Widespread dissemination of research results has made it easier for anyone to borrow ideas from other fields, thereby creating new bridges between subdisciplines of the mathematical sciences or between the mathematical sciences and other fields of science, engineering, and medicine. For example, new research directions can be seen where ideas from abstract probability theory prove to have very deep consequences in signal processing and tantalizing applications in signal acquisition, and where tools from high-dimensional geometry can change the way we perform fundamental calculations, such as solving systems of linear equations. Effortless access to information has spurred the development of communities with astonishingly broad collective expertise, and this access has lowered barriers between fields. In this way, theoretical tools find new applications, while applications renew theoretical research by offering new problems and suggesting new directions. This cycle is extremely healthy.
A recent paper9 evaluated an apparent shift in collaborative behavior within the mathematical sciences in the mid-1990s. At that time, the networks of researchers in core and applied mathematics moved from being centered primarily around a small number of highly prolific authors toward networks displaying more localized connectivity. More and stronger collaboration was in evidence. Brunson and his collaborators speculated that a cause of this trend was the rise of e-communications and the Web—for example, arXiv went online in 1993 and MathSciNet in 1996—because applied subdisciplines, which historically had made greater use of computing resources, showed the trend most strongly.
The Internet provides a ready mechanism for innovation in communication and partnering, and novel mechanisms are likely to continue to appear. As just one more example, consider the crowdsourcing, problem-solving venture called InnoCentive. It is an example of another new Web-enabled technology that may have real impacts on the mathematical sciences by providing opportunities to learn directly of applied challenges from other disciplines and to work on them. InnoCentive is backed by venture capitalists with the goal of using “crowdsourcing”—Web-based methods for parceling out tasks to anyone who wishes to invest time in hopes of achieving results and then receiving payment—to solve problems for corporate, government, and nonprofit clients. When checked on March 16, 2012, the company’s Web site listed 128 challenges that were either open or for which submissions were being evaluated. Of these, 13 were flagged as having mathematical or statistical content. Examples of the latter included challenges such as the development of an algorithm to identify underlying geometric features
9 Brunson, J.C., S. Fassino, A. McInnes, M. Narayan, B. Richardson, C. Franck, P. Ion, and R. Laubenbacker, 2012, Evolutionary Events in a Mathematical Sciences Research Collaboration Network. Manuscript submitted for publication. arXiv:1203.5158 [physics.soc-ph].