Math Historian Saw Decimals in 1440s Treatise and Freaked Out

Glen Van Brummelen uncovers earliest known use of decimal to indicate base-10 number system
By Arden Dier,  Newser Staff
Posted Feb 23, 2024 4:15 PM CST
Math Historian Saw Decimals in 1440s Treatise and Freaked Out
A decimal tangent table from Giovanni Bianchini, showing decimal points in the interpolation columns.   (Historia Mathematica/Cracow, BJ 556, f. 52v)

How old is the decimal? It's a question you've probably never pondered but one that has fascinated certain historians. Fascinated isn't overstating it. When Glen Van Brummelen, a historian of mathematics at Canada's Trinity Western University, spotted a decimal used to indicate tenths of a number in a 15th-century treatise while teaching at a math camp for middle schoolers, "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!'" he tells Nature News. This early appearance of such a decimal, it turns out, is a very big deal to math historians. Science Alert calls "a mind-blowing discovery."

While versions of the decimal have been used as far back as the 900s, German mathematician Christopher Clavius was thought to have been the first to break down whole numbers by tenths, hundredths, and thousandths, in a 1593 treatise on the astrolabe, called Astrolabium. What Van Brummelen had discovered was the same usage in a much older text. In the 1440s, European astronomers made calculations using the sexagesimal numeric system of dividing a 360-degree circle into 60 minutes and dividing minutes into 60 seconds. The system uses 60 as its base in the same way our modern decimal system uses 10 as its base, though this makes multiplication difficult, requiring multiple conversions of values, per Nature News.

Giovanni Bianchini, a Venetian merchant who practiced astrology, found a simpler way—one that marked "a step forward for humanity," José Chabás, a historian of astronomy unconnected with the discovery, tells Live Science. It was while reviewing Bianchini's treastise Tabulae primi mobilis B that Van Brummelen and a colleague noticed he was dividing angles into minutes and seconds but giving the values as numbers with decimals using the base-10 system. Van Brummelen, author of a study published online for Historia Mathematica, believes the method originated with Bianchini, who would've learned calculations using real-world measures through his background in economics. Clavius would've been aware of his work, Chabás says. (More mathematics stories.)

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