Yes and No to this article. Yes, abstraction is important, and yes yes, the point of mathematical abstraction is not to be vague, but to create a level of expre

Yes and No to this article. Yes, abstraction is important, and yes yes, the point of mathematical abstraction is not to be vague, but to create a level of expression where one can be precise. No, the point of abstraction can be to be vague, and to delimit the boundary of a concept that is not quite clear (yet). It is not a mathematical abstraction then, but something you are experimenting with to find the right kind of laws that are supposed to govern that concept. Most real-world programs contain many such concepts for which either no good mathematical abstraction exists, or for which nobody has had yet the time and money to find a good mathematical abstraction.