Just to also a couple existing comments here, a problem solver is not necessarily an applied person or an engineer. It's someone who looks for interesting unsol

Just to also a couple existing comments here, a problem solver is not necessarily an applied person or an engineer. It's someone who looks for interesting unsolved questions, and invents what needs inventing to get a solution. By contrast, an engineer uses well established techniques (with creativity!) to build bridges that they know can be built. Diving into unsolved mathematical problems - especially the ones that have picked up a reputation - is inherently a riskier endeavor. As the text says: 'the interesting problems tend to be open precisely because the established techniques cannot easily be applied.'