Depends. I think the most important quality is engineering intuition. Recognizing what you are seeing, and what to do with it.
Can you please elaborate? I love math and data. However I'm not good with "hands on" things.
Me neither. That's why I left engineering, plus it became boring to me.
Intuition is the ability to quickly identify the problem, and by searching your knowledge be able to find a possible solution, perhaps sketch a solution. Later, you may open books or search for papers to finalize the solution.
What do you do now?
I changed to Economics.
Zero hands on, and bunch of math
That sounds interesting. Is the money good in economics?
Yes, but it is better for PhD graduates.
It's the imagination, followed by ability to quantify things
I'm simply a co-op engineer working with other engineers, but the two attributes I've found to be most important in other engineers I've seen are humility and dedication. If you have graduated with a BS, it proves you can figure out the types of problems you're given. But it doesn't necessarily qualify you as a 'team player'. The engineers I've seen who are willing to help others, take criticism with a positive attitude, and work hard seem to be the happiest and succeed the most. That's just what I've seen, anyways. And they're the ones I like spending the most time around, and I ask them questions when I need help. The 'sensitive' or 'touchy' engineers who refuse to take correction can be very difficult to work with.
EDIT: I listed these two attributes assuming one has at least decent capabilities in performing one's job. If an engineer can't use a computer, calculator, perform basic to intermediate math, or be able to analyze a system or problem then it's going to be difficult to do anything as an engineer, really.
Intuition is a pretty good answer. Some intuition comes from experience and some is more an abstract ability.
Intuition gives you two things very important to design:
1.) The ability to see problems before they happen. How well can you look at a solution and see the problem areas before ever building and testing the design. This saves a ton of time and money.
2.) Troubleshooting. How quickly can you divide a problem up to isolate a problem and determine a solution. This all feeds back into 1 as can you predict what new problems your fixes may cause, because that happens a lot.
I second that! I believe that you need to focus to get a job done applying just as much math (...and tools and frameworks and software... etc.) as needed to get this job done.
I have sometimes observed that professionals new to a field fail because they try to turn a customer project into sort of an academic exercise - as if it would be required to get a paper out of the project. Sometimes rules of thumb are sufficient.
It depends if this turns you down because it makes tasks too menial or if you consider this the specific challenge in engineering.
In addition I believe communication skills are important, also if your official role is that of a technical expert.
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