I found many sites where Quenya numerical system was explain, but nothing about mathematical opperation like :

+ - / * (I don't speak about advanced notion like x² or square), but there is nothing written by tolkien about basic equation ?!?

  • Tolkien never think avout this, and don't create mathematical symbol, he as philologist, not mathematician.
    – Matrix
    Aug 6, 2023 at 2:24
  • Tolkien never even had to invent the Tengwar numerals (not Quenya, which is a language, not a writing system). Hell, Tolkien never had to invent the Elvish languages and scripts for Middle-earth (he had to for his own pleasure though). I agree with Draconis that symbols for +-*/= likely didn't exist in the Third Age, and I don't think Tolkien needed to include them in the books even if he had them in mind.
    – Eugene
    Sep 21, 2023 at 12:29
  • Also know that we know of the Tengwar numerals because Christopher Tolkien found some notes and published them years after Tolkien's death. It's not like Tolkien wrote a book telling the readers: see the Elvish had numeric symbols but no +-*/=. George R.R. Martin never even designed an alphabet for Westeros. Is that also a mistake of him?
    – Eugene
    Sep 21, 2023 at 12:32
  • @Eugene GRR is not a linguist, its a mistake of curse, but it's not his job to create languages^^ It's not a question of pleasure (if you are linguist of sunday maybe), but profesional linguist must think about reel evolution of langages ;) It's impossible with so much time, there is no mathematical symbol. But it's not my question, or a debate, I just would be sure there is nothing about this in all work of Tolkien. Question closed. you can interpret that however you want now...
    – Matrix
    Sep 22, 2023 at 23:34
  • It wasn't Tolkien's job either when he was writing a novel as a novelist. Let's put aside whether it's plausible that they didn't invent such symbols in Ages. You are mistaken! Tolkien never said there weren't such symbols. What if Christopher Tolkien never found his father's notes on Tengwar numbers or never made them public? I guess you would then claim it was a mistake of Tolkien not to have invented any numbers? If so, I assure you there are a lot more than numbers that are lacking in Tolkien's languages. We don't even have a complete pronoun table of Sindarin.
    – Eugene
    Sep 23, 2023 at 10:29

1 Answer 1


I don't believe so, no. The idea of writing equations with symbols like that is actually a very recent invention, historically speaking; ways of representing numbers go back to the very beginnings of writing, but the equals sign wasn't invented until the 1500s! So it's not surprising that the elves didn't have such a thing (or at least that Tolkien never mentioned it in the existing sources).

  • no, I think it's a mistake of Tolkien. He juste dont think about this... Babylonian (-1700 JC) already resolve equation. So your beliefs are incorrect.
    – Matrix
    Aug 2, 2023 at 15:39
  • 1
    @Matrix The Babylonians were doing math, but they didn't have an equivalent of +, ×, =, etc. The idea of writing an equation out like "a²+b²=c²" is a very modern thing.
    – Draconis
    Aug 2, 2023 at 15:45
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    @Matrix to elaborate on Draconis' point a little, Newton's Second Law is commonly expressed as F=ma today, but in Newton's time it was written out in words something like "the force is proportional to the product of the mass and the acceleration". Writing things out in words was the norm until very recently. There was no dedicated mathematical notation, people did algebra (or arithmetic or whatever maths they were doing) on expressions written out in words
    – Tristan
    Aug 3, 2023 at 12:44
  • 1
    so for 1+1 this would historically have been written "the sum of one and one" or "the sum of two ones" or similar. Having a specific notation for maths was not seen as necessary historically, and likely wouldn't have been by Tolkien
    – Tristan
    Aug 3, 2023 at 12:44
  • 1
    Apparently, the Egyptians did have a sort of ideogram for “plus” and for “minus,” which were Gardiner D54 𓂻 and D55 𓂽, respectively. You could tell which was which by telling whether the legs were pointing towards the beginning or the end of the line. But I guess that would have been closer to a scribal abbreviation (like our modern &) than mathematical notation, per se.
    – Wtrmute
    Aug 22, 2023 at 16:31

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