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I'm doing a Bachelor of Pure Mathematics in Unisversity, and while reading through the book that outlines the course selections, I found one that is listed as "rarely offered", which the department says will likely never be offered again. It is titled "The History of Math", and the synopsis of the course reads as follows:

How did the many powerful theories of modern mathematics develop, and which major mathematicians influenced and shaped this development?

How did the many powerful theories of modern mathematics develop, and which major mathematicians influenced and shaped this development? In this course, this historical development of mathematics is exemplified by concentrating in some detail on the history of the calculus from its early beginnings through its 18th-century progress to the introduction of mathematical analysis in the 19th century, and the further developments to set theory, the beginnings of topology, and to the structural point of view of the 20th century. Its emphasis is on a deeper understanding of the dynamic nature of mathematics and of the interrelations among various branches of mathematics. This should lead to a better understanding of familiar mathematical topics and also allows the introduction of new mathematical content from a modern point of view.

This is a shame, because I am deeply interested in finding out how some of the popular theories were developed and molded to be taught at lower levels. The one I can think of in particular is how Newton et al came up with the Fundamental Theory of Calculus.

So, aside from haphazardly looking up and reading poorly written (or lacking information) articles on wikipedia, are there any good books that cover this sort of material?

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  • $\begingroup$ First thing may be to note Leibniz with Newton for the development of calculus. $\endgroup$
    – Lord Soth
    Apr 21, 2013 at 22:44
  • $\begingroup$ I am sure you already know this, but as an online resource, I can recommend www-history.mcs.st-and.ac.uk $\endgroup$
    – Lord Soth
    Apr 21, 2013 at 22:45
  • $\begingroup$ "Newton et al" sounds like he was part of some team doing it, which he was not. $\endgroup$
    – Jonathan
    Apr 21, 2013 at 22:46
  • $\begingroup$ I apoligize - Newton was the first name that came to mind, and I didn't know his relationship (if any) to the other big names in Calculus. $\endgroup$
    – Mirrana
    Apr 21, 2013 at 22:53
  • $\begingroup$ Possibly Related: math.stackexchange.com/questions/31058/… $\endgroup$
    – GovEcon
    Apr 21, 2013 at 23:07

3 Answers 3

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Victor Katz is renowned for his writing and research in the History of Mathematics. I read an earlier edition of the text History of Mathematics while taking an undergraduate course in the History of Math during a Spring term (it was the required text for the class.) It is an excellent book. We couldn't cover the entire text over one semester, so I persisted in reading it to completion over the summer which followed.

You can go as far back as you'd like (it goes very far back in history!), or pick up where your interest is piqued.

If you can't take the course, for credit, or as an "auditor", I'd recommend this book for your library. It is a good complement to "doing" hard-core math. That's not to say that it's necessarily "easy", because it invites you to engage in mathematics using only the tools available at a given point in history and in a given culture. At any rate, I found the text to be very engaging, it helped me appreciate the field of mathematics more than I ever thought I could, and it has served me well as a reference, too.

I just noticed that there is a "brief" version of Katz's History of Mathematics which might not be as overwhelming, and likely highlights the best and the biggest breakthroughs in mathematics, as they developed over time.

You might also want to peruse the following list: Resources: History of Mathematics, to find some helpful recommendations.

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Books

  • A History of Mathematics: From Mesopotamia to Modernity by By: Luke Hodgkin
  • The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics' Author: Clifford A. Pickover
  • A concise history of mathematics, By Dirk Jan STRUIK
  • A History of Mathematics, By Uta C. Merzbach, Carl B. Boyer
  • Additionally worth a visit, the AMS list
  • Lastly, you might want to peruse the great priced Dover Math History collection

Web Sites

Universities

  • You might want to peruse your local universities
  • You might want to use the online resources at your university to peruse other schools' libraries
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  • $\begingroup$ I completely agree (it's true for me, too!) Where is that list about MSE addicts? ;-) $\endgroup$
    – amWhy
    Apr 22, 2013 at 4:43
  • $\begingroup$ I feel exactly the same way! I have so many other hobbies and miss them all! I have to find a balance that works! $\endgroup$
    – Amzoti
    Apr 22, 2013 at 4:44
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Mathematics and Its History by John Stillwell is an excellent survey of the history of mathematics, pitched at undergraduate level. All of Stillwell's books are superb, in my opinion, and this is no exception.

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