There is a considerable difference between a mathematician’s view of the world and a computer-scientist’s. To a mathematician all structures are static: they have always been and will always be; the only time dependence is that we just haven’t discovered them all yet. The computer scientist is concerned with (and fascinated by) the continuous creation, combination, separation and destruction of structures: time is of the essence. In the hands of a mathematician, the Peano axioms create the integers without reference to time, but if a computer scientist uses them to implement integer addition, he finds they describe a very slow process, which is why he will be looking for a more efficient approach. In this respect the computer scientist has more in common with the physicist and the chemist; like these, he cannot do without a solid basis in several branches of applied mathematics, but, like these, he is willing (and often virtually obliged) to take on faith certain theorems handed to him by the mathematician. Without the rigor of mathematics all science would collapse, but not all inhabitants of a building need to know all the spars and girders that keep it upright. Factoring off certain detailed knowledge to specialists reduces the intellectual complexity of a task, which is one of the things computer science is about.
Dick Grune and Ceriel J.H. Jacobs, “Parsing Techniques – A Practical Guide“