that bring cutting-edge mathematical sciences to bear on significant industrial problems. Examples include uncertainty quantification in the automotive industry and numerical simulation of ablation surgery. Overall, IMA has trained over 300 postdoctoral fellows since 1982, and about 80 percent of them are now in academic positions. The IMA also offers programs for graduate students, most notably its regular workshops on mathematical modeling in industry, in which students work in teams under the guidance of industry mentors on real-world problems from their workplace. Through this program, many mathematical scientists have been exposed early in their careers to industrial problems and settings.
As an example of value provided beyond academe, IPAM has been instrumental in introducing modern imaging methods to the National Geospatial-Intelligence Agency (NGA). Several individuals from NGA attended IPAM’s 2005 summer school, Intelligent Extraction of Information from Graphs and High-Dimensional Data, which convinced them and their agency to explore further. Subsequently, NGA organized a series of three workshops at IPAM on advancing the automation of image analysis. This led to hiring by NGA of several new mathematics Ph.D.s with expertise in image analysis, as well as a major funding initiative. IPAM has similarly held workshops for the Office of Naval Research (ONR) on aspects of machine reasoning, which may lead to an ONR funding initiative. IPAM’s program Multiscale Geometry and Analysis in High Dimensions led to the explosive growth of applications of compressed sensing, followed by a large funding program at DARPA.
In addition to the institutes, NSF/DMS and other financial supporters of mathematics have in recent years created other funding programs to encourage and nurture research groups, which help investigators to address broad and cross-cutting topics.
Changing Models for Scholarly Communication
The first thing that comes to mind when one thinks of interconnectivity these days is the Internet and the World Wide Web. These affect practically all human activity, including the way that mathematical scientists work. The maturation of the Internet has led in the past 15-20 years to the availability of convenient software tools that painlessly lead to the quick dissemination of research results (consider for instance the widely used arXiv preprint server, http://arxiv.org/), the sharing of informal ideas through blogs and other venues, and the retrieval of information through efficient search engines. These new tools have profoundly changed both the modes of collaboration and the ease with which mathematical scientists can work across fields. The existence of arXiv has had a major influence on scholarly communication in the mathematical sciences, and it will probably become