I'm not sure what exactly you're asking here. Of course universities want professors who have actually solved mathematical problems or discovered something new. Industry doesn't really care; it's mostly concerned with taking existing discoveries and finding applications for them. Even in the more ambitious or creative fields, you're not going to find available applications for most of mathematics, and even fewer for ones that people will actually pay for.
That having been said, it's easy to get a reasonably high-paying and prestigious job in industry as a generic newly-minted PhD, and it's trivial if you're a professor with decent bona fides. The main difficulties are finding something that you'd be interested in and switching from the academic mindset and environment (freedom to choose your own research topics, collaboration with colleagues, long-term or pure research) to the industry ones (management and hierarchies, demand for short-term results, and far less choice in what you pursue).
Since I don't know your background, I'll also point here that "solving problems" isn't exactly the goal of mathematics, at least for problems that are along the lines of Math Olympiad, etc. offerings. They're more like "Classify all groups that can act sufficiently nicely on $S^n$," or "Find whether there's an analogue of the Atiyah-Singer theorem for this new kind of structure," or "Determine whether all curves of this particular algebraic structure arise from this arithmetic structure." They're multi-year projects that draw from and add to the work of many other mathematicians, and they're open-ended and ongoing projects rather than self-contained, contrived homework problems.