Talk:Roman numerals

Here in this article as well as in elder discussions, there have been repeated claims that this writing had been normal since Ancient Rome or that they would need a proving example of "VIIII". When reading sources of the High Middle Ages, you probably won't find any usages of substraction. Look up the diplomata of Frederick Barbarossa, and you will find dozens of pure addition writings. https://www.dmgh.de/mgh_dd_f_i_2/index.htm#page/44/mode/1up Universal-Interessierter^de (talk (de)) 01:58, 9 March 2025 (UTC)

Chrisomalis (2010) Numerical Notation: A Comparative History (p. 111 ff.) says:

Starting in the late republican period, the subtractive principle was occasionally used for writing multiples of 4 or 9 (or rarely 8) of powers of 10. As would later become the rule with modern Roman numerals, placing a lower-valued power of 10 to the left of a higher numeral-sign indicated subtraction of the former from the latter (IX for 9, XL for 40, but never using sub-base signs as the subtrahend – i.e., VC is unacceptable for 95). This reduced the length of numeral-phrases – four or five numeral-signs were replaced by two. Similarly, in the Augustan period and into the early empire, the use of the subtractive XIIX and XXIIX for 18 and 28 were common, and IIX and XXC for 8 and 80 are also attested (Gordon and Gordon 1957: 176–181). Addition was used almost exclusively in the early republican period, and is the more usual form even in later classical inscriptions (Sandys 1919: 55–56).4 Subtractive numerals are more common where a numeral is at the end of a line of an inscription, allowing the engraver to avoid crowding many numeral-signs into a limited space (Cajori 1928: 31). They may be more common in informal texts than in formal inscriptions (Gordon and Gordon 1957: 180–181; Cagnat 1964: 30–31). Despite Guitel’s (1975: 202–203) denigration of subtractive notation because it lacks the simplicity of the pure additive principle, it is a very economical way of structuring numeral-signs. The Latin lexical numerals use the subtractive principle for 18 and 19 (duodeviginti, undeviginti), perhaps explaining the origin of this practice. Note, however, that while duodeviginti and undeviginti are subtractive, novem (VIIII/IX), quatuordecim (XIIII/XIV), nonaginta et novem (LXXXXVIIII/XCIX), and all other Latin lexical numerals are not. The purely additive form was most common but the subtractive version was also attested from ancient sources.

[...] Subtractive forms were used more frequently in the Middle Ages, though purely additive forms (e.g., IIII) were still common. [...]

–jacobolus (t) 04:47, 9 March 2025 (UTC)

I and X are the only symbols that may be possibly subtracted from a higher value in a Roman numeral.

IV, IX, XL, and XC are the only possibilities for subtractive notation with very few exceptions. The juxtaposition has a different meaning for larger numerals.

D = 500 (half mill)

CD = M = 1000 (full mill)

DD = 5000 (half big mill)

CCDD = CMD = 10,000 (full big mill)

DDD = 50,000 (half huge mill)

CCCDDD = CCMDD = 100,000 (full huge mill)

— Justina Colmena ~biz (talk) 22:39, 11 February 2026 (UTC)

According to the Sourcebook in the Mathematics of Medieval Europe and North Africa (doi:10.23943/princeton/9780691156859.003.0002),

The subtractive principle—that is, the rule that a smaller number placed to the left of a larger shall be subtracted from it (e.g., IX = 9)—was sometimes used during the Middle Ages, but one might see both IIII and XL in the same document (representing 4 and 40, respectively).

–jacobolus (t) 09:11, 9 March 2025 (UTC)

David Eugene Smith (1926) says:

Out of 119 inscriptions of the period 250 B.C. to 500 A.D., of which the dates are approximately known, and in which the number four appeared, 79 were found to contain the form IIII or IIII, while 40 had the form IV.

Going onward from that, Smith points out that the form IX was very rare in the Middle Ages, but that subtractive notation was used for larger numbers (e.g. XCC for 190), and speculates that maybe IX was avoided for religious superstition because it was the initials of Jesus Christ. –jacobolus (t) 18:04, 9 March 2025 (UTC)

You seem to have some good references, it would propbably be best to fix the article which I suspect has accumulated a lot of false "wikipedia facts". Your referenced text also clearly states that subtractive "reduced the length of the numeral-phrases" and implies that is the reason it was used, it would be nice to add this sky-is-blue statement to the article with this reference. Spitzak (talk) 20:20, 9 March 2025 (UTC)

Yeah, the article's text definitely misrepresents available scholarship. If anyone wants to put this right it would be appreciated. I don't feel like doing a careful literature survey right now. –jacobolus (t) 21:18, 9 March 2025 (UTC)

