In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    Yet only now, with the publication of Voyaging, the first of two volumes that will constitute the definitive biography, do we have a truly vivid and comprehensive picture of Darwin as man and as scientist. Drawing upon much new material, supported by an unmatched acquaintance with both the intellectual setting and the voluminous sources, Janet Browne has at last been able to unravel the central enigma of Darwin's career: how did this amiable young gentleman, born into a prosperous provincial English family, grow into a thinker capable of challenging the most basic principles of religion and science? The dramatic story of Voyaging takes us from agonizing personal challenges to the exhilaration of discovery; we see a young, inquisitive Darwin gradually mature, shaping, refining, and finally setting forth the ideas that would at last fall upon the world like a thunderclap in The Origin of Species.

    For almost four centuries this astonishing story of a woman’s absolute power over the Vatican has been successfully buried—until now.

    At times a painter, sculptor, inventor, draftsman, and anatomist, Leonardo's life cannot easily be summarized. And yet, Nicholl skillfully traces the artist's early days as an illegitimate child in Tuscany; his apprenticeship with Verrocchio in Florence; his service with some of the most powerful Renaissance families; his relationships with Michelangelo and Machiavelli; and his final days at the French royal court. In addition, Nicholl looks beyond the well-known stories of Leonardo's famous masterpieces, and gives us a glimpse into the artist's everyday life. We learn of Leonardo's penchant for jokes, his fascination with flight, his obsessive note making, and even what he ate. Nicholl weaves these details together in a fascinating portrait that goes far towards revealing the enigmatic figure who continues to fascinate present-day readers.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    Simon looks at his distinguished and varied career, continually asking himself whether (and how) what he learned as a scientist helps to explain other aspects of his life.A brilliant polymath in an age of increasing specialization, Simon is one of those rare scholars whose work defines fields of inquiry. Crossing disciplinary lines in half a dozen fields, Simon's story encompasses an explosion in the information sciences, the transformation of psychology by the information-processing paradigm, and the use of computer simulation for modeling the behavior of highly complex systems.Simon's theory of bounded rationality led to a Nobel Prize in economics, and his work on building machines that think--based on the notion that human intelligence is the rule-governed manipulation of symbols--laid conceptual foundations for the new cognitive science. Subsequently, contrasting metaphors of the maze (Simon's view) and of the mind (neural nets) have dominated the artificial intelligence debate.There is also a warm account of his successful marriage and of an unconsummated love affair, letters to his children, columns, a short story, and political and personal intrigue in academe.

    Presenting to the world his remarkable observations using the recently invented telescope--the craters of the moon, the satellites of Jupiter--Galileo dramatically challenged our idea of the perfection of the heavens and the centrality of the Earth in the universe. Indeed, the appearance of the little book is regarded as one of the great moments in the history of science. Planned to coincide with the 400th anniversary of the publication of the Starry Messenger, this is a major new biography of Galileo, a fresh and much more rounded view of the great scientist than found in earlier works. Unlike previous biographers, Heilbron shows us that Galileo was far more than a mathematician: he was deeply knowledgeable in the arts, an expert on the epic poet Ariosto, a fine lutenist. More important, Heilbron notes that years of reading the poets and experimenting with literary forms were not mere sidebars--they enabled Galileo to write clearly and plausibly about the most implausible things. Indeed, Galileo changed the world not simply because he revolutionized astronomy, but because he conveyed his discoveries so clearly and crisply that they could not be avoided or denied. If ever a discoverer was perfectly prepared to make and exploit his discovery, it was the dexterous humanist Galileo aiming his first telescope at the sky. In Galileo, John Heilbron captures not only the great scientist, but also the creative, artistic younger man who would ultimately become the champion of Copernicus, the bête-noire of the Jesuits, and the best-known of all martyrs to academic freedom.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    In this new major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire oeuvre. This is the first book which deal comprehensively and in depth with Einstein's science, both the successes and the failures.Running through the book is a completely non-scientific biography (identified in the table of contents by italic type) including many letters which appear in English for the first time, as well as other information not published before.Throughout the preparation of this book, Pais has had complete access to the Einstein Archives (now in the possession of the Hebrew University) and the invaluable guidance of the late Helen Dukas--formerly Einstein's private secretary.

    Book by Waring, Chris

    Rather, they recruited an elite group of young women who, with only pencil, paper, and mathematical prowess, transformed rocket design, helped bring about the first American satellites, and made the exploration of the solar system possible. For the first time, Rise of the Rocket Girls tells the stories of these women--known as "human computers"--who broke the boundaries of both gender and science. Based on extensive research and interviews with all the living members of the team, Rise of the Rocket Girls offers a unique perspective on the role of women in science: both where we've been, and the far reaches of space to which we're heading.

    Here are Einstein, Fleming, Bohr, McClintock, Paul ing, Watson and Crick, Heisenberg and many others. With remarkable insight, Lightman charts the intellectual and emotional landscape of the time, portrays the human drama of discovery, and explains the significance and impact of the work. Finally he includes a fascinating and unique guided tour through the original papers in which the discoveries were revealed. Here is science writing at its best–beautiful, lyrical and completely accessible. It brings the process of discovery to life before our very eyes.

    And, it's true, many of them do. But Paul Erdos never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn't learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made "Uncle Paul" a great man.

    It has been inspired by the scientific ferment that swept through Britain at the end of the 18th century, and which Holmes now radically redefines as 'the revolution of Romantic Science'.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.