These are some works relevant to the topic of the seminar. I have been lazy about bibliographical details, but Google will supply these. To avoid copyright violations, some of the links are to copies kept in a password-protected directory.

General references

The following collections contains a number of related essays: The following provide some high-level reflection on mathematical understanding:

Mathematical concepts

Traditional philosophical views: Contemporary views: There is a vast literature on concepts more generally. These may be helpful: Historians of mathematics often use the term:

Mathematical explanation and proof

Mathematical problem solving

In addition, there are very many problem collections and solving guides in mathematics, of which the following is a small sample. The following may be helpful in characterizing mathematical expertise more generally:

Cognitive science and mathematics education

Some of the general cognitive literature on analogy may be helpful: David Marr's book, Vision, describes and important and influential approach to thinking about cognitive representations and processes.

Visualization and diagrammatic reasoning

Insights from the history of mathematics

Mathematical language

Applied mathematics

Automated reasoning

Considering automated reasoning in mathematics would take as too far afield, but here are two general references: The field used to be divided into "logic-based" methods and "human" or "heuristic" methods. The latter not as popular these days, but some logic-based methods are tending back in that direction. The following provide a sense of early work along those lines.