title_body: Is mathematics considered a constructed language? 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?
upvoted_answer: 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.