What are some examples of mathematical conlangs?

I'm curious as to if there are any full existing conlangs that allow you to do arithmetic or mathematical manipulations from a conlang perspective.

The closest that I've found for this is this set of short clips on YouTube, Inventing a Number System. But I'm curious as to if there might be more examples, especially examples that have a mathematical grammar of some sort.

(Note: I do apologize if this post is a bit fuzzy, as the idea is still kind of fuzzy in my mind. This is also my first post to this forum. I can revise the post if needed.)


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    When you say mathematics, are you also including advanced language aspects that mathematicians use to formulate theorems and proofs, or would you like to focus on just words and grammar concerning counting and arithmetic? – EdvinW Jan 17 at 14:40
  • You might find Lojban and other engineered languages interesting. – bradrn Jan 18 at 9:55
  • @EdvinW I think I'm more interested at the moment in something more specific like counting and arithmetic, but I would also be interested in more advanced features of mathematics as well. I would love to expand out into more abstractions, such as summation notation, and maybe even mathematical induction and functions. My interest is mainly in describing arithmetic and mathematics itself in a human language-like way versus a general purpose language like Lojban. Lojban does look promising though. This does get me to realize that I need to be more specific with what I want to accomplish. – zacts Jan 18 at 14:42
  • Is lojban the type of thing you might be looking for? – jMdA Jan 30 at 6:26

There's a language based on stack-based programming languages (like Forth) that eliminates syntactic ambiguity called Fith. The name is a deliberate pun on Forth.

Basically, when parsing the language you have a stack of objects that you have to keep track of, as well as some global state like the default number that can be explicitly changed.

The idea of layering a human language on top of a Forth-like grammar is flexible enough that you could extend Fith or make radically different design decisions without losing some of its nice properties.

  • That's rather a "programming" than a "mathematical" conlang ;) – Victor VosMottor Jan 20 at 21:52
  • I consider programming a type of math, but opinions may differ. – Gregory Nisbet Jan 20 at 22:06
  • IMHO programming is not any kind of math at all, they are related though. – Victor VosMottor Jan 21 at 10:55
  • This looks really cool. I'll definitely look into it. Thanks. – zacts Jan 23 at 12:39

Slightly tangential, but Richard Feynman invented his own mathematical notation (mostly trigonometric functions), as mentioned in his autobiography "Surely You're Joking, Mr. Feynman!":

While I was doing all this trigonometry, I didn't like the symbols for sine, cosine, tangent, and so on. To me, "sin f" looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign. Now the inverse sine was the same sigma, but left -to-right reflected so that it started with the horizontal line with the value underneath, and then the sigma.

He stopped using his notation when he inadvertently slipped into it when discussing some math with his friend, because he realized the need for a common (even if inferior) notation.

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