In 'Infinitesimal,' Amir Alexander reveals the provocative history of calculus and the groundbreaking concept of the infinitesimal. The book traces the intellectual battles that shaped mathematics and its acceptance, positioning infinitesimals as both a vital tool and a source of controversy. Alexander deftly intertwines the lives of brilliant mathematicians and the philosophical dilemmas they faced. Delve into how this 'dangerous' mathematical theory has not only transformed science but also influenced the very fabric of modern thought. What risks did these pioneers take, and how did their revolutionary ideas challenge the status quo?
By Amir Alexander
Published: 2015
"The greatest ideas are often the most dangerous, and it is only by daring to confront the infinite that we can hope to understand the world around us."
Pulsing with drama and excitement, Infinitesimal celebrates the spirit of discovery, innovation, and intellectual achievement-and it will forever change the way you look at a simple line. On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. 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.
Amir Alexander is a celebrated author and historian known for his engaging explorations of mathematical concepts and their historical contexts. His notable works include 'Geometric Forerunners of Non-Euclidean Geometry' and 'Duel at Dawn: Heroes, History, and the Fight for Freedom'. Alexander's writing style is characterized by its clarity and accessibility, making complex ideas relatable to a broad audience. He combines scholarly rigor with a narrative flair, seamlessly blending history and mathematics to captivate readers.
Key information about the book.
Support local bookstores: BookShop gives a portion of each sale to independent bookshops!
In "The Lessons of History," Will and Ariel Durant distill the sweeping narrative of human civilization into profound insights that span cultures and epochs. They explore the recurring themes of war, economics, religion, and human nature that shape our collective journey. With razor-sharp clarity, the Durants argue that the past holds invaluable lessons that can guide our present and future decisions. What patterns emerge when we closely examine the ebb and flow of societies? This thought-provoking work invites readers to reflect on the intricacies of humanity's story and consider how we might navigate the path ahead.
In "A Brief History of Time," Stephen Hawking takes readers on a captivating journey through the cosmos, exploring the nature of time, black holes, and the universe's beginnings. With stunning clarity, he unravels complex scientific concepts, inviting everyone—from curious laypersons to seasoned physicists—to ponder the mysteries of existence. Hawking's charismatic storytelling challenges our perceptions of reality and time itself, posing profound questions about the universe's fate. As he merges science with philosophy, the reader is compelled to reflect on their place in a vast, enigmatic cosmos. Prepare to be inspired and awed by a narrative that transcends mere facts, pushing the boundaries of human understanding.
In 'The City in History,' Lewis Mumford explores the evolution of urban life from ancient times to the modern metropolis. He argues that cities are not just physical structures but reflections of human values and societal progress. Mumford delves into the interplay between architecture, technology, and culture, revealing how they shape the human experience. With incisive critiques and vivid historical examples, he presents a vision of the ideal city that promotes both individuality and community. This thought-provoking journey challenges readers to reconsider the role of cities in their own lives and the future of civilization.
In 'The History of the Decline & Fall of the Roman Empire,' Edward Gibbon meticulously chronicles the mighty empire's descent into chaos and obscurity. With eloquent prose, Gibbon unveils the interplay of political intrigue, moral decay, and military defeats that eroded Rome's power. His analysis does not merely recount events but delves into the philosophical implications of decline and the lessons for future societies. As empires rise and fall, engage with the timeless questions Gibbon poses about civilization itself. Dive into this monumental work to understand how history shapes our present and future.
In 'A History of Economic Theory', Jürg Niehans takes readers on a captivating journey through the evolution of economic thought. From ancient philosophies to contemporary paradigms, the book unravels how ideas have shaped economic practices across cultures and eras. With each chapter, Niehans reveals the intellectual battles and breakthroughs that have defined the discipline. Rich in historical context, this work challenges readers to consider the relevance of past theories in today's economy. Dive into this scholarly adventure and discover how the past continually influences our understanding of wealth and value.
In 'A History of God', Karen Armstrong embarks on a fascinating journey through the evolution of the concept of God from ancient times to the modern era. She explores how various religions—Judaism, Christianity, and Islam—have shaped humanity's understanding of the divine, revealing the complexities and contradictions in these beliefs. Highlighting the influence of culture, politics, and philosophy, Armstrong invites readers to reconsider their perceptions of faith and spirituality. This thought-provoking narrative raises profound questions about the nature of belief and the future of religious thought. Are we on the brink of a new understanding of God, or are we simply repeating history?
In 'A Brief History of Everything', Ken Wilber takes readers on an enlightening journey through the evolution of consciousness and the unfolding of human history. He skillfully weaves together insights from philosophy, science, and spirituality, offering a holistic perspective on our existence. Discover how various cultural paradigms intersect and influence our understanding of reality. This thought-provoking exploration challenges conventional views and invites readers to contemplate their place in the cosmos. What if the key to our future lies in understanding the past in a radically new way?
In 'A Short History of Nearly Everything,' Bill Bryson embarks on a whimsical journey through the annals of science, unraveling the mysteries of the universe and humankind's place within it. With wit and humor, he demystifies complex concepts, from the Big Bang to atoms, making them accessible to the layperson. Bryson introduces us to eccentric scientists and their groundbreaking discoveries, igniting a sense of wonder about the world we inhabit. This book is not merely a history; it's a celebration of curiosity, sparking an appreciation for the intricacies of life and the universe. Prepare to be entertained and enlightened as you explore the 'why' and 'how' behind nearly everything.
Showing 8 of 30 similar books

