First, consider a definition of creativity. A creative person does things that have never been done before. Particularly important instances of creativity include discoveries of new knowledge in science and medicine, invention of new technology, composing beautiful music, or analyzing a situation (e.g., in law, philosophy, or history) in a new way. It is important to distinguish among three different characteristics: intelligence, creativity, and academic degrees. Intelligence is the ability to learn and the ability to think. Creativity was defined in the previous paragraph, as the ability to produce new things or new knowledge. Academic degrees are what one gets after one has sat through years of classes, passed the examinations, and completed all of the other requirements (e.g., senior thesis, doctoral dissertation, etc.). In comparing and contrasting these three traits, I note that: Most people who create significant things are intelligent.
There are many people with an earned doctoral degree who do not have a single creative idea in their head. They are intelligent and highly skilled problem solvers, but someone else must formulate the problem for them (e.g., give them an equation to solve). Thus intelligence and academic degrees are not evidence of creativity.
Students who are both intelligent and highly creative often make mediocre grades in school. Genius is a vague term: sometimes it indicates a person with an unusually high score on an IQ test, other times it indicates an extraordinarily creative person (e.g., Mozart or Einstein). I don't like the word genius, not only because of this vagueness, but also because it often has the connotation in colloquial American language of indicating a freak, weird, or abnormal person. I am interested in understanding and encouraging creativity, not pasting pejorative labels on creative people. Further, someone who is not a genius can still make a valuable contribution to progress.
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