The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron.

A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs.

The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery.

Though the book is written as a narrative, it aims to develop an actual method of investigation based upon "proofs and refutations".

[2] The method has been applied to the analysis and presentation of problem solving in mechanics by high school to college level students.