A Brief History of Analysis : With Emphasis on Philosophy Concepts and Numbers Including Weierstraß Real Numbers The Invention of the Mathematical Formula Numbers Distances Points but No Crooked Lines Lines and Variables Individual: An Old Term or What Does the Continuum Consist of Are There Infinite Numbers An Unresolved Argument Between Leibniz and Johann Bernoulli Johann Bernoullis Rules of Differential What Does Equal Mean Euler Absolutizes Formal Arithmetic Accents in Algebraic Analysis According to Euler Bolzano: The Republican Revolutionary of Analysis Cauchy: The Bourgeois Revolutionary as a Restorer The Interregnum: Analysis on Swampy Ground Weierstrass: The Last Attempt at a Substantial Analysis The Detachment of Analysis from Reality and the Introduction of Actual Infinity into the Fundamentals of Mathematics Analysis With or Without Paradoxes. This book explores the origins of mathematical analysis in an accessible clear and precise manner. Concepts such as function continuity and convergence are presented with a unique historical point of view. In part this is accomplished by investigating the impact of and connections between famous figures like Newton Leibniz Johann Bernoulli Euler and more. Of particular note is the treatment of Karl Weierstraß whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey this book examines how analysis was formed how it has changed over time and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students instructors and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.