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 have not 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.
(Dick Grune and Ceriel J. H. Jacobs)