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Infinitesimal

Author: Amir Alexander

Publisher: Simon and Schuster

Published: 2014-07-03

Total Pages: 368

ISBN-13: 1780745338

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.

Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World

Author: Amir Alexander

Publisher: Macmillan

Published: 2014-04-08

Total Pages: 369

ISBN-13: 0374176817

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Explores "the epic battle over a mathematical concept that shook the old order and shaped the world as we know it. On August 10, 1632, five leaders of the Society of Jesus convened in a somber 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"--

Duel at Dawn

Author: Amir Alexander

Publisher: Harvard University Press

Published: 2011-10-15

Total Pages: 320

ISBN-13: 0674061748

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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 became Romantic heroes like poets, artists, and musicians. The ideal mathematician was now an alienated loner, driven to despondency by an uncomprehending world. A field that had been focused on the natural world now sought to create its own reality. Higher mathematics became a world unto itselfÑpure and governed solely by the laws of reason. In this strikingly original book that takes us from Paris to St. Petersburg, Norway to Transylvania, Alexander introduces us to national heroes and outcasts, innocents, swindlers, and martyrsÐall uncommonly gifted creators of modern mathematics.

Geometrical Landscapes

Author: Amir R. Alexander

Publisher: Stanford University Press

Published: 2002

Total Pages: 318

ISBN-13: 9780804732604

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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.

Finding Zero

Author: Amir D. Aczel

Publisher: Macmillan + ORM

Published: 2015-01-06

Total Pages: 199

ISBN-13: 1466879106

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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 ride. The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.

Proof!

Author: Amir Alexander

Publisher: Scientific American / Farrar, Straus and Giroux

Published: 2019-09-10

Total Pages: 320

ISBN-13: 9780374254902

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An eye-opening narrative of how geometric principles fundamentally shaped our world One night in 1661, Nicholas Fouquet, a superintendent under Louis XIV, was arrested. His crime was peculiar: He had dared to construct a grand geometrical garden. In doing so, he violated an irrefutable hierarchy: that geometry, in its perfection, was a testament to divine right. The elegant, symmetrical designs were more than just ornament; they were proofs of incontestable certainty, and thus the authority to rule. But how did the French royalty fall in love with this peculiar landscape design? Wherefore Versailles? In Proof!, the award-winning historian Amir Alexander argues that Euclidean geometry has been uniquely responsible for how our societies are structured. It has shaped how our cities are built and been used as a rationale to explain political structures. The proofs in Euclid’s Elements were not only just true but were certain by reason alone. Alexander tracks the rediscovery of Euclidean geometry in fifteenth-century Italy and recounts the French royalty’s centuries-long love affair with geometrical gardening, which acted as a visual symbol of the king’s consolidation of power during a time of violence and upheaval, and which culminated with the gardens at Versailles. Proof! tells the monumental story of the geometries that were carved into our world, the beliefs they supported, and the ways they shape our lives to this day.

Mathematics without Apologies

Author: Michael Harris

Publisher: Princeton University Press

Published: 2017-05-30

Total Pages: 468

ISBN-13: 0691175837

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An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

God and Galileo

Author: David L. Block

Publisher: Crossway

Published: 2019-05-17

Total Pages: 247

ISBN-13: 1433562928

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"A devastating attack upon the dominance of atheism in science today." Giovanni Fazio, Senior Physicist, Harvard-Smithsonian Center for Astrophysics The debate over the ultimate source of truth in our world often pits science against faith. In fact, some high-profile scientists today would have us abandon God entirely as a source of truth about the universe. In this book, two professional astronomers push back against this notion, arguing that the science of today is not in a position to pronounce on the existence of God—rather, our notion of truth must include both the physical and spiritual domains. Incorporating excerpts from a letter written in 1615 by famed astronomer Galileo Galilei, the authors explore the relationship between science and faith, critiquing atheistic and secular understandings of science while reminding believers that science is an important source of truth about the physical world that God created.