Create something impactful or just generalize results?
The people who can truly follow your advisor's advice are actually very rare. The advice is good, but not necessarily the best way to begin your career. In the long term you want to look at what can be done that is entirely fresh, but in the short term, you need to finish your degree and find employment. 

If you want to make a big impact, IMO, you need to be able to work in a highly collaborative environment in which a lot of productive people are willing to share ideas in seminars and such. Depending on your current university, that may already be happening around you. But when it comes to finding employment, seek a place with a larger, rather than a smaller, faculty. Or, if it is small, make sure that they collaborate closely on semi-related ideas. 

However, you need to follow your advisor's advice enough so that s/he will approve of and sign your dissertation. Most people at your stage of career are happy enough with A++. But it is even better if in doing that you gain insight into the larger issues of mathematical creativity.