""Getting things to work using whatever your state of the art is, in the time and resource constraints that you are working within - THAT is what's key""
And math and physics are great facilitators toward this aim.
In the engineering realm there are Technicians and Engineers.
The difference being the amount of theoretical training.
Technicians follow established rule sets for assembling things that work out of the most economical parts in their bin.
Engineers do the same. But they also occasionally establish new rules using applied math and physics and thus make great contributions.
The math and physics sometimes allow the Engineer to see something in the data that doesn't jump out to those will less theoretical training.
So i have to disagree to some extent.
1 A hacker uses limited technician level training to make and modify things by trial and error.
2 The technician knows how the parts fit together so they will work and makes or modifies things by using his extensive knowledge.
3 The engineer knows the math and physics and can create new things never before done by seeing deeper relationships between objects.
Now before the tomatoes start flying I must add.
Hackers can be Engineers,
Engineers can be Technicians,
Technicians can be Hackers or Engineers.
....
Category N can be Category M
The label doesn't make the person.