Aubrey Marcus is an influential entrepreneur, author, and podcaster, best known for founding Onnit, a health and wellness company dedicated to optimizing human performance. He authored the acclaimed book "Own the Day, Own Your Life," which offers practical advice on improving daily routines for overall well-being. Marcus's contributions to literature extend through his insightful podcasts and articles that delve into personal development, mental health, and holistic living. As a thought leader, he has inspired countless individuals to pursue a balanced and fulfilling life. His work continues to resonate with a global audience, promoting a message of self-empowerment and holistic health.

Brian Greene is an American theoretical physicist and author, best known for his work on string theory and popularizing science through his books and media appearances. Greene’s books, including The Elegant Universe and The Fabric of the Cosmos, have helped bring complex concepts in physics to a general audience. He is also the co-founder of the World Science Festival, which promotes public engagement with scientific topics. Greene’s research and ability to communicate scientific ideas have made him one of the most influential figures in theoretical physics. His work continues to inspire curiosity about the universe and our understanding of it.

Brian Earp is a distinguished ethicist and interdisciplinary researcher, renowned for his extensive work in medical ethics, philosophy, and psychology. He serves as the Associate Director of the Yale-Hastings Program in Ethics and Health Policy at Yale University. Earp has co-authored several influential books, including "Love Drugs: The Chemical Future of Relationships," which explores the ethical implications of using pharmaceuticals to enhance romantic relationships. His scholarly articles have been widely published in leading academic journals, making significant contributions to debates on bioethics, sexuality, and human enhancement. Earp is also recognized for his engaging public outreach, effectively bridging the gap between academic research and public discourse.

Brian Cox is a Scottish actor and director, best known for his roles in films like Braveheart and Adaptation, as well as for his portrayal of media mogul Logan Roy in the hit HBO series Succession. Cox is renowned for his commanding screen presence and his ability to convey complex, often morally ambiguous characters. He has had a distinguished career in both film and theater, earning numerous awards, including a Golden Globe for his performance in Succession. In addition to his acting work, Cox is a vocal advocate for arts education and has been involved in various charitable initiatives. His longevity and versatility have made him a respected and influential figure in the entertainment industry.

Bret Victor is a renowned American interface designer and computer scientist celebrated for his innovative contributions to interactive design and human-computer interaction. He is best known for creating dynamic, explorable explanations, which have significantly influenced the way educational content is presented and understood. Victor's seminal work, "Inventing on Principle," advocates for the integration of immediate feedback in creative processes, inspiring a new wave of interactive programming environments. As a former member of the Apple Human Interface team, he played a pivotal role in shaping modern user interfaces. Through his organization, Dynamicland, Victor continues to explore and expand the boundaries of immersive, collaborative computing environments.

Amanda Palmer is an American singer-songwriter, author, and performance artist, best known for her work as a solo artist and as part of the band The Dresden Dolls. Palmer is known for her theatrical performances, genre-blending music, and her strong connection with her fanbase. She has been a pioneer in crowdfunding, raising millions to fund her creative projects through platforms like Kickstarter and Patreon. Palmer is also the author of The Art of Asking, where she explores themes of vulnerability, creativity, and connection. Her work transcends traditional music, blending performance art, activism, and community engagement.
“The greatest ideas are often the most dangerous, and it is only by daring to confront the infinite that we can hope to understand the world around us.”
Infinitesimal
By Amir Alexander
Discover a world of knowledge through our extensive collection of book summaries.