Math & Science

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.

Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.

Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach--that is, to incorporate prior knowledge when reasoning with incomplete information--in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli's Fallacy explains why something has gone wrong with how we use data--and how to fix it.

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.

This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.

Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition--one that will be essential reading for popular-science buffs and historians of science alike.

The year's finest writing on mathematics from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2014 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here John Conway presents examples of arithmetical statements that are almost certainly true but likely unprovable; Carlo Séquin explores, compares, and illustrates distinct types of one-sided surfaces known as Klein bottles; Keith Devlin asks what makes a video game good for learning mathematics and shows why many games fall short of that goal; Jordan Ellenberg reports on a recent breakthrough in the study of prime numbers; Stephen Pollard argues that mathematical practice, thinking, and experience transcend the utilitarian value of mathematics; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes an introduction by editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

The year's finest mathematics writing from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.

Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

The year's finest mathematical writing from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2019 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice--and taking readers behind the scenes of today's hottest mathematical debates.

In this volume, Moon Duchin explains how geometric-statistical methods can be used to combat gerrymandering, Jeremy Avigad illustrates the growing use of computation in making and verifying mathematical hypotheses, and Kokichi Sugihara describes how to construct geometrical objects with unusual visual properties. In other essays, Neil Sloane presents some recent additions to the vast database of integer sequences he has catalogued, and Alessandro Di Bucchianico and his colleagues highlight how mathematical methods have been successfully applied to big-data problems. And there's much, much more.

In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable writings on mathematics.

This is a must-read for anyone interested in where math has taken us--and where it is headed.

From the cubit to the kilogram, the humble inch to the speed of light, measurement is a powerful tool that humans invented to make sense of the world. In this revelatory work of science and social history, James Vincent dives into its hidden world, taking readers from ancient Egypt, where measuring the annual depth of the Nile was an essential task, to the intellectual origins of the metric system in the French Revolution, and from the surprisingly animated rivalry between metric and imperial, to our current age of the "quantified self." At every turn, Vincent is keenly attuned to the political consequences of measurement, exploring how it has also been used as a tool for oppression and control.

Beyond Measure reveals how measurement is not only deeply entwined with our experience of the world, but also how its history encompasses and shapes the human quest for knowledge.

"A monumental effort." --New York Review of Books

"An excellent piece of science writing. . . . Cassidy does not so much exculpate Heisenberg as explain him, with a transparency that makes this biography a pleasure to read." --Los Angeles Times

"Cassidy has written the definitive biography of a great and tragic physicist." --Richard Rhodes, author of the Pulitzer Prize-winning The Making of the Atomic Bomb

Since the fall of the Soviet Union, long-suppressed information has emerged on Werner Heisenberg's role in the Nazi atomic bomb project. In Beyond Uncertainty, Cassidy interprets this and other previously unknown material within the context of his vast research and tackles the vexing questions of a scientist's personal responsibility and guilt when serving an abhorrent military regime.

David C. Cassidy is the author of Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb; A Short History of Physics in the American Century; J. Robert Oppenheimer and the American Century; and Einstein and Our World. He is the recipient of the Abraham Pais Prize for History of Physics from the American Physical Society, the Science Writing Award from the American Institute of Physics, the Pfizer Award from the History of Science Society, and an honorary doctorate from Purdue University. Dr. Cassidy is Professor of Natural Sciences at Hofstra University and resides in Bay Shore, New York.

Why birds are smarter than we think

Birds have not been known for their high IQs, which is why a person of questionable intelligence is sometimes called a "birdbrain." Yet in the past two decades, the study of avian intelligence has witnessed dramatic advances. From a time when birds were seen as simple instinct machines responding only to stimuli in their external worlds, we now know that some birds have complex internal worlds as well. This beautifully illustrated book provides an engaging exploration of the avian mind, revealing how science is exploding one of the most widespread myths about our feathered friends--and changing the way we think about intelligence in other animals as well.

Bird Brain looks at the structures and functions of the avian brain, and describes the extraordinary behaviors that different types of avian intelligence give rise to. It offers insights into crows, jays, magpies, and other corvids--the "masterminds" of the avian world--as well as parrots and some less-studied species from around the world. This lively and accessible book shows how birds have sophisticated brains with abilities previously thought to be uniquely human, such as mental time travel, self-recognition, empathy, problem solving, imagination, and insight.

Written by a leading expert and featuring a foreword by Frans de Waal, renowned for his work on animal intelligence, Bird Brain shines critical new light on the mental lives of birds.

What draws us to the beauty of a peacock, the flight of an eagle, or the song of a nightingale? Why are birds so significant in our lives and our sense of the world? And what do our ways of thinking about and experiencing birds tell us about ourselves? Birdscapes is a unique meditation on the variety of human responses to birds, from antiquity to today, and from casual observers to the globe-trotting "twitchers" who sometimes risk life, limb, and marriages simply to add new species to their "life lists."

Drawing extensively on literature, history, philosophy, and science, Jeremy Mynott puts his own experiences as a birdwatcher in a rich cultural context. His sources range from the familiar--Thoreau, Keats, Darwin, and Audubon--to the unexpected--Benjamin Franklin, Giacomo Puccini, Oscar Wilde, and Monty Python. Just as unusual are the extensive illustrations, which explore our perceptions and representations of birds through images such as national emblems, women's hats, professional sports logos, and a Christmas biscuit tin, as well as classics of bird art. Each chapter takes up a new theme--from rarity, beauty, and sound to conservation, naming, and symbolism--and is set in a new place, as Mynott travels from his "home patch" in Suffolk, England, to his "away patch" in New York City's Central Park, as well as to Russia, Australia, and Greece.

Conversational, playful, and witty, Birdscapes gently leads us to reflect on large questions about our relation to birds and the natural world. It encourages birders to see their pursuits in a broader human context--and it shows nonbirders what they may be missing.

"An ambitious, important, and utterly captivating book."--Mary Roach, New York Times bestselling author of Replaceable You and Stiff

A revealing investigation into how industrial farming poses a growing threat to America's bees

Each February, a vast yet largely invisible migration takes place across the United States. Semi-trucks stacked high with honey bee colonies head to California's Central Valley, carrying nearly 99 percent of the nation's domesticated bees. There, the bees pollinate millions of acres of blooming almond orchards before fanning out across the country for apples, berries, and other crops. This massive undertaking sustains both beekeepers and farmers--but it comes at a heavy price.

In Bitter Honey, Jennie Durant takes readers behind the scenes to reveal the human and ecological cost of industrial farming for bees, beekeepers, and all of us who depend on them. Bees today face a gauntlet of threats: parasites and disease, pesticide exposure, and climate extremes--all magnified by Big Ag. Beekeepers, meanwhile, endure grueling practices just to survive, often losing half their hives each year.

But this isn't a story of defeat. Durant introduces us to the beekeepers, farmers, and activists pioneering new ways to support both wild and managed bees. The stakes are high: nearly three-quarters of our major food crops depend on bees and other pollinators. Bitter Honey exposes the crisis threatening the nation's bees and spotlights the advocates working to protect them for generations to come.

Paul Hawken has spent more than a decade researching organizations dedicated to restoring the environment and fostering social justice. From billion-dollar nonprofits to single-person dot.causes, these groups collectively comprise the largest movement on earth, a movement that has no name, leader, or location and that has gone largely ignored by politicians and the media.

Blessed Unrest explores the diversity of the movement, its brilliant ideas, innovative strategies, and centuries of hidden history. A culmination of Hawken's many years of leadership in the environmental and social justice fields, it will inspire all who despair of the world's fate, and its conclusions will surprise even those within the movement itself.