Multiplying Roman Numerals Like the Romans Did [Math Mini]

The Roman Numeral system is particularly different from our decimal number system in this key respect: it has no place value. Rather than represent values by some power of 10 (or otherwise), roman numerals represent value additively. Each symbol stands for a certain value, and to get the complete number you just add all the values up. This makes it hard to write large numbers, and it makes it *especially* hard to multiply. Basically, if you were good at multiplication in ancient Rome, you were at the height of mathematical sophistication.

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[diogorrify]

Why did you sum II with II and get IIII and not IV? You sneaky..

[epiendless]

I saw an article about this years ago, and my immediate thought was, that's how I'd do binary long multiplication in machine code. Shift and add.

[LLivLLaffLLuv]

This system is great, but oh my god am I glad for the modern number system

[rosy-rho]

The multiplication algorithm is interesting but I’m far more interested in their motivation for this algorithm. How did they come up with it? Did they try other algorithms earlier on?

[crclayton]

What’s your source for this? Did some Roman actually document their methodology and we still have it preserved or is this just a guess at one possible way they could’ve done it?

[bryanfain]

How did the Romans perform long division?

[bhargavk]

Apparently, Romans had abacus. You can do these sort of multiplication conveniently without paper and pen using abacus.

[sundareshvenugopal]

I was wondering if it is possible to do math without zero. The romans seemed to have had no problem. Since zero is often suggestive and representative of empty or nothing is it really necessary ? For continuos math, where concepts such as limits come into play I do not know. Even otherwise, if two quantities are equal, it means, they are identical, there is no difference between them, in other words their difference is zero or nil.

[bioemiliano]

lol this is basically what I do in my head

[FreddieVee]

After watching that, I take no pride in being of Roman descent.

[bryanfain]

How did the Romans perform long division?