The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition.

This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction.

This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

chapter 1|16 pages

What Is Mathematics?

chapter 2|24 pages


chapter 3|38 pages


chapter 4|18 pages

Deduction and Abstraction

chapter 5|40 pages


chapter 6|24 pages

Informal Reasoning in Mathematics

chapter 7|30 pages

Representation in Mathematics

chapter 8|26 pages


chapter 9|32 pages


chapter 11|42 pages

Esthetics and the Joys of Mathematics

chapter 12|24 pages

The Usefulness of Mathematics

chapter 15|32 pages

Mathematics in School

chapter 16|38 pages

Mathematical Problem Solving

chapter 17|10 pages

Final Thoughts