A recent addition asserts the earliest attested uses [of nulla for 0] are not until fairly late into the empire (around 200 AD), considerably earlier than we had. @AnAlpineSymphony:, do you have a source for this? It's also awkward in that 200 AD isn't fairly late in even the western Roman Empire, and because we go on to say For instance ... in a manuscript from 525 AD which doesn't follow at all, so for the time being I'll revert it, until we've got a WP:RS and know how we want to rephrase this part. NebY (talk) 19:14, 28 May 2025 (UTC)

@Spitzak: Thank you for retaining part of my edit! I'd like to discuss this further, since I still feel the article is improved, rather than worsened, by removing this footnote entirely. My position is based on this line of thought. The first part of the sentence ("IV and IX [...] have fewer characters than IIII and VIIII", is obvious to the point of triviality, and so goes just as well without saying. My issue is with the factual claim in the second part of the sentence: "IV and IX [...] are less likely to be confused (especially at a quick glance) with III and VIII"). I see how one could suppose this on the theoretical basis that it is difficult to quickly distinguish three vertical lines from four. On the other hand, I can also imagine other things that we don't state in the article: maybe IV and IX pose special difficulties for quick comprehension, because they are formed according to a different principle than the majority of Roman numerals (subtractive rather than additive), and they are the mirror image of distinct numerals (VI and XI), which seems like it could make them more confusable for a dyslexic. Taking the step of explicitly pointing out that "IV and IX [...] are less likely to be confused (especially at a quick glance) with III and VIII" carries a certain implication of significance (which is I assume why the footnote previously started with the disclaimer "Without theorising about causation"): it makes it seem like this is a notable benefit of the subtractive notations, or a factor that contributed to their use. That is not obvious, and for that reason I am not yet convinced that it is really true: subtractive notation might have come into use for its ability to save space even if it provided no net benefit in terms of readability/reduced confusability. Therefore, I think the article is better off not making claims about how confusable different notations are unless there are any sources that make reliable statements about this (I could imagine running experiments to support it, but I don't expect anyone to have done so). At minimum, I think this statement ought to be followed by an in-line citation to the specific portion of a reliable source that supports it, per the Verifiability policy. Urszag (talk) 20:11, 30 October 2025 (UTC)

A numeral is the representation of a number; a numerical value. The plural form (numerals) would be two or more. It would not be the system used to form the things of the collection. Further, "Roman numerals is" is tortured English. Should be "A Roman numeral is ...". I didn't just make that change since I'm very sure others will have cow about this change. Stevebroshar (talk) 10:22, 18 November 2025 (UTC)

My impression is that this article was named so that the various articles Arabic numerals, Brahmi numerals, Egyptian numerals, etc. would be consistent. Another possibility might be to use a title such as Roman numeral system. –jacobolus (t) 20:32, 18 November 2025 (UTC)

Yes, we'd like such consistency if possible, and we do have a lot of "X numerals" articles - see {{Numeral systems}}. Some start with "X numerals is the numeral system", some with "X numerals are the numeral system", and some go a different way, including two of your examples.

Arabic numerals: The ten Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are the most commonly used symbols for writing numbers.^{[citation needed]} The term often also implies ...

Egyptian numerals: The system of ancient Egyptian numerals was used in ...

I rather like that one. Grafting it into the current text would give

The system of Roman numerals originated in ancient Rome and remained the usual ... NebY (talk) 21:10, 18 November 2025 (UTC)

To be honest though, @Stevebroshar this doesn't seem like the most important thing to worry about: I would recommend you spend time trying to improve the content of the articles instead of trying to twiddle the names around. –jacobolus (t) 23:22, 18 November 2025 (UTC)

D and M, or IↃ and CIↃ, were a "half mill" and a "full mill" for 500 and 1,000 respectively.

IↃↃ and CCIↃↃ were a "half big mill" and a "full big mill" for 5,000 and 10,000 respectively.

IↃↃↃ and CCCIↃↃↃ were a "half huge mill" and a "full huge mill" for 50,000 and 100,000 respectively.

A Chinese numeral was then placed over any one of these Roman mill symbols to indicate the power of 1,000 by which the mill symbol should be multiplied, (that is, the *illion to be represented, multiplying by 500, 1000, 5000, 10000, 50000 or 100000),

一 for 1,000

二 for 1,000,000

三 for 1,000,000,000

四 for 1,000,000,000,000

etc.

The ancient Romans were no strangers to hyperinflation and/or counterfeit coinage and the necessity of working with very large numbers. Justina Colmena ~biz (talk) 08:57, 11 January 2026 (UTC)

Ancient Romans did not use Chinese numerals. –jacobolus (t) 21:33, 11 January 2026 (UTC)

That is in fact where the "short scale" of numeration common in the United States (but not in modern Europe) originated. Chinese numerals used as exponents of 1000 were interpreted as "fireworks" — if the ancient Romans (or even Greeks for that matter) handled numbers 500,000,000,000,000 or larger, then they would have had to work entirely in a Chinese decimal system of sorts if they did not borrow certain symbols for certain purposes. Today we use a common variant of Arabic numerals and work out sums, differences and products from right to left.

