Hierarchy of expertise

1. Know fundamental concepts.
2. Solve well formulated problems using existing methods/libraries.
3. Increase your knowledge of methods/libraries and be more proficient in choosing the best solution method for a given problem.
4. From ambiguous statements and missing information, create well formulated problems by making reasonable assumptions/approximations and solve them.
5. Develop novel/more efficient solutions to existing problems.
6. Discover new problems.
7. Solve new problems.