Indeed. That is why I am interested in different schools of thought in mathematics. For example, the ancient Greeks were builders rather than mathematicians, and therefore solved different problems or similar problems in another way. I would not know how to prove Pythagoras' theorem without the Greek school of thought. On the other hand, the Arabic school of thought brought us abstract thinking. It took aerodynamics to add boundary layer theory to computational mathematics.
The most interesting thing can occur when those schools of thought are mixed. Hodographic transformation as used in aerodynamics is very similar to a Burrows-Wheeler transform in computer science, but the application is totally different. Who knows what other differential equations solving techniques could yield better data compression, for example?