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Duel at Dawn
In the fog of a Paris dawn in 1832, variste Galois, the 20-year-old founder of modern algebra, was shot and killed in a duel. That gunshot, suggests Amir Alexander, marked the end of one era in mathematics and the beginning of another. Arguing that not even the purest mathematics can be separated from its cultural background, Alexander shows how popular stories about mathematicians are really morality tales about their craft as it relates to the world. In the eighteenth century, Alexander says, mathematicians were idealized as child-like, eternally curious, and uniquely suited to reveal the hidden harmonies of the world. But in the nineteenth century, brilliant mathematicians like Galois b...
Proof!
An eye-opening narrative of how geometric principles fundamentally shaped our world On a cloudy day in 1413, a balding young man stood at the entrance to the Cathedral of Florence, facing the ancient Baptistery across the piazza. As puzzled passers-by looked on, he raised a small painting to his face, then held a mirror in front of the painting. Few at the time understood what he was up to; even he barely had an inkling of what was at stake. But on that day, the master craftsman and engineer Filippo Brunelleschi would prove that the world and everything within it was governed by the ancient science of geometry. In Proof!, the award-winning historian Amir Alexander traces the path of the geom...
Infinitesimal
On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.
Liberty's Grid
The surprising history behind a ubiquitous facet of the United States: the gridded landscape. Seen from an airplane, much of the United States appears to be a gridded land of startling uniformity. Perpendicular streets and rectangular fields, all precisely measured and perfectly aligned, turn both urban and rural America into a checkerboard landscape that stretches from horizon to horizon. In evidence throughout the country, but especially the West, the pattern is a hallmark of American life. One might consider it an administrative convenience--an easy way to divide land and lay down streets--but it is not. The colossal grid carved into the North American continent, argues historian and writ...
Geometrical Landscapes
This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the 16th century. Leading mathematicians began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. Many of those who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period?the infinitesimal methods, which the author shows was no coincidence.
The Art of Logic in an Illogical World
How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.
An Eventful Life
This is an amazing story, found in a tattered notebook, misplaced for decades and filled with scribbled writing, that contained Alexander Amir's memoir: growing up in Eastern Europe, soldiering in the First World War, and bringing his family to Israel when antisemitism in his native Transylvania became intolerable.
Finding Zero
The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel's lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the r...
Circles Disturbed
Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us ...
When Novels Were Books
The novel was born religious, alongside Protestant texts produced in the same format by the same publishers. Novels borrowed features of these texts but over the years distinguished themselves, becoming the genre we know today. Jordan Alexander Stein traces this history, showing how the physical object of the book shaped the stories it contained.
