Under contract!

As of 9am this morning, the Illustrated Theory of Numbers is under contract with the American Mathematical Society!  So now is a good time to write about the process of choosing a publisher and settling on contract details.  My sample size of book contracts is now 1, so I wouldn’t extrapolate too much from my personal experience.

Why the AMS?

I spoke with two other publishers along the way, and ended up with the AMS for a few reasons.  First, the AMS Mission is “To further the interests of mathematical research, scholarship and education, serving the national and international community through publications, meetings, advocacy and other programs.”  The AMS(registered as a 501(c)(3) not-for-profit) represents the research and educational interests of mathematicians like myself — and I doubt that this is the case for the large textbook publishers (e.g., Pearson, McGraw Hill, Elsevier).

Other reasons that I am excited to work with the AMS are the following:

  • I believe that the production quality of the book will be good, while the price will be about half that of the market-leading textbooks in elementary number theory.
  • The editor, Sergei Gelfand, and others were at all times professional and responsive and helpful.
  • The AMS seemed to understand my goals for the book, and their goals and mine seem very close.
  • The AMS was responsive to my pickiness about design and layout, while reasonable about their own capabilities.
  • I trust the AMS as an organization — that if something goes awry, I have more support than strictly provided by the contract.


I consider some of the illustrations in the book to be a form of artistic output.  I may adapt some of them and create posters, clothing, mugs, etc..  So it was important to me that the AMS maintain the rights to publish the book and derivative works, except that I would maintain the right to produce (and possibly sell) artistic works.  This is described in the contract.

I have some worries about electronic distribution of the text.  As a reader, I appreciate that I can download whole books from Springer through my library.  But as an author, I don’t really want a downloadable publication-quality PDF of the whole book to circulate freely on the internet.  I think that some texts (e.g., the vast majority of research literature, publicly funded research and education projects) should circulate freely or very close to freely.  But since the Illustrated Theory of Numbers is a personal project, not funded by the NSF or anyone else, and contains original artwork, I think it’s fair to protect copyright a bit.  I also hope to make enough money for a little vacation too.

I’m not 100% satisfied with the language around electronic distribution in the contract, but I think it’s about as good as it gets.  Due to the rapidly changing landscape of electronic publication, the contract gives the publisher flexibility.  One place where I requested a change was in electronic sales upon termination of the agreement.  If the contract is terminated at some stage, rights to sell e-books also terminate shortly after.  Although the language is not entirely to my satisfaction, I am placing my trust in the AMS to represent my interests as an author and their financial interests in protecting copyright.

Royalties with the AMS are based on a percentage of “net income”.  This (apparently standard) term refers to the amount of money the AMS takes in from selling the book, minus some costs for returns.  It’s thankfully not the same as “net profit” — the costs of production are not deducted.  I found the percentage reasonable and generous.

Better late than never!

I have decided to chronicle my efforts to write and publish a book, the Illustrated Theory of Numbers. These efforts really began about seven or eight years ago, the first time I taught an introductory number theory class (Math 115 at UC Berkeley). Around the same time, I had started working with K-12 teachers, and I was inspired to take a visual and dynamic approach. Some unusual aspects of my class were: I introduced Gaussian integers and Eisenstein integers from the beginning, I used Conway’s topograph to study binary quadratic forms, and I followed Zolotarev’s proof of quadratic reciprocity.

Since then, I have taught similar material at UC Santa Cruz, and at the MMSS summer program at the University of Michigan. Each time I teach number theory, I find a few new approaches. Making number theory elementary might not be a virtuous goal in itself, but illustrating number theory is most rewarding.

When I first learned about number theory, I didn’t like it. I was given (or maybe I bought) a copy of Hardy and Wright’s classic text (An Introduction to the Theory of Numbers). From what I hear, this book has inspired generations of number theorists. But to me, early in my undergraduate career, it seemed like a large collection of unmotivated algebraic and analytic tricks. I didn’t get it. Instead, I enjoyed topology and complex analysis.

Later as an undergraduate, I had the great benefit of taking many (five, I think) courses with Goro Shimura. The first, I think, was a course on Riemann surfaces, meant as a second course in complex analysis. The second was a course in number theory. Incredibly, to me at the time, Shimura introduced aspects of number theory in parallel to what he had taught about Riemann surfaces — primes were analogous to points on a Riemann surface, and I was hooked. Around the same time, I took a “junior seminar” with John Conway, who taught us his beautiful approach to quadratic forms via the “topograph”. Since then, I have always taken a geometric approach to teaching number theory.

A few things have convinced me to write a number theory text — to enter a somewhat saturated market. First is that I cannot find any number theory texts which I find visually beautiful and suitable as an introductory text. This is the gap I hope to fill. A one-day course with Edward Tufte opened my eyes to the possibilities and importance of visual design. As Tufte explored visual design related to statistics in his first book (Visual Display of Quantitative Information), I hope to explore visual design related to introductory number theory in my first book. Hopefully I will not resort to taking out a second mortgage to self-publish!

Last year after teaching Math 110 at UCSC for the second time, I found myself with about 12 unpolished chapters of an illustrated number theory text. Now (with the security of tenure), I have begun polishing these chapters, adding more content and illustrations, with the goal of submitting parts of the book to a publisher by the end of the summer.

I have polished the first three chapters now, so this blog does not begin at the beginning. But with the next few posts I’ll try to catch up and share my experiences.