This book provides a thrilling history of the famous priority dispute between Gottfried Wilhelm Leibniz and Isaac Newton, presenting the episode for the first time in the context of cultural history. It introduces readers to the background of the dispute, details its escalation, and discusses the aftermath of the big divide, which extended well into rThe Early Challengesnd the story is very intelligibly explained – an approach that offers general readers interested in the history of sciences and mathematics a window into the world of these two giants in their field. From the epilogue to the German edition by Eberhard Knobloch:Thomas Sonar has traced the emergence and the escalation of this conflict, which was heightened by Leibniz’s rejection of Newton’s gravitation theory, in a grandiose, excitingly written monograph. With absolute competence, he also explains the mathematical context so that non-mathematicians will also profit from the book. Quod erat demonstrandum!

A blow-by-blow account of the celebrated controversy over the invention of the calculus.

This vibrant and gripping history ultimately exposes how these twin mathematical giants (Newton, Leibniz) were proud, brilliant, at times mad, and in the end completely human.

The Newton vs. Leibniz calculus controversy is a significant chapter in the history of mathematics, one that continues to captivate scholars and enthusiasts alike. It centers on the independent and parallel development of calculus by two of the greatest minds of the 17th century, Sir Isaac Newton and Gottfried Wilhelm Leibniz. This controversy has sparked debates, fueled nationalistic pride, and exemplified the complexity of scientific priority and the ambiguities of intellectual property. In the late 17th century, both Newton, an English mathematician and physicist, and Leibniz, a German mathematician and philosopher, independently formulated the principles of calculus. Their groundbreaking work laid the foundation for this branch of mathematics, enabling the study of change and motion, and became integral to various scientific and engineering disciplines. Newton's method, known as "the method of fluxions," involved the concept of infinitesimals and was published in his seminal work "Philosophiæ Naturalis Principia Mathematica" in 1687. Leibniz, on the other hand, used a notation system based on differentials and integrals, which was more accessible and user-friendly. He presented his findings in 1684, well before Newton's publication. The controversy unfolded when the priority of the invention was questioned. Accusations of plagiarism, unfair claims, and nationalistic sentiments clouded the discourse. Newton, who was known for his disputes and his leadership of the Royal Society, actively promoted his calculus while discrediting Leibniz's work. Leibniz, in his correspondence, defended his methods and highlighted the distinctiveness of his approach. Ultimately, the dispute had far-reaching consequences. In 1711, the Royal Society declared in favor of Newton, which had a detrimental impact on Leibniz's reputation. This decision contributed to the lingering belief that Leibniz had plagiarized Newton, despite historical evidence to the contrary. Modern scholarship recognizes that both Newton and Leibniz independently and legitimately developed calculus. They had different notations and approaches, but the fundamental principles they established were equivalent. This controversy serves as a reminder of the complexities of scientific discovery and the importance of fair recognition for intellectual contributions. Today, calculus remains a cornerstone of mathematics and science, and both Newton and Leibniz are celebrated for their enduring legacies. The Newton vs. Leibniz controversy, while shedding light on the challenges of scientific priority, also underscores the profound impact of these two visionaries on the world of mathematics and the intellectual history of humankind.

An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics.

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.