What do you think?
Mathematics and Its History: A Concise Edition
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course.
The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted.
Mathematics and Its A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed.
From reviews of previous
“Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel…. The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition
"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted.
Mathematics and Its A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed.
From reviews of previous
“Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel…. The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition
"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
415 pages, Kindle Edition
First published May 1, 1997
About the author
John Stillwell
55 books62 followersJohn Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 17 of 17 reviews
December 28, 2023
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.
July 31, 2013
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.
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.
July 28, 2014
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.
October 7, 2018
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!
Interesting note: 40 pages of bibliography!
November 2, 2020
Good, but I would have preferred a bit more history and clearer chronological order.
December 31, 2018
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.
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.
July 13, 2020
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).
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).
February 4, 2018
The comprehensive book contains a lot of very useful and well organized information and facts about the evolution of mathematics.
June 26, 2019
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...
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...
May 12, 2020
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.
September 11, 2021
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.
June 25, 2020
Extremely good overview of math and math history.
Want to Read
August 3, 2020Stillwell, John, Mathematics and Its History (Undergraduate Texts in Mathematics), Springer, 2020
I get from Luke Heaton, A Brief History of Mathematical Thought
I get from Luke Heaton, A Brief History of Mathematical Thought
April 8, 2024
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.
November 15, 2025
my bible
April 26, 2022
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.
Read
July 1, 2017On 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.
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.
Displaying 1 - 17 of 17 reviews