Mathematics and Its History

by John Stillwell

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."(David Parrott, Australian Mathematical Society)This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Genres: Mathematics, History, Science, Nonfiction, Stem, Philosophy, History Of Science

682 pages, Hardcover

First published May 1, 1997

About the author

John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University

Reviews

[Mark Moon]

I loved this book! There's a great selection of very cool math here, with the history mostly going up to the mid-twentieth century. The exercises are particularly wonderful; they walk you through some exciting things that extend the content of the preceding section.

[Chris]

If you are curious about mathematics but it passed you by in school, this might be the book for you.

Definitely better than anything with a title like "Algebra For Stupid People", he covers the people who formed the ideas, why they thought it was interesting, and the idea itself.

It's broad rather than deep so serious historians might find it lacking. But the breadth makes it perfect for normal people / non-experts.

[Nishant Pappireddi]

This was a very fun book to read, since it introduced my to many subjects I probably would not have encountered otherwise, such as Elliptic functions. The math itself wasn't that deep; this book was just a survey of various subjects within mathematics, but it was still pretty informative. The biographical notes at the end of each chapter made up the "history" part of the book, while everything else made up the "mathematics" part.

[Jenni]

Decent book with a broad range of topics. History parts are very interesting. Formulas tough to get for non-mathematically inclined people (non-native school makes it worse).

Interesting note: 40 pages of bibliography!

[Paul Floyd]

Good, but I would have preferred a bit more history and clearer chronological order.

[Chris]

One of a few mathematics books I would recommend to non-mathematicians.


It's more readable than Morris Kline's 3-volume series, perhaps because Stillwell talks more about the mathematics than about the history. It makes for an excellent survey of mathematical ideas for the uninitiated.

[Thomas]

Interesting approach as this book covers different fields, trying to explain what they deal with and how mathematicians got there.

In my opinion, this book isn't for total beginners. To be able to understand a substantial amount of it, I think you should at least have done some undergraduate math, have an idea of what a vector space is, etc. otherwise it will most likely be very difficult to follow.

Also, in my opinion this book is biased towards number theory, elliptic curves, etc.

It doesn't cover math applications (not even to cryptography).

[George Hohbach]

The comprehensive book contains a lot of very useful and well organized information and facts about the evolution of mathematics.

[Andrew Foote]

This is a fascinating book which managed to hold my attention continuously for the three days I was reading it. I haven't done any of the exercises yet---I adopted the reading strategy of making a first pass over the text first---but the content has been sufficiently interesting that I think I will do all of them on a second read. I suspect this may be the way I can satisfy a desire I've been having for some time to feel like I have the beginnings of a handle on mathematics as a whole unified system, rather than an assortment of disconnected topics I happen to have taken a particular interest in or done a course about at university. In particular, the book has given me a much greater appreciation of geometry, something that has always been a significant gap in my mathematical knowledge, since it was almost entirely neglected in my education. Geometry is obviously one of the most fundamentally important parts of mathematics, so this was closing off a lot of stuff, and now I feel like a vast new realm of things to investigate has been opened up to me.

The main criticism I have with this book is that it doesn't cover the developments of the 20th and 21st centuries in that much detail. Its account of the modern period is focused on the strand consisting of set theory, logic, computability theory, etc., which, while hugely significant, is just one strand of modern mathematics, and as I understand it a somewhat non-mainstream one. In fact, since I do find this particular strand of modern mathematics particularly fascinating, I had already investigated it quite a bit, and didn't find much novel knowledge to be learned in these chapters. I was hoping to learn something about the parts of modern mathematics which are still quite alien to me, like category theory. But that is the nature of history books: they end just as they're getting to the most interesting part, the present...

[Brent]

I enjoyed reading this historical mathematics book. I intended to gain some insight on mathematicians of the past as well as glean techniques that might prove useful for future personal research or project topics for my students. This book did not let me down.

[Michael Hooper]

Quite a comprehensive overview of the history of mathematics, definitely requires some level of pre-established undergraduate knowledge in algebra and calculus, but definitely worth the read, as I learned things I didn’t know during my undergraduate years.

[Kent Sibilev]

Extremely good overview of math and math history.

[Ilib4kids]

Stillwell, John, Mathematics and Its History (Undergraduate Texts in Mathematics), Springer, 2020

I get from Luke Heaton, A Brief History of Mathematical Thought

[Lucille Nguyen]

A delightful little romp through the history of mathematics and how various mathematical concepts connect to one another. An excellent read for the curious reader.

[Cinder]

my bible

[Alberto]

I took a course in the history of mathematics using the Eves textbook, which is quite good, but this book is in a whole other league.

[Khaled Qaraman]

On Youtube you can find a wonderful explanation of this book by Prof. N J Wildberger :

https://www.youtube.com/playlist?list...

Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, Stevin's decimal system, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology, the origins of group theory, hyperbolic geometry and more. Meant for a broad audience, not necessarily mathematics majors.