In Welsh, there are four categories of numbers:

• masculine = numbers to count masculine nouns with

• feminine = numbers to count feminine nouns with

• Decimal numbers (sometimes called the "modern counting system")

• Vigesimal numbers (sometimes called the "traditional/old counting system"

Masculine and feminine numbers only really exist up to 5. We use masculine numbers when quantifying masculine nouns (e.g. dogs) and feminine nouns when quantifying feminine nouns (e.g. cats)

We use the vigesimal or “traditional/old” number system, which works (broadly speaking) in units of 20s, when we are dealing with numbers involving:

• weights

• measurements

• distances

• ages

• dates

• time

Mutating numbers

• un > soft mutation to singular feminine nouns

  • un gath (one cat)

• dau and dwy (two)  > soft mutation to nouns, and take a soft mutation when preceded by the definite article y

  • dau fwrdd (two tables)

  • dwy gadair (two chairs)

  • y ddau fwrdd (the two tables)

  • y ddwy gadair(the two chairs)

• tri (three) > aspirate mutation to nouns

  • tri chi (three dogs)

• pump (five) becomes pum when followed immediately by a noun

  • pum cath (five cats)

  • pump o gathod (five cats)

• chwech (six) becomes chwe and causes an aspirate mutation when a singular noun comes immediately after, e.g. chwe chath (six cats)

• Deg (ten) turns into deng when counting things

  • deng munud (10 minutes)

• or when it appears in a compound number (i.e. two numbers stuck together)

  • deuddeng mlynedd (12 years).

• In ordinal numbers larger than 10 the thing being counted is placed between the first and second parts of the number

  • e.g. unfed ganrif ar hugain (21st Century).

What’s “42” in Welsh?

There are two options:

Pedwar deg dau or dau a deugain

Welsh has two counting systems. One is decimal (i.e. centred on a base of tens) and the other is vigesimal (i.e. centred on a base of twenties). When we talk about a “base of tens” what we mean is that the system pivots around 10 when we form numbers above 10. In English, we have such a decimal system. “Seventy” is “7 lots of ten” (“-ty” from the Old English tig meaning ten). But lots of languages don’t form their numbers in reference to 10. In our Welsh example,  Pedwar deg dau is the decimal version, literally “four ten two”. Dau a deugain is the vigesimal version, literally “two  two-twenty”.

Perhaps somewhat apocryphally, Welsh has ended up with two number systems because Patagonian Welsh speakers in Argentina created a decimal system for use in their Welsh medium schools and this number system was then imported across the Atlantic. This leads to a bit of a muddled situation in Wales, which often confuses learners, where there are two versions of all numbers between 11-99. We tend to use these different systems in different contexts. So we talk about someone being pedwar ugain for age (literally “four twenty” for 80) and driving trigain miles (literally “three twenty” for 60), but we’re more likely to talk about there being dau ddeg (“two ten”, 20) chairs or other things we’re counting. Weights, measurements, money, time and ages are still mostly referred to using the “old” (i.e. vigesimal) system. However, this is rapidly changing as more and more adult learners become part of the Welsh language community and as school children just see the old numbers as exactly that: old.

The ancient Babylonians apparently had a sexigesimal number system (with a base of 60), well, they sort of did. That’s objectively weird. Welsh’s number system being vigesimal based isn’t weird. Loads of languages have a system which is (at least in part) based on this: French, Basque, Inuit languages to name but a few. What’s perhaps intriguing about Welsh’s “old” system is that’s it’s slightly mixed. 15 is an important pivot sometimes:

16Un ar bymthegOne on fifteen19Pedwar ar bymthegFour on fifteen35Pymtheg ar hugainFifteen on twenty

The old system is full of inconsistencies. The pattern in the teens is, for example, broken by the words pymtheg for 15 and deunaw for 18 (“two nine”). If 14 is pedwar ar ddeg (“four on ten”), then why isn’t 15 just pump ar ddeg (“five on ten”)? And why not have 18 as wyth ar ddeg (“eight on ten”)?

The system isn’t really strictly about a base of 20 as opposed to 10 either- sometimes it’s both. 90 is deg a phedwair ugain (“ten and four twenty”). Danish is a language that makes good use of the idea of using 20 as the base. Danish is a (largely) vigesimal system, but interestingly the 20 bit has been lost slightly. Sindstyve is the part of Danish numbers meaning x20 which isn’t really pronounced in modern spoken Danish anymore. So tredsindtyve for 60 is just pronounced tres nowadays.

Here are some numbers in Danish that make the Welsh system look completely boring.

50halvtreds [(3-½) x 20]~“half of 20 less than 3 times twenty”60tres [3 x 20]~“3 times twenty”70halvfjerds [(4-½) x 20]~“half of twenty less than four times twenty”80firs [4 x 20]~“four times twenty”90halvfems [(5-½) x 20]~“half of twenty less than five times twenty”

“Half of twenty less than five times twenty” is much more exciting than Welsh’s version of 90. Instead of trying to crowbar the vigesimal theme throughout, Welsh just opts for “ten and four twenties” for 90 and combines a decimal and a vigesimal system, much like French. Danish, however, is loyal to the vigesimal cause and renders 10 by talking about it as half twenty.

If you only speak English and you're learning a vigesimal number system, then this can cause a headache. But this headache is compounded by the fact that there are actually two different number systems to learn in Welsh. Another thing that causes my learners and tutees to despair is feminine number forms (dwy gath (two cats) but dau gi (two dogs). Yet another trauma is the placement of the noun in quantified noun phrases, e.g. dwy gath ar hugain ("two cat on twenty" for 22 cats) and pedair punt a deugain ("four pound on two twenty" for £44). Ordinal numbers seem to cause even more distress: y bedwaredd ar bymtheg a phedwar ugain  ("the fourth on fifteen and four twenty" for 99th). The learners that make the most progress are always those who look at this kind of linguistic irregularity and think "there's a challenge!". Human languages have created a seemingly infinite number of interesting and different systems for things like numbers. Getting our heads around something like Danish or Welsh numbers might be tricky, but it's a good bit of linguistic legwork and a means of realising our linguistic potential. English numbers are so boring! We can do so much better!