History of Math Shaken Up As Fundamental Point 150 Years Older Than Thought

The origins of the decimal point, something millions of people use daily, may be much older than we first thought.

It was initially considered to have originated in 1593, having been used by German mathematician Christopher Clavius in his creation of astronomical tables.

Now, however, the decimal point has been discovered to have been used 150 years prior, by a Venetian merchant, according to a new paper in the journal Historia Mathematica.

According to the paper, a man named Giovanni Bianchini invented a system of decimal fractions in the 1440s, which he used in metrology and spherical astronomy.

This discovery was made after a mathematician studied parts of a manuscript written by Bianchini, and noticed that some of the numbers had dots in the middle of them, just like a modern decimal point.

"The first known appearance of the decimal point in German astronomer Christopher Clavius's sine table in 1593 had been puzzling: why invent a powerful new system of arithmetic, use it in such a narrow context, and then abandon it? In Giovanni Bianchini's Tabulae primi mobilis B from around 1440, we find its origin within a complete system of decimal fractional arithmetic that Bianchini had invented to measure distances, as well as to practice astronomy and cast horoscopes for his court at the Duchy of Ferrara," paper author Glen Van Brummelen, a math historian at Trinity Western University, told Newsweek.

This implies that decimal points were first used to represent non-whole numbers a century and a half earlier than we first thought.

Bianchini was a merchant who took on an administrative role with the d'Este family, where he managed assets and investments. He also published astronomy texts, plotting planetary motion and predicting when an eclipse would occur. It was in his astronomical texts that the decimal point first appeared.

Van Brummelen theorizes that Clavius likely got the idea to use the decimal point from viewing one of Bianchini's texts, which is why he never used it again.

"Clavius's introduction of the decimal point in the curious context of an interpolation column in a Sine table, and the fact that he never used it again, is simply explained: he had access to Bianchini's Sine table (or to someone who himself had borrowed from Bianchini), and he copied the structure of that table in his own work," he writes in the paper.

Bianchini himself is suggested to have come up with the decimal point as a result of his travels, as he is likely to have passed through the Islamic world multiple times. This is where many math concepts were being developed, and it is possible that this influenced Bianchini to develop a way of representing non-whole numbers.

"We don't know exactly how he came up with the idea. It might have been in his work with the biffa, an instrument that was used for surveying. Imagine that you have to find, say, the hypotenuse of a triangle, and you know the two other sides have lengths like "4 feet, 3 inches" and "5 feet, 7 inches". To use the Pythagorean Theorem, you have to square these lengths (multiply them by themselves). But what is "4 feet, 3 inches" times "4 feet, 3 inches"? It's much easier to multiply 4.25 feet by 4.25 feet. My guess is that he borrowed his work on the biffa into his astronomy, where the calculations were much more intense," Van Brummelen said.

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Update, 2/26/24, 4:15 p.m. ET: This article was updated with comment from Glen Van Brummelen.