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I am enjoying reading this book, although I still have about the last 25% to finish. The book is a scholarly history of Mathematical (and, to a lesser extent, Physics) developments from roughly the time of Galileo through to (I am anticipating) the 17th or 18th Century. For those who have studied the Calculus, the general discussions will be riveting as a narration of the historical developments (and controversies) that led up to the concept of the infinitesimal, accepted in the modern notation as, for example, "dx". Entwined with the somewhat clumsy and rambling development preceding the Calculus is the politicized environment fostered by the Jesuit Order of the Church. The Jesuits, as it turned out, were on the wrong side of developments.
People today tend to be critical of the Church as having hindered scientific and mathematical developments in the roughly 1300 to 1700 time frame, but one should keep in mind that the Church was the dominant and most extensive learned community, at least in the European theatre, at that time. There really was no other comparable organization to play the role of cultural integrator. True, there were individuals (such as Galileo) who illuminated the way, but then, as now, organized progress was the off-spring of large organizations.
The Jesuits were on the wrong side of the philosophy of the infinitesimal, which later was developed by Leibnitz (in Germany) and Newton (in England) to create the most powerful mathematical philosophy known to date. If the resulting Calculus had been known, for example, to Edmund Halley, his tour de force of demonstrating the periodicity of his comet's orbit would have been enormously less tedious. Incidentally, Newton's and Leibnits' work, although very similar, were not identical to each other ... but each accused the other of plagiarism!
We tend to think of historical developments as being linear. But for those who live those developments, they are not. This book illustrates the often meandering and error filled missteps associated with human progress, and how human pride, obstinacy, and sometimes, downright dishonesty and raw politics play a role.
The Calculus was a concept whose time had come, we recognize today, but we sometimes fail to realize that the development was via human stumbling, intrigue, politics, pride and even, it seems, stubborn orneriness at times! Human affairs do not follow clean and neat orderliness: the point is very clearly illustrated by this book.
If you take the time to read this book, your patience will be richly rewarded.