By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    Einstein's Heroes takes you on a journey of discovery about just such a miraculous language--the language of mathematics--one of humanity's mostamazing accomplishments. Blending science, history, and biography, this remarkable book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and especially James Clerk Maxwell, whose work directly inspired the theory of relativity. RobynArianrhod bridges the gap between science and literature, portraying mathematics as a language and arguing that a physical theory is a work of imagination involving the elegant and clever use of this language. The heart of the book illuminates how Maxwell, using the language of mathematics in a newand radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of theradio wave, teasing it out of the mathematical language itself. Here then is a fascinating look at mathematics: its colorful characters, its historical intrigues, and above all its role as the uncannily accurate language of nature.

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    In 2004, four Latino teenagers arrived at the Marine Advanced Technology Education Robotics Competition at the University of California, Santa Barbara. They were born in Mexico but raised in Phoenix, Arizona, where they attended an underfunded public high school. No one had ever suggested to Oscar, Cristian, Luis, or Lorenzo that they might amount to much - but two inspiring science teachers had convinced these impoverished, undocumented kids from the desert who had never even seen the ocean that they should try to build an underwater robot. And build a robot they did. Their robot wasn't pretty, especially compared to those of the competition. They were going up against some of the best collegiate engineers in the country, including a team from MIT backed by a $10,000 grant from ExxonMobil. The Phoenix teenagers had scraped together less than $1,000 and built their robot out of scavenged parts. This was never a level competition—and yet, against all odds... they won! But this is just the beginning for these four, whose story—which became a key inspiration to the DREAMers movement—will go on to include first-generation college graduations, deportation, bean-picking in Mexico, and service in Afghanistan. Joshua Davis' Spare Parts is a story about overcoming insurmountable odds and four young men who proved they were among the most patriotic and talented Americans in this country—even as the country tried to kick them out.

    Growing up in a working-class Long Island family, Massimino catapulted himself to Columbia and then MIT, only to flunk his qualifying exams and be rejected twice by NASA before making it to the final round of astronaut selection—where he was told his poor eyesight meant he’d never make the cut. But even that couldn’t stop him from finally earning his wings, making the jump to training in T-38 Air Force jets and preparing his body—and soul—for the journey to the cosmos.Taking us through the surreal wonder and beauty of his first spacewalk, the tragedy of losing friends in the Columbia shuttle accident, and the development of his enduring love for the Hubble telescope—which he’d be tasked with saving on his final mission— Massimino has written an ode to never giving up and the power of teamwork to make anything possible. Spaceman invites us into a rare, wonderful world where the nerdiest science meets the most thrilling adventure, and pulls back a curtain on just what having “the right stuff” really means.

    

    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.” If we can toss aside our fears and learn to approach them clearly—understanding how our own preconceptions lead us astray—statistics can point to ways we can live better and work smarter.As “perhaps the best popular economics writer in the world” (New Statesman), Tim Harford is an expert at taking complicated ideas and untangling them for millions of readers. In The Data Detective, he uses new research in science and psychology to set out ten strategies for using statistics to erase our biases and replace them with new ideas that use virtues like patience, curiosity, and good sense to better understand ourselves and the world. As a result, The Data Detective is a big-idea book about statistics and human behavior that is fresh, unexpected, and insightful.

    This brilliant work heralds the new age of nanotechnology, which will give us thorough and inexpensive control of the structure of matter.  Drexler examines the enormous implications of these developments for medicine, the economy, and the environment, and makes astounding yet well-founded projections for the future.