Twenty Centuries of Mathematics: Digitizing and Disseminating the Past Mathematical Literature, Volume 49, Number 7

Mathematicians have talked quietly for some time about the need to digitize the past mathematical literature. During 2001 the conversations became more intense as several new digitizing projects were announced. Should we coordinate those projects? Could we integrate the recent literature that is already in digital form? How could we digitize far greater amounts of older material? The goal was to create a virtual library containing much of the past literature—a library that could eventually grow into a “World Mathematics Library”. In a conversation in mid-2001, Philippe Tondeur (the director of the Division of Mathematical Sciences at NSF) outlined his vision for such a library. While I was sympathetic, I pointed out that one needed a plan, or at least an outline, and that even with a plan there were many obstacles. Philippe persuaded me to write this “concept paper” based on our conversation and consequently turned my pessimism into a proposal. Since that time a group headed by Cornell University was awarded a planning grant to consider the next steps in carrying out a massive digitizing project. Mathematicians and agencies from other countries have expressed interest in an international effort. And the impossible sums of money needed for funding seem almost possible (even if most of the other obstacles remain). The opinions expressed in this paper are the author’s and do not necessarily represent opinions of the American Mathematical Society. M athematics has always relied on its scholarly literature. From the time of Euclid’s Elements1 (about 300 B.C.), mathematics has thrived because key literature has been passed from generation to generation. In modern times the process has accelerated, changing the way mathematicians carry out research. Because it is impossible to study and digest all relevant literature in a broad area, mathematicians find themselves navigating the literature—moving from one paper or book to another, perusing results and proofs, and relying on references in order to link to the next item. The linking process has become more important as the literature has grown, and it is one of the reasons electronic publication has great potential benefit for mathematical research. Reliance on past literature is common to all disciplines, but time scales differ. In some areas of science, literature more than a few years old has value mainly for historical reference. For mathematicians, work from ten, twenty, or even one hundred years ago is relevant and useful in research. Like all scientists, working mathematicians will use and reference more recent work the most, but having the ability to access the older literature is of essential value to research mathematicians. Even when only a small fraction of the references come from literature in the distant