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Eli5: How did the Romans do complex mathematical calculations with Roman numerals and without using zero?

In: Other

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They mostly didn’t. Mathematics in antiquity was mostly the physically practical forms of math. Things like arithmetic, basic algebra, and basic geometry. More complex mathematics such as advanced geometry, advanced algebra, calculus were not invented yet.

Doing numerical operations on Roman numerals was tedious, and in general they avoided it. Instead, if something needed to be summed they would use an abacus. For engineering applications, they typically used geometry, the tools of which were a straight edge and a semicircle and can be done entirely without using numbers.

The Romans mostly used math for practical purposes…accounting, construction, engineering. And Roman numerals don’t have place meaning…an M is 1000 no matter where it is. As a result, they didn’t really need an explicit zero.

And addition, subtraction, and multiplication in Roman numerals isn’t hard. Somewhat tedious if you’re doing large values, but once you’re used to it not really any worse than memorizing times tables (which you don’t have to do for multiplying Roman numbers).

Division does suck…but they had abacuses. And abacuses inherently do place-based numbers. So if you needed to do “heavy” math you’d just use an abacus and that takes care of most of what makes it look like it would suck if done by hand.

Uncoincidentally, the Romans didn’t do much with pure mathematics. But that wasn’t what they were trying to do either.