I'm looking for a book for a friend. I'd like to find a mostly historical, non-technical treatment of the story of Weierstrass, Cauchy, Riemann, and their work placing Newton and Leibniz' calculus on firm, rigorous foundations. Ideally, such a book would discuss what Newton and Leibniz did, why it wasn't really solid, and how nineteenth century analysts were able to fix it.

Thanks in advance for any suggestions!

  • $\begingroup$ If you want the true history of calculus, you would need to go back and go east further, and look at the Indian scholars Bhaskara and Madhava $\endgroup$ – Leg May 20 '15 at 14:49
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    $\begingroup$ I would recommend Howard Eves' An Introduction to the History of Mathematics, particularly the second half. It's non-technical, very informative, but I do not know if it really has the depth you or your friend may be after. $\endgroup$ – Daniel W. Farlow May 20 '15 at 14:50
  • $\begingroup$ @user17762: I'm not looking for the "true history of calculus" right now. I'm looking for the story of Newton's lack of rigor, and how it was addressed by the nineteenth century analysts. I'm not claiming that's the entire or "true" history of calculus, but it's the chapter I'm looking for right now. $\endgroup$ – G Tony Jacobs May 20 '15 at 14:52
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    $\begingroup$ You can see C.B.Boyer, The History of the Calculus and Its Conceptual Development (1949) and C.H.Edwards Jr, The historical development of the calculus (1979) $\endgroup$ – Mauro ALLEGRANZA May 20 '15 at 15:04
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    $\begingroup$ I have no answers to your specific question, but your post was a pleasure to read. Nice writing. $\endgroup$ – zhw. May 23 '15 at 5:49

Much longer comment turned answer:

Howard Eves' An Introduction to the History of Mathematics seems like a perfect fit. The chapters that would be of particular use are chapters 11 through 14 (relevant sections included on the side):

  • Chapter 11: The Calculus and Related Concepts [11.9 Newton; 11.10 Leibniz]
  • Chapter 12: The Eighteenth Century and the Exploitation of the Calculus
  • Chapter 13: The Early Nineteenth Century and the Liberation of Geometry and Algebra [13.5 Cauchy]
  • Chapter 14: The Later Nineteenth Century and the Arithmetization of Analysis [14.10 Weierstrass and Riemann]

Of course, there are many other math history books that may be suitable but Eves' is a classic. It's very well-written, non-technical, and there are problems at the end of each chapter that address historical points made in the text.

It should probably be noted that analysis is almost inherently a technical subject; thus, you may grab a book different than Eves' with more depth, but what you make up in depth will probably be lost in increasing technicality (if that made sense).

  • $\begingroup$ That sounds great. I've given my friend a link to this page; I hope she finds this answer helpful! I may have to check out this book myself..... $\endgroup$ – G Tony Jacobs May 20 '15 at 20:15
  • $\begingroup$ @GTonyJacobs I would definitely check it out (you, yourself, that is)! I've actually undertaken a mammoth project to write up solutions to all of the problem studies in the book, something that will likely take a few years, but the book is just that good. It is very comprehensive. And the problem studies are not at all trivial. Within the book, Eves will oftentimes refer the reader on to articles in the Monthly or the College Mathematics Journals, articles I am sure you know are great and sometimes refreshing, challenging to read. It may be my favorite math book actually. Cheers! $\endgroup$ – Daniel W. Farlow May 20 '15 at 20:49

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