even more important. The growth of such sites has already had a great impact on the traditional business model for scientific publishing, in all fields. It is difficult to say what mode(s) of dissemination will predominate in 2025, but the situation will certainly be different from that of today.
The widespread availability of preprints and reprints online has had a tremendous democratizing influence on the mathematical sciences. Gone are the days where you had to be in Paris to be among the first to learn about Serre or Grothendieck or Deligne’s latest ideas. Face-to-face meetings between mathematical scientists remain an essential mode of communication, but the tyranny of geography has substantially lessened its sway. However, the committee is concerned about preserving the long-term accessibility of the results of mathematical research. Rapid changes in the publishing industry and the fluidity of the Internet are also of concern. This is a very uncertain time for traditional scholarly publishing,6 which in turn raises fundamental concerns about how to share and preserve research results and maintain assured quality. Public archives such as arXiv play a valuable role, but their long-term financial viability is far from assured, and they are not used as universally as they might be. The mathematical sciences community as a whole, through its professional organizations, needs to formulate a strategy for maximizing public availability and the long-term stewardship of research results. The NSF could take the lead in catalyzing and supporting this effort.
Thanks to mature Internet technologies, it now is easy for mathematical scientists to collaborate with researchers across the world. One striking instance of this globalization of the mathematical sciences is the first “polymath” projects, which were launched in 2009.7 To quote from Terence Tao, these “are massively collaborative mathematical research projects, completely open for any interested mathematician to drop in, make some observations on the problem at hand, and discuss them with the other participants.”8 Another recent phenomenon is global review of emerging ideas. Not only do such projects contribute to advancing research, but they also serve to locate other researchers with the same interest and with the right kind of expertise; they represent an ideal vehicle for expanding personal collaborative networks. However, new modes of collaboration and “publishing” will call for adjustments in the methods for quality control and for rewarding professional accomplishments.
6 See, for example, Thomas Lin, Cracking open the scientific process. The New York Times. January 17, 2012.
7 See Timothy Gowers and Michael Nielsen, 2009, Massively collaborative mathematics. Nature 461: 879-881.
8 Quoted from http://terrytao.wordpress.com/2009/09/17/a-speech-for-the-american-academy-of-arts-and-sciences. Accessed March 19, 2012.