An artesian reform of the French numbering system


Descartes artésien

Twice in my life, I have been at a meeting where a French person has stood up and said very seriously that it is obvious that French should be the global form of communication since French is the most logical of all languages.
To this, I have a number of replies, but one will suffice:



Anyone with even an elementary knowledge of French (as spoken in France) will be aware of the fact that in order to say ninety-seven one has to crawl through mathematical hoops and phrase it as “four-twenty-seventeen” (quatre-vingt-dix-sept). I could in fact have picked any number from eighty to ninety-nine to make the same point. The sequence goes from four-twenties (80) through four-twenty-six (86) and four-twenty-eleven (91) all the way to four-twenty nineteen (99). Actually, this whole business starts even earlier, in the seventies, which start with sixty-ten (70) and end with sixty-nineteen (79).
Now, this doesn’t sound like the kind of thing you would want in a country which glories in being “Cartesian”, even though Descartes himself entangled himself in many intractable problems; “Descartes et des échecs” (cards and chess or Descartes and failures) as the once-famous but now almost forgotten 18th Century philosophe Jean-Jacques Klaxx once quipped. This bizarre numbering system would fit in much better with the many oddities the English are proudly afflicted with (except that if this had happened in English they would also have made sure that the spelling and/or the pronunciation would be inconsistent too. For example, Four-twenty (80), Fourenty-one (81), Frenty-twoo (82) and so on. 
The French Revolution gave us metres, litres, centimetres, millilitres, etc. – the whole metric shebang, in fact, and for a while even the ten-day week. Why didn’t they ever deal with this, then?
Apparently, this is a hangover from an ancient Celtic base-twenty numbering system which it was too traumatic to abandon. I feel that an attachment to the old system is quite admirable and yet this is all too unsystematic. French numbers behave like smooth énarques until they get to sixty-nine and then suddenly develop Tourette syndrome and undergo uncontrollable spasms and jerks until they get to one hundred, where they return to normal, until they experience another seizure on one-hundred-and-seventy.
This surely will not do for a nation which purports to be a regular geometrical figure (l’Héxagone) and has turned economic planning into an art form. France is a great country; it deserves a great numbering system. Therefore, I have come up with a way of making the whole thing more systematic and therefore more French. I cannot claim in any way to be Cartesian, howeverso I shall call my reform artesian; 1) because it makes things gush up unexpectedly and 2) as a tribute to one of my favourite French authors, Raymond Queneau, who in his poem Petite Cosmogonie Portative once spoonerised “astuce cartésienne” into “castuce artésienne”. (Look at this if you want an explanation.)
My system has three parts, which is also very French.


Rule one: ANY number can be expressed by the nearest multiple of 20 plus the remainder added on.


  • 53 – Deux-vingt-treize (Two-twenty-thirteen)
  • 145 – Sept-vingt-cinq (Seven-twenty-five)
  • 420 – Vingt-vingt-vingt (Twenty-twenty-twenty)

Rule two: In the same way that you can add numbers up to nineteen onto sixty, you can also do that on any other multiple of ten.

  • 42- Trente-douze (thirty-twelve)

Rule three (La règle universelle). When people have got used to that (and think of the progress in mathematical skills it will produce among the general population), the next and final stage is the following: any number can be expressed as the sum of any two other mathematical operations.

We start with multiplications + additions (like the already existing four-twenty ten-nine, quatre-vingt-dix-neuf, for 99).

  • 104 – Quatre-vingt-vingt-quatre (Four-twenty twenty-four) (80 +24)
  • 123 – Trois-trente-trente-trois (three-thirty-thirty-three) (90+33)

I am sure, however, that people will move on to multiplication + multiplication formulas once they realise how many beautiful numbers this can generate. As an example, I give you this wonderful sequence (which may – who knows? – be endowed with surprising mathematical properties).

  • 26 – deux-trois quatre-cinqs (two-threes four-fives) 2*3 +4*5 = 6+20
  • 32 – trois-quatres cinq-six (three-fours five-sixes) 3*4 + 4*5 = 12+20
  • 62 – quatre-cinqs six-septs (four-fives six-sevens) 4*5 + 6*7 = 20+42
  • 86 – cinq-six sept-huits (five-sixes seven-eights)  5*6 + 7*8 = 30+56

Homework: Try and find an aesthetically pleasing artesian formula for the number 1789.






  1. Vanna scalia

    You’re brilliant as usual, but it is such fun translating numbers from French and getting them almost right! Vanna

  2. Caroline Curta

    Nice comment Vania!
    I wonder what Phil eats for breakfast to come up with such ‘élucubrations’

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