use it in such a narrow context and then abandon it?” as Van Brummelen tells Newsweek’s Jess Thomson. Clavius’ behavior makes more sense if he was simply copying Bianchini’s work.

While “some versions” of decimals are much older, a “consistent system” didn’t emerge until Bianchini and Clavius, as Live Science’s Stephanie Pappas writes. Before that, mathematicians relied primarily on fractions and other complicated configurations. When decimal points went mainstream, they helped make complex calculations simpler across a wide array of situations.

“That’s actually the power of our decimal fractional number system—the fact that you can use the same number system to balance your checkbook, to measure distances, to transfer it to all sorts of different contexts,” Van Brummelen tells NPR. “It’s a universal system … It shows that mathematics comes from all sorts of concerns all over human experience.”