Full-color illustrations.

    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.

    Although the laws of physics create a powerful impression that time is flowing, in fact there are only timeless `nows'. In The End of Time, the British theoretical physicist Julian Barbour describes the coming revolution in our understanding of the world: a quantum theory of the universe that brings together Einstein's general theory of relativity - which denies the existence of a unique time - and quantum mechanics - which demands one. Barbour believes that only the most radical of ideas can resolve the conflict between these two theories: that there is, quite literally, no time at all. The End of Time is the first full-length account of the crisis in our understanding that has enveloped quantum cosmology. Unifying thinking that has never been brought together before in a book for the general reader, Barbour reveals the true architecture of the universe and demonstrates how physics is coming up sharp against the extraordinary possibility that the sense of time passing emerges from a universe that is timeless. The heart of the book is the author's lucid description of how a world of stillness can appear to be teeming with motion: in this timeless world where all possible instants coexist, complex mathematical rules of quantum mechanics bind together a special selection of these instants in a coherent order that consciousness perceives as the flow of time. Finally, in a lucid and eloquent epilogue, the author speculates on the philosophical implications of his theory: Does free will exist? Is time travel possible? How did the universe begin? Where is heaven? Does the denial of time make life meaningless? Written with exceptional clarity and elegance, this profound and original work presents a dazzlingly powerful argument that all will be able to follow, but no-one with an interest in the workings of the universe will be able to ignore.

    Now, in an exciting, fast-paced historical narrative ranging across two centuries, Mark Ronan takes us on an exhilarating tour of this final mathematical quest. Ronan describes how the quest to understand symmetry really began with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or atoms of symmetry. Most of these building blocks fit into a table, rather like the periodic table of elements, but mathematicians have found 26 exceptions. The biggest of these was dubbed the Monster--a giant snowflake in 196,884 dimensions. Ronan, who personally knows the individuals now working on this problem, reveals how the Monster was only dimly seen at first. As more and more mathematicians became involved, the Monster became clearer, and it was found to be not monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe. This story of discovery involves extraordinary characters, and Mark Ronan brings these people to life, vividly recreating the growing excitement of what became the biggest joint project ever in the field of mathematics. Vibrantly written, Symmetry and the Monster is a must-read for all fans of popular science--and especially readers of such books as Fermat's Last Theorem.

    Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.

    This Penguin Classics edition is edited with an introduction by James Moore and Adrian Desmond.In The Origin of Species, Charles Darwin refused to discuss human evolution, believing the subject too 'surrounded with prejudices'. He had been reworking his notes since the 1830s, but only with trepidation did he finally publish The Descent of Man in 1871. The book notoriously put apes in our family tree and made the races one family, diversified by 'sexual selection' - Darwin's provocative theory that female choice among competing males leads to diverging racial characteristics. Named by Sigmund Freud as 'one of the ten most significant books' ever written, Darwin's Descent of Man continues to shape the way we think about what it is that makes us uniquely human.In their introduction, James Moore and Adrian Desmond, acclaimed biographers of Charles Darwin, call for a radical re-assessment of the book, arguing that its core ideas on race were fired by Darwin's hatred of slavery. The text is the second and definitive edition and this volume also contains suggestions for further reading, a chronology and biographical sketches of prominent individuals mentioned.Charles Darwin (1809-82), a Victorian scientist and naturalist, has become one of the most famous figures of science to date. The advent of On the Origin of Species by Means of Natural Selection in 1859 challenged and contradicted all contemporary biological and religious beliefs.If you enjoyed The Descent of Man, you might like Darwin's On the Origin of Species, also available in Penguin Classics.

    Taking as territory everything from the Big Bang to the rise of civilization, Bryson seeks to understand how we got from there being nothing at all to there being us. To that end, he has attached himself to a host of the world’s most advanced (and often obsessed) archaeologists, anthropologists, and mathematicians, travelling to their offices, laboratories, and field camps. He has read (or tried to read) their books, pestered them with questions, apprenticed himself to their powerful minds. A Short History of Nearly Everything is the record of this quest, and it is a sometimes profound, sometimes funny, and always supremely clear and entertaining adventure in the realms of human knowledge, as only Bill Bryson can render it. Science has never been more involving or entertaining.

    It explains all this and much more. It discloses the best time to have a sex change, how to have a virgin birth, when to seduce your sisters or eat your lover. Quirky and brilliant, it takes as its starting point all creatures great and small worried about their bizarre sex lives, and the letters they write to the wise Dr Tatiana, the only agony aunt in all creation with a prodigious knowledge of both natural history and evolutionary biology.

    Medicine, anatomy, astronomy, mathematics and cosmology were all invented in their world. Plato, Aristotle, Pythagoras, Archimedes and Hippocrates were amongst its stars, master architects all of the modern as well as the ancient.

    Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.