Math is for communication between mathematicians and programming languages are ultimately compromises for the purposes of precision and the limits of computers.

Math is for communication between mathematicians and programming languages are ultimately compromises for the purposes of precision and the limits of computers. Trying to carry the precision necessary for implementation throughout all notation quickly obscures the math beyond comprehension. Basically you're importing all the complexity that arises in programming (leaky abstractions, implementation details, etc) into math for little benefit. For the same reason we still speak in languages full of vagaries and ambiguities instead of constructed languages: For the most part, they get the job done, and when more precision is necessary we have alternatives (legalese, mathematical notation, PL's). For example, in the book "Structure and Interpretation of Classical Mechanics," the authors choose more precise language (scheme code) to make common misconceptions of notation clearer.