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The Shape of Inner Space
String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
The Shape of a Life
A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi ...
A History in Sum
In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixt...
The Gravity of Math
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical...
Popular Science
Popular Science gives our readers the information and tools to improve their technology and their world. The core belief that Popular Science and our readers share: The future is going to be better, and science and technology are the driving forces that will help make it better.
The Characteristics and the Life Cycle of Stars
Presents a collection of essays that examines the characteristics and life cycles of stars, and analyzes how stars are formed, what goes on during the life of a star, and what happens when stars die.
Popular Science
Popular Science gives our readers the information and tools to improve their technology and their world. The core belief that Popular Science and our readers share: The future is going to be better, and science and technology are the driving forces that will help make it better.
The Web of Meaning
“A profound personal meditation on human existence . . . weaving together . . . historic and contemporary thought on the deepest question of all: why are we here?” —Gabor Maté M.D., author, In the Realm of Hungry Ghosts As our civilization careens toward climate breakdown, ecological destruction, and gaping inequality, people are losing their existential moorings. The dominant worldview of disconnection, which tells us we are split between mind and body, separate from each other, and at odds with the natural world, has been invalidated by modern science. Award-winning author Jeremy Lent, investigates humanity’s age-old questions—Who am I? Why am I? How should I live?—from a fres...
Rail and the City
An architect makes the case for rail transit as the critical infrastructure for a fluidly functioning and environmentally sustainable urban society. The United States has evolved into a nation of twenty densely populated megaregions. Yet despite the environmental advantages of urban density, urban sprawl and reliance on the private car still set the pattern for most new development. Cars guzzle not only gas but also space, as massive acreage is dedicated to roadways and parking. Even more pressing, the replication of this pattern throughout the fast-developing world makes it doubtful that we will achieve the reductions in carbon emissions needed to avoid climate catastrophe. In Rail and the ...
