Math History A Long-form Mathematics Textbook

Math History: A Long-Form Mathematics Textbook shows readers how people throughout history thought about math. It discusses what problems they cared about, how they expressed those problems, and how they solved them. It also aims to show the growth of math over time. It examines the problems that gave rise to new fields, the ideas that allowed those fields to flourish, and the theorems and conjectures that propelled them to their modern form. Finally, it communicates the human side of math—the people who impacted it and the world in which they lived, how various cultures differed in their approach, and how the mathematical project has spanned the globe. The first four chapters of this book cover the development of number systems, ancient mathematical methods, the transition to proofs, and axiomatic mathematics with a focus on Euclidean geometry. The final six chapters each track the history of a specific topic. These topics are number theory, algebra, early calculus, modern analysis, topology and combinatorics. It surveys math pretty broadly, but its focus is on the math topics that an undergraduate math major will encounter.