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?
Best Answer
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.