Mathematics consists of various names, relationships, etc. that have been consciously constructed and developed over time. On the other hand its a "formal" language whose scope is extremely specialized compared to a regular language. How else does mathematics compare/contrast with constructed languages?


I think Programming and Mathematics fail to meet the standard because, despite being more precise, they are ultimately nowhere near as expressive as a language like English.

Per request I will expand on my answer. Take, for example, the English sentence "Jane missed the bus this morning and couldn't get to the office in time her interview, needless to say, she was not selected for the position." There is no way to express that in any programming language that I know of.

var Jane = {Name:"Jane", Employment:"Unemployed", Bus:data.Buses[4]};
data.Buses[4].Depart("2019-10-05 07:30:00");
Jane.ArriveAt(data.Buses[4], "2019-10-05 07:45:00");

I won't go on trying the futile exercise of typing out a description of events in Javascript. Note that without knowing English the code makes no sense. Anything in code that isn't a keyword like "if" or "foreach" or "function" isn't part of the language and so you can only describe procedures for moving bits around, one way to illustrate this is to convert my Javascript to do the same thing, but with different variable names - the program will be exactly the same as far as the language specification goes and the resulting executable.

var x = {a:"", b:"Unemployed", c:y.z[4]};
y.z[4].dp("2019-10-05 07:30:00");
x.w(y.z[4], "2019-10-05 07:30:00");

If those two paragraphs mean the exact same thing as far as the language is concerned, you've completely failed to communicate anything useful. Computer scientists working on artificial intelligence are working to make systems where "bus" is a keyword, there is an idea of "bus" in the language. Until that technology is fully realized, we will be stuck with programming languages that are limited to describing things a computer can understand, a much lesser standard than what a human can. This is what I mean by less expressive.

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    Hello and welcome to the site! Could you please edit this to explain a little more what you mean by expressive? – curiousdannii Oct 5 '19 at 11:28
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    But on the other hand, there are many programming and math concepts that natural languages can't convey successfully, or at least not well (because the concept of Jane missing the bus, etc., was conveyed, just not well). Different languages are used for different things. I'm not saying that math (or programming) is a conlang, but I don't think you've proved it isn't. – Rory M. Tims Dec 4 '19 at 16:44

If we consider that the purpose of a constructed language is simply and purely created for Human interractions (like esperanto), mathematics cannot be considered as a conlang because it lacks one important thing that human language has: Context.

When I say:

He said it last time

We need to both have the same context to understand the meaning. Mathematics and Computer programming languages doesn't reach at all this level of tacit agreement.

However, now I also believe that mathematics help Human to understand and express things in a more abstract way. To make a rough comparison, we could then consider a constructed language as General Purpose programming Language + Context and mathematics as Domain Specific programming Language

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