The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) by Carl B. Boyer (PDF)

Description

This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek “method of exhaustion” and Zeno’s paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It took me three attempts to finish this book. Why? Because although there is a wealth of VERY interesting information the writing style is turgid to say the least. Yes, I understand that this was the prevailing style for “academic” books in the thirties and forties but even with that excuse things could have been explained in a less bombastic style.Having stated the above I am glad that I kept at it because I learnt that the arrow of history was clearly pointing to someone or some group of mathematicians coming up with the Calculus as we know it today. Also much of the rigor we know today (Limits etc) are quite recent inventions. All in all I believe this book is worth reading IF, AND ONLY IF, you are truly interested in the history of mathematics. One of the reviewers trashed this text because it was supposedly western centric. This argument would hold water if someone could recommend a text supporting the argument with specifics.One more caveat – it would be best to read this text if one has a good working knowledge of calculus. This is implied by the author in many places.

⭐The history of calculus is an interesting one. The concept came first and the proofs followed much later. My issue with the book is that the author is too wordy. He wants to sound smart and majestic, but he comes off as pompous.Example: “…it has at the same time been regarded by idealistic metaphysics as a manifestation that beyond the finitism of sensory percipiency there is a transcendent infinite which can be but asymptotically approached by human experience and reason.” WHAT!!??

⭐I bought this book for my class course and I found that this book is written and edited in a very properway. Every next chapter has some kind of connectivity with the previous chapter. I will recommend this book to others.

⭐I am still reading it, but am half way through. The book has a lot of interesting information. For the first time I understand how Archimedes found the volume of a sphere by “weighing” it, and that is only one of many great insights. I am not giving it five stars because, as others have said, it is written a style that may have been common at the time, but to the modern reader can be frustrating. I think the same information, with the same nuance where necessary, could be written in a less tedious manner today.

⭐Boyer is a historian of mathematics, and I have his larger history text, which I like much better. I honestly expected a history of the calculus to be more of a fascinating read. The author does an excellent job of taking you through some of the finer points of this history and reasons why, for example, Archimedes should not be given credit for discovering the calculus, but why there is some justification for such a claim. The thing is, these finer points of the history are mentioned quite frequently even with regard to mathematicians whom I have never heard of. It seems that someone is always saying that so-and-so really discovered the calculus, and Boyer always points out why in fact they did not. The writing also can be rather verbose at times (this is sometimes entertaining). I do not see this text as appealing to a lay reader with an interest in the history of one of the greatest intellectual acheivements of all time: the calculus. I see this as appealing more to historians of mathematics or other such related fields. I started this book twice, and the second time, I made it about three fifths of the way through. It’s hard to read a lot at once. It’s a history book, not a book about the history. There are a fair amount of diagrams, and the math is interesting, if at times confusing, to follow. I can’t say that my understanding of calculus is much deeper after reading the majority of the book, though it certainly does have a larger and more technical context.

⭐This is a truly enlightening history of calculus from Eudoxus to Weierstrass. This 1949 book by Carl Benjamin Boyer, republished by Dover, places the developments of Newton and Leibniz within the long sequence of historical developments of calculus including Pythagoras, Zeno, Eudoxus, Aristotle, Euclid, Archimedes, Oresme, Viète, Stevin, Cavalieri, Torricelli, Kepler, Galileo, Descartes, Fermat, Wallace, Barrow, Leibniz, Newton, Maclaurin, Euler, Lagrange, Lacroix, Bolzano, d’Alembert, Cauchy, Weierstrass, Cantor, and Dedekind, roughly in that order.Within this context, it becomes crystal clear that the old arguments about the relative precedence of Newton and Leibniz are a relatively minor matter. Both of them relied heavily on a very long sequence of earlier developments, and both of them fell very far short of a satisfactory, logically self-consistent, meaningful formalism, which required another 200 years to develop.This book has about a thousand footnotes. It is very thoroughly researched indeed. Boyer describes how various opposing forces were at work in the development of the calculus. Very important, for example, was the weight of tradition, such as the method of exhaustion of the ancient Greeks, which was held in high esteem. There was a strong resistance to abandonment of geometrical intuition as the basis of calculus, although ultimately a satisfactory axiomatization of the real numbers permitted calculus to be liberated from its geometric origins. Unsatisfactory concepts of infinity and the infinitesimal strongly constrained or encouraged many mathematicians to reject some formulations while accepting others.One thing which worried me a lot is how much of modern calculus is still taught in the same way as many centuries ago, using ways of thinking which are obsolete, meaningless or logically circular. In fact, one of the themes of this book is how ancient ill-founded concepts have frequently been “rediscovered” and adopted by mathematicians, long after they had been superseded by better-founded concepts.I ended with the suspicion that our modern-day calculus (or “analysis”) is not the end of the road. Even our current calculus is a mixture of intuition, metaphysics, pragmatism and sometimes empty formalism. This book seems to put some of our currently accepted calculus concepts in doubt.

⭐A fascinating and detailed look at the more than 200 year struggle to define and refine ‘The Calculus’. Any lover of Mathematics will enjoy this history.

⭐excellent

⭐Reading this book today makes one feel tremendously satisfied and sad alike. Modern books on the history of mathematics pale in contrast to this one (I would mention one exception, The History of Pi, but it was written in the 60s or 70s so I think its not really an actual book either, and you have to forgive his Woodstock Festival reamrks about the world).The title of the book mentions the “conceptual development”, and thats were the book excels at, describing how the procedural evolution of maths got to the (invention? discovery?…who knows…) of Calculus.It has never ceased to amaze me how accurately the differential ecuations describe the real physical fenomena or how Riemanns topology gave Einstein the mathematical foundation needed for his theory 100 years later and so on (if you are intrigued by the inner nature of mathematics DONT buy “Is God a Mathematician”, a book more suited for an Oprah show than for someone really interested on the real nature of mathematics). Some reviewers were more critic with certain aspects of the book, fair enough, as humans we are fable, but I seriously doubt a better book on this subject has ever been written. Regrettably there are many books on the history of mathematics but most of them fail, not this one, as someone said , Boyer is the Edward Gibbon of the history of maths.Thanks Newton, Euler, Rieman, Pitagoras, Pointcare, Leibniz, Cantor…I saw further because I stood on your shoulders.

⭐Excellent

⭐Das Werk eines kompetenten Autors. Eine spannende Lektüre. Allerdings werden für das volle Verständnis mathematikhistorische Grundkenntnisse vorausgesetzt, also für Einsteiger ist das Buch weniger geeignet.

⭐

Keywords

Free Download The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) in PDF format
The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) PDF Free Download
Download The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) 1959 PDF Free
The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) 1959 PDF Free Download
Download The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) PDF
Free Download Ebook The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics)