The purpose of this blog is to start a conversation about math books. What makes a math book useful, important, timely, a pleasure to read? How do books influence and shape mathematics? How does/should evolving technology change how we access books and use them in teaching and research? When (if ever) is the right time in a mathematician’s career to write a book?
When I first thought about working at the AMS book program a little less than two years ago, I asked myself: why books? The usual thoughts ran through my mind. Who has the time to write them or even read them these days? The returns for the incredible time and effort required to complete a polished book don’t seem worth it for the active mathematician who is proving new theorems in the precious times between organizing or speaking at seminars and conferences, attending or chairing department meetings, and of course teaching. Students and researchers can get up-to-date information quickly and easily through web searches, and pdf files posted online, making books seem superfluous. Mathematical output in the form of new research articles published count for more to university administrators than do books authored.
Yet my doubts about the value of books quickly dissipate as soon as I am in a room surrounded by them. One cannot help but be impressed by the wealth of knowledge and endeavor contained in a well-written and well-edited book. Books contain glimpses into the mind and thought processes of the mathematicians we admire and the beautiful mathematics that they bring to light. I am reminded of what an important role textbooks play in drawing one in and opening one’s eyes to new worlds and language, teaching through thoughtful presentations and familiarizing through well-chosen examples and exercises. Research monographs are another form that appeal to me because they have the space, which journal articles don’t, for setting the stage for its subject. The voice of the writer can lead one through a mathematical journey through a rich landscape of ideas.
The worth of a mathematician’s career is often measured in the short-term by the theorems they were the first to prove, and the number of papers they publish in the best journals, but the long-term importance of a career may also be measured by the influence the mathematician had over the development of their field. This includes inviting students into the subject, giving the subject a clear place within larger movements in mathematics, and giving others glimpses into the future and the inspiration to carry the work forward. Books are convenient vehicles for this purpose: filling the gap when personal contact with the leaders of mathematics is not available, or supplementing when it is. In this way, books have the potential to resonate in unpredictable corners of the world long after they are written.
What do you value in books? What role do they play in your research and teaching? I invite you, the reader, to share your answers by commenting on this blog. Suggestions for topics and contributed posts are also welcome.
Polynomial Methods in Combinatorics, by Larry Guth
This book reaches across disciplines, is accessible, and the ideas are the kind that one likes to have in one’s problem solving arsenal (read more about this book).
How to use this blog:
Comments and Suggested Topics: Please send comments and blog topic ideas using the comment entry form below.
Featured books: There will be a section at the end of each blog featuring a book (does not have to be an AMS book). Your suggestions are very welcome! Please include a short explanation of why you think the book is special, and epitomizes what math books are good for.
AMS Blog Policy: This blog will not include discussion of publishing practices, book or journal prices, or other matters of business or administration. Comments will be vetted accordingly.
Personally, I think that the best advantage of writing a book (at the undergraduate level) is to share our teaching plan and approach with other teachers. I also think that writing an influential book can be as valuable as writing several high-level research papers. This is because writing a good book may inspire generations of students and help them to become great mathematicians in the future. With this in mind, I believe that expository books can be quite valuable for the mathematics community, although I am aware that such books may receive less attention than textbooks.
Dear Hossein,
Thank you for the post. You bring up an important theme: sharing teaching through books. I will follow up on that in a future posting.
-Eko
To me, books tell stories that are located in a specific time and place. Same with works of art. Math books are part of the story we tell about ourselves.
Thank you for this lovely comment.
The books are, in mathematics, the best masters… 😉
In my opinion the most popular maths book is Lancelot Hogben’s Mathematics for the Million which should be considered light reading in conjunction with more formal tuition for 15 year olds upwards, who will probably be surprised that maths has a history. His politics may be a little too left wing for some. He is however rather heavy on early world maps.