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). [This article was published in August 2002 issue of the journal "Notices of the American Mathematical Society"]