"Correlation does not imply causation". This mantra has been invoked by scientists for decades and has led to a virtual prohibition on causal talk. But today, that taboo is dead. The causal revolution, sparked by Judea Pearl and his colleagues, has cut through a century of confusion and placed causality - the study of cause and effect - on a firm scientific basis.

Work with data like a pro using this guide that breaks down how to organize, apply, and most importantly, understand what you are analyzing in order to become a true data ninja.

From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you'll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.

Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia's views on crime and punishment, the psychology of slime molds, what Facebook can and can't figure out about you, and the existence of God.

If you're like most people, geometry is a dimly remembered exercise you gladly left behind in the dust of ninth grade. It's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face.

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, and insight.

Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true - yet never provable - continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.

Nate Silver built an innovative system for predicting baseball performance, predicted the 2008 election within a hair’s breadth, and became a national sensation as a blogger - all by the time he was 30. He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of the website FiveThirtyEight. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data.

Today we think statistics are the enemy, numbers used to mislead and confuse us. That’s a mistake, Tim Harford says in The Data Detective. We shouldn’t be suspicious of statistics - we need to understand what they mean and how they can improve our lives: they are, at heart, human behavior seen through the prism of numbers and are often “the only way of grasping much of what is going on around us”.

Futurists insist that AI will soon eclipse the capacities of the most gifted human mind. What hope do we have against superintelligent machines? But we aren't really on the path to developing intelligent machines. In fact, we don't even know where that path might be. Erik Larson takes us on a tour of the landscape of AI to show how far we are from superintelligence and what it would take to get there.

In the 21st century, humanity is reaching new heights of scientific understanding - and at the same time appears to be losing its mind. How can a species that developed vaccines for COVID-19 in less than a year produce so much fake news, medical quackery, and conspiracy theorizing? Pinker rejects the cynical cliché that humans are an irrational species - cavemen out of time saddled with biases, fallacies, and illusions.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves. Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to turn the tide in the fight against AIDS.

The smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Nuclear weapons and self-replicating spacecrafts. All bear the fingerprints of one remarkable, yet largely overlooked, man: John von Neumann.

Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.

Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.

"Correlation does not imply causation". This mantra has been invoked by scientists for decades and has led to a virtual prohibition on causal talk. But today, that taboo is dead. The causal revolution, sparked by Judea Pearl and his colleagues, has cut through a century of confusion and placed causality - the study of cause and effect - on a firm scientific basis.

This in-depth discussion of New Testament scholarship and the challenges of history as a whole proposes Bayes's Theorem, which deals with probabilities under conditions of uncertainty, as a solution to the problem of establishing reliable historical criteria. The author demonstrates that valid historical methods - not only in the study of Christian origins but in any historical study - can be described by, and reduced to, the logic of Bayes's Theorem. Conversely, he argues that any method that cannot be reduced to this theorem is invalid and should be abandoned.

Many scientific and philosophical ideas are so powerful that they can be applied to our lives at home, work, and school to help us think smarter and more effectively about our behavior and the world around us. Surprisingly, many of these ideas remain unknown to most of us. In Mindware, the world-renowned psychologist Richard Nisbett presents these ideas in clear and accessible detail, offering a tool kit for better thinking and wiser decisions.

From the best-selling author of Thinking, Fast and Slow, the co-author of Nudge, and the author of You Are About to Make a Terrible Mistake! comes Noise, a revolutionary exploration of why people make bad judgments, and how to control both noise and cognitive bias.

Do doctors really know what they are talking about when they tell us vaccines are safe? Should we take climate experts at their word when they warn us about the perils of global warming? Why should we trust science when our own politicians don't? In this landmark book, Naomi Oreskes offers a bold and compelling defense of science, revealing why the social character of scientific knowledge is its greatest strength - and the greatest reason we can trust it.

Can there be freedom and free will in a deterministic world? Renowned philosopher Daniel Dennett emphatically answers "yes!" Using an array of provocative formulations, Dennett sets out to show how we alone among the animals have evolved minds that give us free will and morality. Weaving a richly detailed narrative, Dennett explains in a series of strikingly original arguments - drawing upon evolutionary biology, cognitive neuroscience, economics, and philosophy - that far from being an enemy of traditional explorations of freedom, morality, and meaning, the evolutionary perspective can be an indispensable ally.

Throughout his distinguished and unconventional career, engineer-turned-molecular-biologist Douglas Axe has been asking the questions that much of the scientific community would rather silence. Now, he presents his conclusions in this brave and pioneering book. Axe argues that the key to understanding our origin is the "design intuition" - the innate belief held by all humans that tasks we would need knowledge to accomplish can be accomplished only by someone who has that knowledge.

Nobel Laureate Eugene Wigner once wondered about "the unreasonable effectiveness of mathematics" in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that - mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true.

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were - and still are. The Structure of Scientific Revolutions is that kind of book.

What is history, and why should we study it? Is there such a thing as historical truth? Is history a science? One of the most accomplished historians at work today, John Lewis Gaddis, answers these and other questions in this short, witty, and humane book. The Landscape of History provides a searching look at the historian's craft as well as a strong argument for why a historical consciousness should matter to us today.

The Great Mental Models: General Thinking Concepts is the first book in The Great Mental Models series designed to upgrade your thinking with the best, most useful and powerful tools so you always have the right one on hand. This volume details nine of the most versatile all-purpose mental models you can use right away to improve your decision making, your productivity, and how clearly you see the world.

In The Genetic Lottery, Harden introduces listeners to the latest genetic science, dismantling dangerous ideas about racial superiority and challenging us to grapple with what equality really means in a world where people are born different. Weaving together personal stories with scientific evidence, Harden shows why our refusal to recognize the power of DNA perpetuates the myth of meritocracy, and argues that we must acknowledge the role of genetic luck if we are ever to create a fair society.

Columnist and publisher Michael Shermer, once an evangelical Christian and a creationist, argues that Intelligent Design proponents invoke a combination of ad science, political antipathy, and flawed theology in their new brand of creationism. He refutes their pseudoscientific arguments and then demonstrates why conservatives and people of faith can and should embrace evolution. Why Darwin Matters is an incisive examination of what is at stake in the debate over evolution.

Over a storied career, Daniel C. Dennett has engaged questions about science and the workings of the mind. His answers have combined rigorous argument with strong empirical grounding. And a lot of fun. Intuition Pumps and Other Tools for Thinking offers seventy-seven of Dennett’s most successful “imagination-extenders and focus-holders” meant to guide you through some of life’s most treacherous subject matter: evolution, meaning, mind, and free will.

Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot.

At its simplest, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes’s theorem is a description of almost everything. But who was the man who lent his name to this theorem?

Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.

This 10-part history of mathematics reveals the personalities behind the calculations: the passions and rivalries of mathematicians struggling to get their ideas heard. Professor Marcus du Sautoy shows how these masters of abstraction find a role in the real world and proves that mathematics is the driving force behind modern science.

Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. Sharon Bertsch McGrayne here explores this controversial theorem and the human obsessions surrounding it.

"Correlation does not imply causation". This mantra has been invoked by scientists for decades and has led to a virtual prohibition on causal talk. But today, that taboo is dead. The causal revolution, sparked by Judea Pearl and his colleagues, has cut through a century of confusion and placed causality - the study of cause and effect - on a firm scientific basis.

We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning.

From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you'll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.

Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia's views on crime and punishment, the psychology of slime molds, what Facebook can and can't figure out about you, and the existence of God.

In Your Brain Is a Time Machine, brain researcher and best-selling author Dean Buonomano draws on evolutionary biology, physics, and philosophy to present his influential theory of how we tell and perceive time. The human brain, he argues, is a complex system that not only tells time but creates it; it constructs our sense of chronological flow and enables "mental time travel" - simulations of future and past events.

Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence - and even more so if we hope to participate in the future, rather than being simple bystanders.