Thanks to those of you who commented on my previous post on ebooks. This conversation brings home to me that what will drive substantial math ebook innovation (apart from simply making existing math books readable on electronic devices) will be a joint work between mathematicians, programmers (and possibly publishers to egg them on) that anticipates accurately the way math students and researchers will want to write and read. It may be the kind of change that will happen solely from within mathematics, perhaps in small steps.
In my memory, the steps leading to the advent of email and tex were rapid. Some of you remember the 1980s when email and tex were just coming into common use. I had friends whose primary job was technical typing for mathematics faculty, and I still wrote handwritten letters to friends and family, something I have not done in decades. It seems that before we knew it email and tex became commonplace in mathematics, and as I understand it both developed rather organically with mathematicians playing a large role.
A similarly extraordinary, though much more subtle, transformation in our way of lives is happening (has happened?) as a result of personal webpages. Although universities have standardized faculty webpages, most math faculty have their own personal ones, and they have become increasingly significant and indispensable to the way mathematicians function socially, culturally, and practically.
Personal webpages have become vital sources of open access information that is for the most part non-monitored and free form; and because there are few rules governing them, they are also expressions of a mathematician’s individuality. If one wants to know something about a particular person, one can glean a lot from their webpage and what and how they choose to present. The page is at once personal and public, and I cannot think of anything that existed pre-internet that played the same role. Some are stark and minimal, while others have rather highly developed narratives; some include images, moving gifs, links, and computer programs in addition to the invaluable list of publications, vita and teaching information. Personal webpages have become a sort of publication that combines the fun of personality and self-expression with the ability to present a swath of convenient and useful content connected to the author’s activities, interests, and work.
The use of personal webpages by mathematicians has grown to the point that they have become regular “go to” resources for mathematicians to find lecture notes, teaching ideas, theorems, and software. Contrast this to the 80s (my personal reference point) when students and researchers spent a lot more time in libraries than we do now. As older readers of this blog will remember: we used to search through indexes of heavy volumes of Mathematical Reviews to find out what was known about a given topic and where to find the articles; then we’d search through the stacks and shelves of identically bound journals to find the correct year and volume number; and once we found the article we would carry the heavy book over to a desk and read awkwardly over the lumps made on the open page by the huge binding, or if we wanted to make the contents portable, we would head to the copy machine hoping we remembered to bring coins. During my last move, I threw away almost two filing cabinets worth of xeroxed papers, that I previously did not have the heart to dispose of though most of the articles are now a snap to find online.
I see the good and bad sides of the ways of the past and now. The time it took to do what is so easy now was also time to think slowly, which is usually a good thing. Now, if one knows who the author is, one can usually simply go to their webpage. From there one can look at references of their papers and search on to other webpages. In the meantime, one may make unexpected discoveries, or if one is not careful, one might even stray onto a new tangent. The journey now is potentially quicker but is more sedentary. One interacts with fewer people, but is exposed to more personal expression. What we have lost in terms of walking and lifting, we have gained in a better passing acquaintance with the people we are citing.
It would seem that the electronic book question is really part of a much bigger question about the relation between technology and information , and creativity and expression. One of the exciting things about mathematics is that at the frontiers of the subject, there is a continual rethinking and creating of “tools” and “pathways” for communication. Unlike in experimental science, to “show” someone what one has discovered, one can only rely on language and symbols, and a feature of mathematicians is not only that they solve deep and difficult problems, but that they develop ways to take others there, by expressing complicated ideas in enlightening and simple ways. It is natural that mathematicians will use all the means of communicating ideas at their disposal: through teaching directly, through writing, through programing, and consciously or unconsciously through their personal webpages.
Getting a view into the personalities of mathematicians can be fascinating and fun, and two of the most interesting personalities in mathematics are Grothendieck and Serre. This book contains letters sent between these two mathematical giants from 1955 to 1987 in the original French with a translation into English.