Chapter 1. Disturbance as a driving force.- Chapter 2. A fictional dialogue on infinitude of primes.- Chapter 3. Encounters with Euclidean propositions.- Chapter 4. Stories on problem-solving instruction.- Chapter 5. Encounters with Cardano's method.- Chapter 6. Synthesizing exception-barring and what-if-not: If not, what yes?.- Chapter 7. From "obviously wrong" methods to surprisingly correct answers.