There is a great old debate of math vs physics, or more commonly of theoretical vs applied sciences, that I saw play out during my years as an engineering student at UCLA.
“In this age of specialization men who thoroughly know one field are often incompetent to discuss another. The great problems of the relations between one and another aspect of human activity have for this reason been discussed less and less in public. When we look at the past great debates on these subjects we feel jealous of those times, for we should have liked the excitement of such argument.The old problems, such as the relation of science and religion, are still with us, and I believe present as difficult dilemmas as ever, but they are not often publicly discussed because of the limitations of specialization.”
“The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessaryto be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing.
Pure mathematics is just such an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.”
(quotes from https://en.wikiquote.org/wiki/Richard_Feynman)
There was a joke going around that I am sure Dr Feynman would appreciate, and it went something like this: an engineer and a mathematician were both given a problem to solve – they are sitting on one side of the room, and on the other side there is a beautiful and disrobed woman. If each step they took could only halve the distance between them, would they ever actually reach her? The mathematician smugly said ‘no, I could only get infinitesimally close, but would never reach her’, whereas the engineer said that within a few steps he’d be close enough to matter. Yes, I think Dr Feynman could appreciate the humor in that one.