Contains the stories of five mathematical journeys into new realms. This work tells these stories by guiding the reader through the words of the mathematicians at the heart of these events, and provides insight into the art of approaching mathematical problems. It is aimed at students, instructors, and the intellectually curious reader.

Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.

1 Geometry: The Parallel Postulate 2 Set Theory: Taming the Infinite 3 Analysis: Calculating Areas and Volumes 4 Number Theory: Fermat's Last Theorem 5 Algebra: Solution of Polynomial Equations