X Marks the Spot is written from the point of view of the users of mathematics. Since the beginning, mathematical concepts and techniques (such as arithmetic and geometry) were created as tools with a particular purpose like counting sheep and measuring land areas.
Understanding those purposes leads to a greater understanding of why mathematics developed as it did. Later mathematical concepts came from a process of abstracting and generalizing earlier mathematics. This process of abstraction is very powerful, but often comes at the price of intuition and understanding. This book strives to give a guided tour of the development of various branches of mathematics (and what they’re used for) that will give the reader this intuitive understanding.
- Treats mathematical techniques as tools, and areas of mathematics as the result of abstracting and generalizing earlier mathematical tools
- Written in a relaxed conversational and occasionally humorous style making it easy to follow even when discussing esoterica.
- Unravels how mathematicians think, demystifying math and connecting it to the ways non-mathematicians think and connecting math to people’s lives
- Discusses how math education can be improved in order to prevent future generations from being turned off by math.
Table of Contents
List of Figures. Preface. Why This Book? The Roots of Mathematics. Sticks and Stones. Abstraction, Mistrust, and Laziness. Algebra, Geometry, Analysis: The Mathematical Mindsets. Theory in Practice. Analytic Geometry. Calculus: Motion and Size. The Language of Motion. Sound, Notes, and Harmonics. Probability and Statistics. Other Geometries: Not So Straight, These Sticks. Algebra and the Rise of Abstraction. Toolkit of the Theoretical Universe. The Smith and the Knight. Building the Theoretical Universe. Computers. The Theoretical Universe of Modern Physics: Toolkit Included. Math Education and Math in Education. Index.
David Garfinkle was born in 1958 and wanted to be a physicist ever since his first year of high school. He got a bachelor's degree from Princeton University in 1980 and a PhD from The University of Chicago in 1985. Since 1991 he has been a physics professor at Oakland University in Michigan.
David is the author of over 100 articles in physics journals. His main areas of research are black holes, spacetime singularities, and gravitational radiation. He performs computer simulations of gravitational collapse to resolve questions about black holes and singularities.
David was named a Fellow of the American Physical Society (APS) with the citation reading "for his numerous contributions to a wide variety of topics in relativity and semiclassical gravity."
David and Richard have written Three Steps to the Universe (U. of Chicago Press, 2008) a book on black holes and dark matter.
For the better part of his early life, Richard Garfinkle thought he wanted to be a mathematician. He went so far as to spend four years studying math at the University of Chicago before discovering that he really wanted to be a writer. He has had several science fiction and fantasy novels published. His first Celestial Matters (Tor 1996) won the Compton Crook award for best first novel. Richard and David have written Three Steps to the Universe (U. of Chicago Press, 2008) a book on black holes and dark matter. For his day job, he programs computers. Richard lives in Chicago with his wife and children.
"Few mathematics books succeed as well as this one in creating a feeling that the author is engaged in discussion with readers. The Garfinkles' focus on "the human heritage of mathematical thinking" offers enrichment, going beyond mere theoretical abstraction. The authors start from basic counting and arithmetic; continue through algebra and geometry; and lead readers to statistics, calculus, topology, and more. This approach is refreshing and should provide readers with insights into how various aspects of mathematics developed. A broad spectrum of expressions and equations appear throughout the text, but the emphasis is not on symbolic manipulation and algorithms. Rather, readers are encouraged to think deeply about the richness that today's mathematics has inherited from the past. The final chapter on education calls for teachers to broaden their traditional classroom approach by incorporating this sense of mathematical heritage. The authors argue persuasively that students retain more from meaningful learning experiences than from temporary memorization, benefit more from a lesson built around interrelated concepts than from a piecemeal presentation of scattered ideas, and succeed by building on past learning rather than mimicking an ever-growing series of unmotivated procedures and tricks. This text demonstrates the value of exploring what originally motivated mathematical ideas, in preference to blindly performing processes."
"Deftly organized into three major sections (The Roots of Mathematics; Theory in Practice; Toolkit of the Theoretical Universe), X Marks the Spot: The Lost Inheritance of Mathematics is enhanced for academia and the reader with figures, an informative introduction (Why This Book?), and a seven page Index. An ideal textbook, X Marks the Spot: The Lost Inheritance of Mathematics is very highly recommended for college and university library Mathematics collections and supplemental studies curriculums."
—Midwest Book Review
"The Garfinkles’ book is written in a light-hearted manner without sacrificing mathematical rigor. The authors begin by taking us on a journey of discovering the roots of mathematics and then delving into what is described as its three primary processes, which they playfully dub as abstraction, mistrust, and laziness.
[. . .] X Marks the Spot is a book for anyone who teaches mathematics at any level. This book will be helpful for any course, particularly in developing the introduction portion of a course. The professor or teacher who is looking for practical examples to help answer the eternal question of “When is this stuff ever used?” will find a multitude of examples to help answer such questions. And those interested in the history and philosophy of mathematics would find this a useful text and a welcome addition to their library. The book is well documented and contains over 200 drawings and illustrations within its over 450 pages."