Explore the surprising connections between math and maps—and the myriad ways they’ve shaped our world and us.

Why are coastlines and borders so difficult to measure? How does a UPS driver deliver hundreds of packages in a single day? And where do elusive serial killers hide? The answers lie in the crucial connection between math and maps.

In Mapmatics, mathematician Paulina Rowińska leads us on a journey around the globe to discover how math and maps are deeply entwined, and always have been. From a sixteenth-century map, an indispensable navigation tool that exaggerates the size of northern countries, to public transport maps that both guide and confound passengers, to congressional maps that can empower or silence whole communities, maps and math have shaped not only our sense of space but our worldview. Rowińska shows that by understanding the math behind maps, we can recognize their biases. And we can appreciate the ingenious tools mathematicians are developing to resolve them.

Written with authority and compassion, wit and unforgettable storytelling, Mapmatics is math exposition at its best. By unpacking the math underlying the maps we depend on, this book illuminates how our world works, and, ultimately, how we can better look after it.

From the sixteenth through the mid-nineteenth centuries, Spain, then Mexico, and finally the United States took ownership of the land from the Gulf Coast of Texas and Mexico to the Pacific Coast of Alta and Baja California—today's American Southwest. Each country faced the challenge of holding on to territory that was poorly known and sparsely settled, and each responded by sending out military mapping expeditions to set boundaries and chart topographical features. All three countries recognized that turning terra incognita into clearly delineated political units was a key step in empire building, as vital to their national interest as the activities of the missionaries, civilian officials, settlers, and adventurers who followed in the footsteps of the soldier-engineers.

With essays by eight leading historians, this book offers the most current and comprehensive overview of the processes by which Spanish, Mexican, and U.S. soldier-engineers mapped the southwestern frontier, as well as the local and even geopolitical consequences of their mapping. Three essays focus on Spanish efforts to map the Gulf and Pacific Coasts, to chart the inland Southwest, and to define and defend its boundaries against English, French, Russian, and American incursions. Subsequent essays investigate the role that mapping played both in Mexico's attempts to maintain control of its northern territory and in the United States' push to expand its political boundary to the Pacific Ocean. The concluding essay draws connections between mapping in the Southwest and the geopolitical history of the Americas and Europe.

Montana has been the "last best place" for so many people. A century ago, Native Americans gathered here to perform the Ghost Dance—a last, doomed attempt to make white settlers vanish and bring back the old ways of life. Today, people are still pouring into Montana, looking for the pristine wilderness they saw in A River Runs through It.

The reality of Montana—indeed, of all the West—has never matched the myths, but this book eloquently explores how the search for a perfect place is driving growth, development, and resource exploitation in Big Sky country. In ten personal essays, John Wright looks at such things as Montana myths; old-timers; immigrants; elk; ways of seeing the landscape; land conservation and land trusts; the fate of the Blackfoot, Bitterroot, and Paradise valleys; and some means of preserving the last, best places.

These reflections offer a way of understanding Montana that goes far beyond the headlines about militia groups and celebrities' ranches. Montana never was or will be a pristine wilderness, but Wright believes that much can be saved if natives and newcomers alike see what stands to be lost. His book is a wake-up call, not a ghost dance.