# How did the Romans do math? **URL:** \ **Category:** Factual Questions\ **Created:** [October 19, 2008, 1:09am UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588 "2008-10-19T01:09:37Z")\ **Posts on this page:** 9\ **Page:** 2
**Author:** ![diggleblop](https://avatars.discourse-cdn.com/v4/letter/d/ac91a4/32.png) [@diggleblop](https://boards.straightdope.com/u/diggleblop)\ **Post date:** [October 20, 2008, 4:14pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/21 "2008-10-20T16:14:26Z")
Probably with something like this: [http://www.break.com/index/marble-based-calculator.html](http://www.break.com/index/marble-based-calculator.html) ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [October 20, 2008, 4:27pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/22 "2008-10-20T16:27:24Z")
\>I would say the most likely correct construction would be DCCIV - seven hundred and four. I’ve read that our modern use of IV was typically not used by the Romans, because it would be inviting trouble to drag Jupiter’s name into one’s banking. We consider J and I to be separate letters, likewise U and V. The Romans had not yet set aside J and U as proper letters, and JUpeter and IVpeter would have been undifferentiated. So, IV was a form of a god’s initials, and off limits for numbering. They would have used IIII. I don’t have a cite or any evidence one way or the other on this, tho. ---
**Author:** ![AHunter3](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ahunter3/32/368_2.png) [@AHunter3](https://boards.straightdope.com/u/AHunter3)\ **Post date:** [October 20, 2008, 4:41pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/23 "2008-10-20T16:41:04Z")
My Mom once showed me how to multiply roman numerals (like CXXVIII \* CXCIX). I’ve blocked it out of my memory, it was rather horrid; it was a very compelling learn-from-experience way of getting the superiority of the Arabic system rather than just being told of it “as a fact”. ---
**Author:** ![Captain\_Carrot](https://avatars.discourse-cdn.com/v4/letter/c/f0a364/32.png) [@Captain\_Carrot](https://boards.straightdope.com/u/Captain_Carrot)\ **Post date:** [October 20, 2008, 5:01pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/24 "2008-10-20T17:01:30Z")
Ah, yeah, my bad, **Napier** , I misinterpreted what you said. ---
**Author:** ![Tuckerfan](https://avatars.discourse-cdn.com/v4/letter/t/eada6e/32.png) [@Tuckerfan](https://boards.straightdope.com/u/Tuckerfan)\ **Post date:** [October 20, 2008, 7:52pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/25 "2008-10-20T19:52:44Z")
> [@Napier](#): > > \>I would say the most likely correct construction would be DCCIV - seven hundred and four. > > I’ve read that our modern use of IV was typically not used by the Romans, because it would be inviting trouble to drag Jupiter’s name into one’s banking. We consider J and I to be separate letters, likewise U and V. The Romans had not yet set aside J and U as proper letters, and JUpeter and IVpeter would have been undifferentiated. So, IV was a form of a god’s initials, and off limits for numbering. They would have used IIII. > > I don’t have a cite or any evidence one way or the other on this, tho. I do, [and nobody really seems to know.](http://www.straightdope.com/columns/read/438/why-do-clocks-with-roman-numerals-use-iiii-instead-of-iv) ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [October 20, 2008, 10:01pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/26 "2008-10-20T22:01:42Z")
Captain Carrot, thanks, not to worry. \>My Mom once showed me how to multiply roman numerals (like CXXVIII \* CXCIX). I think this would be “compound arithmetic”, the method used for instance to add distances that are in miles, feet, and inches or to add angles that are in degrees, minutes and seconds. Something like a hundred years ago there was a commonly used math textbook by Pike, used to punish schoolchildren, or educate them in this valuable skill. I think the disuse of compound arithmetic ranks up there somewhere with the eradication of polio; not as severe an event, surely, but many more people suffered. ---
**Author:** ![CJJ](https://avatars.discourse-cdn.com/v4/letter/c/ecc23a/32.png) [@CJJ](https://boards.straightdope.com/u/CJJ)\ **Post date:** [October 20, 2008, 10:07pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/27 "2008-10-20T22:07:27Z")
> [@Napier](#): > > It is easy to consider Roman numerals as a ridiculously ineffective and quaint way of doing math, and I have no desire to use. But they have their merits. For example, when you read, damaged characters are generally obvious, and usually don’t make the sentence look correct but convey a different meaning. The same is true of Roman numerals. With Arabic numerals, changing one of the characters always produces a different but correct-looking statement. There is an anecdote in Suetonius’ [life of the emperor Galba](http://www.bostonleadershipbuilders.com/suetonius/galba.htm) regarding a large inheritance Galba would have received but which then-emperor Tiberius reduced by deliberately misreading the Roman numerals in the will: > [@](#): > > Most of all, he (Galba) courted the empress Livia, by whose favour, while she was living, he made a considerable figure, and narrowly missed being enriched by the will which she left at her death; in which she distinguished him from the rest of the legatees, by a legacy of fifty millions of sesterces. But because the sum was expressed in figures, and not in words at length, it was reduced by her heir, Tiberius, to five hundred thousand: and even this he never received. Several supplemental marks were used by Roman accountants when dealing with large numbers. An overhead bar, for example, indicated multiplication by 1000, while a variety of marks looking something like parentheses offered even higher multipliers. However, writers also wrote numerals with a long bar overhead simply to set them off from the rest of the prose; not to multiply, but simply to avoid having the letters mistaken for (parts of) actual Latin words. Writers therefore often followed different customs for showing large numbers in prose (see [this site](http://home.att.net/~numericana/answer/roman.htm) for a good explanation). Suetonius implies Tiberius took advantage of these discrepancies so that he could reinterpret the text of the will in a way more favorable to him (he was Livia’s son and so wanted to keep more of the inheritance for himself). ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [October 20, 2008, 10:09pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/28 "2008-10-20T22:09:54Z")
\>I do, and nobody really seems to know. Nice find, Tuckerfan! Now, in this cite, E.L.F. does seem to think he knows, and that whatever author he read knew. The logic seems a little tangled up, because that conversation was about clock faces, and E.L.F. seems to have thoughtlessly said that the same reasoning I mention was the reason Roman clockmakers avoided “IV”. I presume on second thought he’d have corrected himself to say that Romans in general avoided “IV”, and the clockmaking theme had nothing to do with it, but rather just tripped him up. There must be people who know, because there is plenty of Roman writing still around. We just haven’t found any of those people yet. ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [October 20, 2008, 10:15pm UTC](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588/29 "2008-10-20T22:15:05Z")
> **[Roman numerals](https://en.wikipedia.org/wiki/Roman_numerals)** > > Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value. Modern style uses only these seven: > The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process... "The notation of Roman numerals has varied through the centuries. Originally, it was common to use IIII to represent four, because IV represented the Roman god Jupiter, whose Latin name, IVPPITER, begins with IV. The subtractive notation (which uses IV instead of IIII) has become universally used only in modern times. For example, Forme of Cury, a manuscript from 1390, uses IX for nine, but IIII for four. Another document in the same manuscript, from 1381, uses IV and IX. A third document in the same manuscript uses IIII, IV, and IX. " [Previous page](https://boards.straightdope.com/t/how-did-the-romans-do-math/468588.md?page=1)