The professor looks at a glass of water and says something like "its 48.31415% full of H20". The scientist says something like "that glass is 48% full of water".
The logistics engineer says "the glass is about half full -- but in truth its about twice as big as it needs to be". And the design engineer says "if that glass contained twice as much liquid, and that liquid was beer, it would be perfect".
Engineers are people who figure out how to take intellectual ideas and turn them into real things.
Good engineers solve existing problems. Great engineers imagine problems that have yet to occur, and make sure they don't happen.
An engineer is one who solves problems, turns amazing concepts into reality, makes managers and stockholders rich, and gets laid off when the project is finished.
"Mama, don't let your babies grow up to be engineers". Better to be a doctor, lawyer, accountant, politician, or cowboy. Of these, only the doctor or cowboy might find the job as rewarding and enjoyable as engineering.
Engineering is creating complex systems that are occasionally useful, so that they can have a lot of problems, so we can feel good about ourselves fixing them all often after many nights of sweat and tears.
Have to say that "An Engineer is someone who uses science and mathematics to solve problems" sums it up (the fun can be a bonus,but not necessarily required ;-)
If I had to put a qualifier on it or modify it in any way it would be to add "sometimes through trial and error" so as to set a child expectations that it is not always easy !