This has bugged me for years, and I’ve never been able to come up with an answer. We know that the Romans built a lot of great structures, aqueducts, etc., so their engineering skills must have been pretty good, but how in the world did they make those complex calculations using Roman numerals?

Maybe I’m just not able to grasp it, since I’ve been working with numbers that have fixed place notation since grade school, but even adding and subtracting Roman numerals gives me a headache. I always have to convert first and then do the math. Long division? Forget about it. Don’t even mention algebra, trigonometry, etc. For that matter, do Roman numerals even have any notation for non-whole numbers?

Was there some method of calculation that lent itself to working with this kind of notation? Would someone who grew up in Rome be able to do calculations in their head, but be totally stumped by our notation?

Any insights would be appreciated.