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It is often said that Romans (see below) had a terrible number system, which made computations a mess. I do believe this, but I'm suspicious of the claim that nobody had better ways to do computations until Fibonacci brought Eastern techniques to Europe.

This is even more suspicious when you think how big the Roman empire was and that it featured a lot of fiscal checks (such as census), infrastructural works (hence engineering and logistics) and, above all, economic activity (can you believe greedy merchants didn't think of better ways to make calculations?).

So, were arithmetical algorithms so inefficient before Arabic numerals were adopted in Western Europe?

EDIT 1: I use Romans as a proxy for "ancient Western Europe civilization". I suppose anything known to Europeans (e.g. Greeks) in the last centuries BC and first centuries AD was known to Romans as well. Also, I assume anything known before was inherited, i.e. if Egyptians/Babylonians/Etruscan had wonderful arithmetical techniques, I doubt they got lost in history, since these are the kind of things that tend to be spread (see merchants, see what happened with Arab-Indian numerals).

EDIT 2: I'm not asking about numerals, but about techniques of computation. From the comments, I see that the two things had disjoint developments indeed.

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    $\begingroup$ Babylonians had a positional system (base 60) and well developed algorithms for it long before Indians, Arabs or Fibonacci, even before ancient Greeks. It was used by scientists during Hellenistic and Roman times. Even without that, Greeks and Chinese had proto-decimal systems. Egyptian system was less efficient, but they had well developed algorithms for it too. $\endgroup$
    – Conifold
    Jul 10, 2019 at 2:27
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    $\begingroup$ That the Greeks and Romans were bad at computations is a myth. As you point out, they made plenty of calculations, but they did them with an abacus using "calculi" (stones). Working with an abacus involves essentially positional mathematics with the same algorithms that were used up to recent times, except that they are immediately erased. This was in fact one of the reasons why Hindu numerals were adopted by accountants in Fibonacci's time. $\endgroup$
    – Chrystomath
    Jul 10, 2019 at 6:32
  • $\begingroup$ As already commented, people had been doing computations with "abacus" for a long time... but the computations had no record. So not only could one do computations with Hindu-Arabic numberals, but the computation itself was a record. This also lent itself to double-entry book-keeping, which facilitated a much broader scope of trade... because it would be very hard to "fake" accounts, so the owner back home would feel more secure that they weren't being cheated by their agents. $\endgroup$
    – paul garrett
    Jul 11, 2019 at 12:50
  • $\begingroup$ Roman numerals are semi positional. 999 is not IM because you have to deal with the hundreds first, then the tens, then the single digit. So 999 is CM XC IX. I calculate by using complements with 10, so for example 3 and 7 pair up automatically in my head. It seems to me that Roman numerals are if anything even simpler with that way of thinking, (And I want to protest that Fibonacci brought "Eastern" ideas. He was very much a European who under muslim occupation continued business as usual as far as possible. It took centuries for islam to exterminate civilization in occupied Europe.) $\endgroup$
    – LocalFluff
    Sep 15, 2019 at 9:41
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    $\begingroup$ Yeah, Roman numerals aren't counterintuitive, yet computations seems to be a pain in the arse. I do not understand your remark about Fibonacci: he learnt about Arab-Indian numerals in Lybia, not "occupied Europe" (if there was even such a thing in the 13th century). And what's up with extermination? $\endgroup$
    – seldon
    Sep 15, 2019 at 10:08

1 Answer 1

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No, Romans were not at all bad at computations before Arab numerals were introduced to them. In fact, Romans had a perfectly fine way of doing computations that was every bit as good as Arabic numerals. They used a table and stones to do computations, similar to an abacus. Roman numerals were just used to record numbers, not to do long computations. Though shorter computations were, in fact, easier in the Roman system than in the Arab system. This is explained here and is a fascinating read.

Pope Sylvester II (946-1003) introduced Arabic numerals to Europe but without 0. Without 0, Arabic numerals can't compete with an abacus for computation. Thus, they didn't spread for another 200 years, until Fibonacci successfully introduced them through his book Liber Abaci and merchants and others started learning how to use them.

Even so, it took a couple of hundred years more for Europeans to make the conversion. Computations aren't easier with Arabic numerals than with an abacus, and using them for computation requires paper for those computations, so there was a good reason not to use them. One minor advantage is that when you write down the computations, there's a record you can check. It was of this reason that Arab numerals were adopted and not because the Roman system was inefficient.

Note: Everywhere here I have used the term "Arab" numerals or system, but ideally it should be the "Hindu-Arabic" numerals or system. I used this terminology just because in the question it was referred to as Arab.

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  • $\begingroup$ Actually, according to that article you reference the roman system is only good for simple addition. It's terrible for multiplication and much, much worse for division. $\endgroup$
    – Mozibur Ullah
    Jun 2, 2020 at 4:38
  • $\begingroup$ @Mozibur, in my answer, I have said that "Roman numerals were just used to record numbers, not to do long computations." For that purpose abacus was used. Then I have mentioned that for shorter computations Roman numerals were, in fact, better. $\endgroup$
    – Big Brother
    Jun 2, 2020 at 5:56
  • $\begingroup$ @Mozibur, is your doubt clear? $\endgroup$
    – Big Brother
    Jun 3, 2020 at 0:16
  • $\begingroup$ Not really. You say 'the Romans had a perfectly fine way of doing computations that was every bit as good as Arabic numbers.' The advantages of the Arabic notation for numerals in computations are not minor. Take for instance cpu units, they do arithmetic exactly following Arabic numerals. $\endgroup$
    – Mozibur Ullah
    Jun 3, 2020 at 3:25
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    $\begingroup$ @Mozibur, the link which I mentioned says "Essentially, abacuses allowed you to convert Roman figures into a place-based system, do your calculations, then convert back." Thus, in Roman system calculations using abacuses were similar to calculations using Hindu-Arabic numerals. That is why I said that 'Romans had a perfectly fine way of doing computations that was every bit as good as Arabic numbers.' $\endgroup$
    – Big Brother
    Jun 3, 2020 at 5:05

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