On a relation between mathematics, engineering and science

There is a difference between science and mathematics in that mathematics is a bottom-up approach. That is, in mathematics we start with a set of postulates and from this builds up the structure.

Science on the other hand, is a top-down approach. We start with a given system (a part of the world) and then we try to approximate that by some description. This approach gives science the luxury to not feel bad when it is wrong (that it is wrong!). We can be safe that we will be able to perform better in the future: the underlying system do exist and hence what we are trying to describe will work out eventually (or at least, our approximation will come closer).

Mathematics on the other hand takes the bold stand and does not thrust any underlying existing system, but rather want to derive everything by them self - believing that they can formulate a consistent theory by them self. This forces mathematics to have to be absolutely correct from the starts. Since they have so solid ground to stand, but rather only their own assumptions (which mights well be contradicting and incomplete).

Now it is peculiar to note that engineering in this sense is probably closer to mathematics than to science. Engineers take postulates (circuit theory, continuous mechanics or whatever they need) and, thrusting these, try to build something. Now the engineers are in a situation similar to the mathematicians: if there is something wrong with their assumptions the bridge collapses. The scientists do not have to worry about this; the bridge is apparently standing there. The problem is instead: what makes it stand??