Hyperinflation was a fact. Justina Colmena ~biz (talk) 22:58, 11 January 2026 (UTC)

There is no extant evidence whatsoever that ancient Rome imported a number system from China. Fireworks weren't invented until many centuries after the fall of the Western Roman Empire. Please take unsourced fringe speculation someplace else. It's off topic for Wikipedia talk pages. –jacobolus (t) 01:31, 12 January 2026 (UTC)

The article mentions that Big Ben depicts the hours as I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. This is untrue, the clock uses an F instead of an X. You can see for yourself here: https://upload.wikimedia.org/wikipedia/commons/a/a6/Big_Ben_Clock_Face.jpg

This virtual tour created by parliament discusses it further: https://virtualtour.parliament.uk/bigben

"The famous dial features Pugin’s favoured gothic numerals rather than traditional roman numerals – an ‘F’-shaped character replaces X for 10. These numerals are also found on clocks around Parliament." ~2026-24939-2 (talk) 14:53, 12 January 2026 (UTC)

That is an X (not an F). It's just written in a typeface based on a very old style of handwriting (see Blackletter). Here's a full alphabet in the same style: https://luc.devroye.org/Textura_aerotype_Octoberfest.gif –jacobolus (t) 16:52, 12 January 2026 (UTC)

Four o'clock is "IIII" in Roman numerals. The "F" doesn't belong there either. Justina Colmena ~biz (talk) 06:37, 15 January 2026 (UTC)

I don't understand what you mean. Some clocks use IIII to mean 4, and others (such as Big Ben's clock) say IV. These are two different Roman-numeral representations of the same number. There are no Fs. –jacobolus (t) 09:01, 15 January 2026 (UTC)

The Royals didn't like that clock face. Justina Colmena ~biz (talk) 13:01, 15 January 2026 (UTC)

It does indeed look like an F (the image provided confirms this), and as stated, the official website of the Great Clock of Westminster ("Big Ben") also makes this claim. The clockface shows IF, F, FI and FII to represent the numbers 9 through 12.
If indeed the reason is that the architect Augustus Pugin was using a Gothic typeface, then that fact surely also renders it as NOT a series of Roman numerals. Although there is some thought that he did so for religious reasons:
https://1citizenoftheworld.wordpress.com/tag/big-ben/ GregEccleston11 (talk) — Preceding undated comment added 06:28, 23 January 2026 (UTC)

It is not an 'F', and does not even look like an 'F' to anyone who has any familiarity with old typefaces. And the fact that the letters I, V, and X are in a particular font obviously does not make them "not Roman numerals". The site you refer to is "some blog" full of random speculation in broken English. The end. Imaginatorium (talk) 07:03, 23 January 2026 (UTC)

Saying "an ‘F’-shaped character " is imprecise, but in any case, it is not the same thing as "the letter F". Another source of confusion is that "Gothic" as a name for a script/typeface family (as seen at Blackletter#Fraktur) can be opposed to "Roman" as a name for another script/typeface family (the one in which modern English is normally written). This is only remotely connected to the word "Roman" in "Roman numerals": they are not called "Roman" because they are written in Roman script/type. They can equally well be written in other Latin scripts, such as italics. Roman numerals are are called "Roman" because they were used by the Romans. Meanwhile, "Roman" type is called that because its capital forms were based on the Roman capital script used in inscriptions.--Urszag (talk) 13:49, 23 January 2026 (UTC)

So-called "Arabic" numbers are actually and historically Indo-Arabic numbers. Meaning, they came to Europe via the middle-east (Islamic Spain) but they originate from India. So, the bringer is not the source. ~2026-95082-0 (talk) 22:06, 11 February 2026 (UTC)

By far the most-used symbols in Europe were the Arabic numerals so there is nothing wrong with calling them that. Spitzak (talk) 22:10, 11 February 2026 (UTC)

that symbol looks a lot like the greek Sampi to me. Also, looking at the actual Gothic script article linked in the table, they don't seem to have had any letters looking like the Sampi... ~2026-13155-88 (talk) 17:06, 5 March 2026 (UTC)

The symbol used in the table is literally a sampi, but I don't think the indicated original symbol was supposed to be. The sources used for this table are not obvious though. Some probably comes from Cappelli's Lexicon Abbreviaturarum. But I don't see this 900 symbol in there. –jacobolus (t) 18:35, 5 March 2026 (UTC)

