Why is it that sometimes x means multiply, sometimes a dot or * means multiply and sometimes the absence of any symbol means multiply? Why the fuck didn’t we standardize a dedicated symbol for multiply?
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The symbol for multiplication is not x, it’s ×. The problem is it’s really freaking hard to differentiate the two sometimes, and that’s a problem when the most common letter for a variable is x. So the · became used for multiplication as well. On computers we use * because computers used to have a pretty small number of symbols they could use and we didn’t want confusion of x. We didn’t want to use x (it’s a letter, remember), and * was the closest character to either × or · in that small number of symbols, so we chose that.
As for the absence of a symbol meaning multiply, it turns out writing things like 2*a+3*b+8*x is kind of a pain in the ass. While we have PEMDAS, but it’s still annoying to read. 2a+3b+8x is easier to parse.
I want to point out that the asterisk was in use for multiplication hundreds of years ago, for example by Johann Rahn in his treatise *Teutsche Algebra*. At the time it was considered an “unsuccessful symbol for multiplication”. Pierre Hérigone is another creator of an unsuccessful symbol: he used rectangles to announce the start of a series of products separated by commas.
Multiplication by juxtaposition, or simply using no symbol at all and just putting the values together without separation (such as *ab*), can be seen as early as the Bakhshali manuscript and is arguably the longest surviving method to convey multiplication.
Many of these symbols were created simply because someone thought they could do it better. Oughtred’s cross was created because it felt like a natural addition to the already existing symbols (+, -, =, >). Leibniz created dot notation because he felt Oughtred’s cross was easily confused with the letter x.
Fast forward to a world where different places popularized different representations of multiplication and now you have to learn them all if you want to read a mathematical text.
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