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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. The book contains many theorems with their historical proof. Each chapter also includes exercises.
Following each chapter is a People's History section which expands the telling of math history to include surveyors, navigators, artists, merchants and student collectives, who developed practical math which anticipated future research.
The first appendix is on the history of applied math; the second is a mathematician pronunciation guide; the third is a collection of mathematical quotes; the fourth is a history of math words; the fifth is a history of math symbols; and final appendix is a collection 37 biographical sketches of the many fascinating lives of history's premier mathematicians.
More content, including a collection of original sources, may be found at LongFormMath.com.
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