“Without knowledge there can be no skills.”


So, what does cause high levels of mathematical skill, or any other skill? This is the question Simon concerns himself with in the rest of his article. You can read his conclusions in the article, but I will quote briefly.

In every domain that has been explored, considerable knowledgehas been found to be an essential prerequisite to expert skill. Our growing understanding of an expert’s knowledge and the kinds of processes an expert uses when solving problems enables us to begin to explore the learning processes needed to acquire suitable knowledge and problem-solving processes. We have no reason to suppose, however, that one day people will be able to become painlessly and instantly expert. The extent of the knowledge an expert must be able to call upon is demonstrably large, and everything we know about human learning processes suggests that, even at their most efficient, those processes must be long exercised. Although we have a reasonable basis for hope that we may find ways to make learning processes more efficient, we should not expect to produce the miracle of effortless learning.

A quotation from another Simon essay, this time about chess expertise, is also relevant: