Math History

From Leonardo Da Vinci to John Dee and Comenius, from George Eliot to Oliver Sacks and Susan Sontag, polymaths have moved the frontiers of knowledge in countless ways. But history can be unkind to scholars with such encyclopaedic interests. All too often these individuals are remembered for just one part of their valuable achievements. In this engaging, erudite account, renowned cultural historian Peter Burke argues for a more rounded view.

In 2006 an oddball group of bankers, traders and brokers from some of the largest financial institutions made a startling realization: Libor - the London interbank offered rate, which determines the interest rates on trillions in loans worldwide - was set daily by a group of easily manipulated administrators, and they could reap huge profits by nudging it fractions of a percent to suit their trading portfolios. This group generated incredible riches - until it all unraveled in spectacularly vicious, backstabbing fashion.

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.

Mescaline, LSD, and psilocybin mushrooms. There’s been a lot of discussion in the medical world lately about the potential benefits of these and other drugs for certain medical conditions, such as anxiety and depression. As we consider the place of psychedelics in the future, we can draw insight and guidance from the history of how psychedelics have been described, sought after, applied, and prohibited over the centuries. Erika Dyck, professor of history at the University of Saskatchewan, introduces you to the world of hallucinogens.

In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively - secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions - you just need the creativity to see them.

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: Observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria.

Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet, the greatest mathematicians throughout history, from Rene Descartes to Alexander Grothendieck, have insisted that this is not the case.

In March 2006, the world’s richest men sipped champagne in an opulent New York hotel. They were preparing to compete in a poker tournament with ­million-dollar stakes. At the card table that night was Peter Muller, who managed a fabulously successful hedge fund called PDT. With him was Ken Griffin, who was the tough-as-nails head of Citadel Investment Group. There, too, were Cliff Asness, the sharp-tongued, mercurial founder of the hedge fund AQR Capital Management, and Boaz Weinstein, chess “life master” and king of the credit-default swap.

What sparks the flash of brilliance? How does groundbreaking innovation happen? Answering in his infectious, culturally omnivorous style, using his fluency in fields from neurobiology to popular culture, Johnson provides the complete, exciting, and encouraging story of how we generate the ideas that push our careers, our lives, our society, and our culture forward.

We live in the age of the algorithm. Increasingly, the decisions that affect our lives—where we go to school, whether we get a loan, how much we pay for insurance—are being made not by humans, but by mathematical models. In theory, this should lead to greater fairness: everyone is judged according to the same rules and bias is eliminated. And yet, as Cathy O'Neil reveals in this urgent and necessary book, the opposite is true. The models being used today are opaque, unregulated and incontestable, even when they're wrong. Most troubling, they reinforce discrimination.

We all make mistakes. Nobody’s perfect. Not even some of the greatest geniuses in history, as Mario Livio tells us in this marvelous story of scientific error and breakthrough. Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle, and Albert Einstein were all brilliant scientists. Each made groundbreaking contributions to his field - but each also stumbled badly. These five scientists expanded our knowledge of life on Earth, the evolution of the Earth itself, and the evolution of the universe, despite and because of their errors. As Mario Livio luminously explains, the scientific process advances through error.

In the 1970s, amid severe cutbacks in physics funding, a small group of underemployed physicists in Berkeley decided to throw off the constraints of academia and explore the wilder side of science. Dubbing themselves the “Fundamental Fysiks Group,” they pursued a freewheeling, speculative approach to physics. Some dabbled with LSD while conducting experiments. They studied quantum theory alongside Eastern mysticism and psychic mind reading, discussing the latest developments while lounging in hot tubs.

Best-selling author Steven Johnson recounts - in dazzling, multidisciplinary fashion - the story of the brilliant man who embodied the relationship between science, religion, and politics for America's Founding Fathers. The Invention of Air is a title of world-changing ideas wrapped around a compelling narrative, a story of genius and violence and friendship in the midst of sweeping historical change that provokes us to recast our understanding of the Founding Fathers.

Mathematics shapes almost everything we do. From building rockets to the handheld technology that governs our day-to-day lives, we are all in debt to the mathematical geniuses of the past. But the history of mathematics is warped; it looks like a sixteenth-century map that enlarges Europe at the expense of Africa, Asia and the Americas. The Secret Lives of Numbers introduces listeners to a new group of mathematical boundary-smashers, those who have been erased by history because of their race, gender or nationality.

One of the great insights of science is that the universe has an underlying order. The supreme goal of physicists is to understand this order through laws that describe the behavior of the most basic particles and the forces between them. For centuries, we have searched for these laws by studying the results of experiments. Since the 1970s, however, experiments at the world's most powerful atom-smashers have offered few new clues. So some of the world's leading physicists have looked to a different source of insight: modern mathematics.

The lives of millions will be changed after it breaks, and yet so few people understand it, or even realize it runs through their backyard. Dvorak reveals the San Andreas Fault's fascinating history - and its volatile future. It is a prominent geological feature that is almost impossible to see unless you know where to look. Hundreds of thousands of people drive across it every day. The San Andreas Fault is everywhere - and primed for a colossal quake. For decades scientists have warned that such a sudden shifting of the Earth's crust is inevitable.

One of the great mysteries of science is that its fundamental laws are written in the language of mathematics. Graham Farmelo's thrilling new book shows how modern maths has helped physicists to rethink gravity, space, and time. The Universe Speaks in Numbers takes us on an adventure from the Enlightenment to the present with a vibrant cast of characters, illuminating the most exciting and controversial developments in contemporary thought.

Utterly beautiful. Profoundly disconcerting. Quantum theory is quite simply the most successful account of the physical universe ever devised. Its concepts underpin much of the 21st-century technology that we now take for granted. But at the same time it has completely undermined our ability to make sense of the world at its most fundamental level.

It's a signal paradox of our times that we live in an information society but do not know how it works. And without understanding how our information is stored, used and protected, we are vulnerable to having it exploited. In Fancy Bear Goes Phishing, Scott Shapiro exposes the secrets of the digital age. With lucidity and wit, he establishes that cybercrime has less to do with defective programming than with the faulty wiring of our psyches and society. And because hacking is a human story, he tells the fascinating tales of perpetrators.

In March 2006, the world’s richest men sipped champagne in an opulent New York hotel. They were preparing to compete in a poker tournament with ­million-dollar stakes. At the card table that night was Peter Muller, who managed a fabulously successful hedge fund called PDT. With him was Ken Griffin, who was the tough-as-nails head of Citadel Investment Group. There, too, were Cliff Asness, the sharp-tongued, mercurial founder of the hedge fund AQR Capital Management, and Boaz Weinstein, chess “life master” and king of the credit-default swap.