Who are these people? What are these systems? Are you talking about the very first people to create the concept of mathematical abstraction without any knowledge of prior example of other people doing something similar? If so, you are talking about a very small number of people thousands of years ago, people of whom we don't know actually know anything at all. If you are talking about people who currently create advances in mathematical concepts, simply the understanding of other mathematical concepts is rather significant training to that task.
Now on the solving of problems... what is a completely new problem, without any comparable problem in human history. What is a problem that can be successfully solved but has to be solved without any information on the subject? We are beneficiaries of an incomprehensible amount of knowledge, information and ready-to-use solutions
...
Or perhaps you are referring to exceptional individuals such as Srinivasa Ramanujan, who indeed managed to create mathematical contributions with little enough of education... yet such exceptional individuals are exactly that, exceptional. If anything the story should remind us that most of the mathematical contributions to society that we know of are created by individuals who happened to be in a position to have mathematical education, not by the most intelligent or the most talented.
Probabilities are that the world's most intelligent person is a boy born within the last three months born in a small farming community in China and that he is going to live a significantly worse life in every possible way than Dan Quayle.
And yet from another point of view, a large number of scientific advances have been created by pure grinding of numbers and equations, a large number of proofs have been created by simply proving for every possible alternative that they do not work. And from my high school maths classes I remember that often enough the people who did this were quicker than the ones to look for the more abstract, more elegant solution.
Again, if we consider yet another point of view about solving of problems. I claim that the people who are most likely to solve new problems are those who are the most likely to run into problems, that is favour a highly changing environment with which they interact a lot. This suggests that the most prolific problem solver is probably extrovert, sensoric and alpha. Probably solving most problems in an imperfect way but nevertheless solving a huge number of problems each day in one way or another.
*shrug* things not as simple as one might think at first.
For further consideration... Try comparing Andrew Wiles and Jamie Oliver. Which one has been more intelligent? Why?