Looks like it's supposed to be some version of this symbol: 𐍊. But again, I don't see a source. Maybe you want to hunt through the history of this page, figure out who originally added this, and ask them? Edit: the source does seem to be Cappelli; this symbol is shown in the Italian edition of his book, not sure why it was apparently omitted in the German translation. –jacobolus (t) 18:38, 5 March 2026 (UTC)

@JMyrleFuller, can you enlighten us? You added the "ϡ" symbol as 900 back in 2019 but without mentioning a source, at least not in that edit. NebY (talk) 19:22, 5 March 2026 (UTC)

@NebY: I was not the one who chose that symbol. When I originally put the table in, which if I remember right was over 15 years ago, I used an up arrow which was as close as I could approximate Capelli's mark. Unfortunately Capelli doesn't provide any sources or context as to what it was supposed to be and of course, he's long dead now. Whoever did change it to sampi, which I think was before 2019, I think thought it resembled a Gothic form of sampi, in analogy to the 800 being a Gothic form of the Greek omega. Again, this is just my memory of that edit, do not ask me how I remember such a minutia or who did it. J. Myrle Fuller (talk) 22:50, 5 March 2026 (UTC)

Upon inspecting the Gothic alphabet article, it appears that is exactly what was being implied. Capelli's mark matches a mark used for 900 in a Biblical codex cited in the Gothic alphabet article, which likewise attributes it to sampi. J. Myrle Fuller (talk) 22:53, 5 March 2026 (UTC)

As a minor clarification, the Gothic numeral is not attested in any version of the Gothic Bible; it appears (apparently only) in the page of the medieval Codex Vindobonensis 795 where Alcuin discusses the Gothic alphabet, which is shown as the image at Gothic alphabet. (Codex Vindobonensis uses Latin numerals as a gloss for Gothic numerals, rather than using them both as part of the same numeral system.)--Urszag (talk) 12:48, 7 March 2026 (UTC)

I realized after I wrote that. It was a codex, just not a biblical one. J. Myrle Fuller (talk) 20:28, 7 March 2026 (UTC)

With this discussion in mind, I've revised the table to remove the non-Latin letters from it and noted them instead in the paragraph above, since technically, they're not really Roman numerals at all, just Gothic numerals mixed in with medieval Roman scribal abbreviations like some weird hodgepodge (which Capelli's index demonstrates happened quite a bit). J. Myrle Fuller (talk) 00:20, 7 March 2026 (UTC)

The portion of Cappelli currently cited (pp. 413–421) seems to just be a contextless table of forms. However, the table suggests there is also discussion somewhere else in this source: "Cappelli notes that the T with double dot is only attested for Spanish-suited playing cards and may have been derived from the Gothic form of sampi, which used a T-like symbol to represent 900." Can an in-line citation be added pointing to where Cappelli discusses the potential connection to Gothic? I'm not sure I understand yet the reasons why borrowing with the Gothic numeral as an intermediary source would be considered more plausible than borrowing directly from the Greek numeral .--Urszag (talk) 12:48, 7 March 2026 (UTC)

My understanding is that the Gothic alphabet and (including alphabetic numerals) were mostly (but not entirely?) adapted from Greek. It seems plausible that there would be mixture of such numerals with Roman numerals text written by Gothic authors, not necessarily considered as "Greek numerals" per se. But I am not remotely an expert. Maybe there's a source somewhere discussing this? –jacobolus (t) 23:56, 7 March 2026 (UTC)

Admittedly this is likely a very niche topic, far beyond my knowledge or just about any amateur's. All I have to work off is that Cappelli reference book and a bunch of dictionaries I used to read as a kid, which is how I found out about the topic in the first place, and both of those are centuries after the fact. There are likely very few people with the precise expertise in the context of these numerals: we're talking hardcore medieval scholars here, which I obviously am NOT. There's enough context to say they exist and can be listed here, but not much else. J. Myrle Fuller (talk) 20:45, 8 March 2026 (UTC)

I agree that the subject doesn't really need to be belabored in this article. We don't need to mention every manuscript's number usage. There were obviously many variant symbols, idiosyncratic abbreviations, etc. if you look at a millennium of written documents in a wide geographical area. The article currently says that these symbols "today are called 'medieval Roman numerals'", but the term "medieval Roman numerals" seems to be quite obscure, with only a few scholarly papers using that phrase. I share the concern that our article is doing some original synthesis or speculation, not necessarily supported by reliable sources.

One search result isa a 1929 book review, which mentions "In [Heinrich Wieleitner's] Rechnen und Algebra he gives German translations of a considerable number of the significant sources of the subjects taught in arithmetic and algebra. For example, he has two pages upon the late medieval Roman numerals, with extracts from the recently-published 'Traicté d'arismetique pour pratique par gectoners;' ..." But as far as I can tell this is referring to something different (disclaimer: I don't read German). –jacobolus (t) 21:33, 8 March 2026 (UTC)