Part: Historical Development of Analysis

Analysis or calculus is one of the most influential mathematical disciplines. However, the term analysis has had a shifting meaning during the development of mathematics. Also, many key analytical concepts of analysis, including numbers, infinity, continuity, differentiability, and integrability haven't been "discovered" at once, but they evolved gradually, as mathematicians, philosophers, and the general public, became ready to allow the new concepts to change their minds. With this respect, the history of analysis is also a history of the struggle of the human mind with its obstacles and limited imagination.

The following chapters try to bring this development nearer to the reader. While reading them, you are invited to better understand the perception of past generations and epochs. This perception was the reason why mathematics evolved as it evolved, and why concepts seeming obvious today were so hard to understand and accept in the past. It is also important to recognize that contemporary mathematics is better than past mathematics, but it is still not perfect and still evolving. As we might consider past mathematics immature, future generations will consider today's mathematics similarly as "limited" and full of unnecessary obstacles, which we take for granted nowadays.

  1. Chapter: Renaissance and Beginnings of the Infinitesimal Methods
  2. Chapter: Around 1600 - The homogeneity principle and the birth of the mathematical formula
  3. Chapter: Avoidance of Negative Solutions, Descartes' Analysis and Synthesis

Thank you to the contributors under CC BY-SA 4.0!




  1. Govers, Timothy: "The Princeton Companion to Mathematics", Princeton University Press, 2008,
  2. Gericke, Helmuth: "Mathematik in Antike, Orient und Abendland", fourierverlag, 2003, 6th Edition
  3. Acheson, David: "Die Calculus-Story", Anaconda, 2018
  4. Spalt, Detlef: "Eine kurze Geschichte der Analysis", Springer Spektrum, 2019