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But to make this work we need adjustments to reward systems, especially for the mathematical scientists on such teams. One leading researcher who spoke with the committee observed how mathematicians at Microsoft Research are often approached by people from applied groups, which is a fortunate result of the internal culture. One value that mathematicians can provide in such situations that is often underestimated is that they can prove negative results: that is, the impossibility of a particular approach.

This ultimately increases productivity because it helps the organization to focus resources better. This is a contribution of mathematics beyond product-focused work or algorithm development.

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Another set of challenges to interdisciplinary students and researchers stems from their lack of an obvious academic home. Who is in their community of peers? Who judges their contributions? How are research proposals and journal submissions evaluated? At the National Institutes of Health, for example, the inclusion of mathematical scientists in the study sections that review proposals with mathematical or statistical content is an important step, though it is not a perfect process. Tenure review in large.

While it takes longer to build a base of interdisciplinary knowledge, once that base is built it can open doors to very productive research directions that are not feasible for someone with a more conventional background. Universities are changing slowly to recognize that interdisciplinary faculty members can produce both better research and better education. There is a career niche for such people, but it could be improved. For example, it might be necessary to relax the tenure clock for researchers pursuing interdisciplinary topics, and a proper structure must be in place in order to conduct appropriate tenure reviews for them.

This is one way to break down academic silos. A major change in the mathematical sciences over the past decade and more has been the increasing number of mathematical science institutes and their increased influence on the discipline and community. In there was only one such institute in the United States—the Institute for Advanced Study in Princeton, which has a very different character from the institutes created after it.

In the last 20 years we have seen new institutes appear in Japan, England, Ireland, Canada, and Mexico, to name just a few countries, joining older institutes in France, Germany, and Brazil. Overall, there are now some 50 mathematical science institutes in 24 different countries.

The institutes promote research and collaboration in emerging areas, encourage continued work on important problems, tackle large research agendas that are outside the scope of individual researchers, and help to maintain the pipeline of qualified researchers for the future.

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Many of the institute programs help researchers broaden their expertise, addressing the need for linking multiple fields that was emphasized above and in Chapter 3. For example, every year the Institute for Mathematics and its Applications IMA offers intensive two-week courses aimed at helping to introduce established researchers to new areas; recent courses have focused on mathematical neuroscience, economics and finance, applied algebraic topology, and so on.

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All of these institutes have visiting programs, often around a specific theme that varies from year to year, and they invite mathematical scientists from around the world to visit and participate in the programs. This has led to an enormous increase in the cross-fertilization of ideas as people from different places and different disciplines meet and exchange ideas.

In addition, it is quite common for these institutes to record the lectures and make them freely available for downloading. Real-time streaming of lectures is just starting to emerge.

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All of these steps help to strengthen the cohesiveness of the community. Beyond this, the institutes frequently allow researchers to meet people they would not otherwise meet. This is especially crucial in connecting researchers from other disciplines with the right mathematical scientists. Often, scientists, engineers and medical researchers do not know what mathematics and statistics are available that might be relevant to their problem, and they do not know whom to turn to. Likewise, mathematical scientists are often sitting on expertise that would be just what is needed to solve an outside problem, but they are unaware of the existence of these problems or of who might possess the relevant data.

Arguably, the institutes have collectively been one of the most important vehicles for culture change in the mathematical sciences.

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Some illustrations of the impact of mathematical science institutes follow. To help the mathematical sciences build connections, the IMA reaches out so that some 40 percent of the participants in its programs come from. In this way, it has helped to nucleate new communities and networks in topics such as mathematical materials science, applied algebraic geometry, algebraic statistics, and topological methods in proteomics.

The institutes have had success in initiating new areas of research.

Recent Advances in Mathematical and Statistical Methods

For example, IPAM worked for 9 years to nucleate and then nurture a new focused area of privacy research, starting with a workshop on contemporary methods in cryptography in That led to a workshop on statistical and learning-theoretic challenges in data privacy, which brought together data privacy and cryptography researchers to develop an approach to data privacy that is motivated and informed by developments in cryptography, one of them being mathematically rigorous concepts of data security.

A second follow-on activity was a workshop on mathematics of information-theoretic cryptography, which saw algebraic geometers and computer scientists working on new approaches to cryptography based on the difficulty of compromising a large number of nodes on a network. Another IPAM example illustrates that the same process can be important and effective in building connections within the discipline. Traditional methods for dealing with such problems involve techniques such as variable selection, ridge regression, and principal components regression.

Beginning in the s, more modern methods such as lasso regression and wavelet thresholding were developed. These ideas have now been extended in numerous directions and have attracted the attention of researchers in computer science, applied mathematics, and statistics, in areas such as manifold learning, sparse modeling, and the detection of geometric structure. This is an area with great potential for interaction among statisticians, applied mathematicians, and computer scientists. The Mathematical Sciences Research Institute MSRI is focused primarily on the development of fundamental mathematics, specifically in areas in which mathematical thinking can be applied in new ways.

In spite of its primary focus on the mathematical sciences per se, MSRI has long included a robust set of outreach activities. For example, its program Computational Aspects of Algebraic Topology explored ways in which the techniques of algebraic topology are being applied in various contexts related to data analysis, object recognition, discrete and computational geometry, combinatorics, algorithms, and distributed computing.

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  • That program included a workshop focused on application of topology in science and engineering, which brought together people working in problems ranging from protein docking, robotics, high-dimensional data sets, and sensor networks. In , MSRI organized and sponsored the World Congress on Computational Finance, in London, which brought together both theoreticians and practitioners in the field to discuss its current problems. MSRI has also sponsored a series of colloquia to acquaint mathematicians with fundamental problems in biology.

    An example is the workshop jointly sponsored by MSRI and the Jackson Laboratories on the topic of mathematical genomics. Both MSRI and SAMSI have helped build bridges between statisticians and climate scientists through at least six programs focused on topics such as new methods of spatial statistics for climate change applications, data assimilation, analysis of climate models as computer experiments, chaotic dynamics, and statistical methods for combining ensembles of climate models. After a professor of Scandinavian languages at UCLA participated in a IPAM program on knowledge and search engines, which introduced him to researchers and methods from modern information theory, he went on to organize two workshops in and , on networks and network analysis for the humanities; the workshops were funded by the National Endowment for the Humanities and cosponsored by IPAM.

    They led to the exploration of new data analysis tools by many of the humanists who participated. The IMA has a long history of outreach to industry, for instance through its Industrial Postdoctoral Fellowship program and other activities. Examples include uncertainty quantification in the automotive industry and numerical simulation of ablation surgery. Overall, IMA has trained over postdoctoral fellows since , 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. This led to hiring by NGA of several new mathematics Ph.

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    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. 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. 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 , 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. 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.

    go to site 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. 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.

    The New York Times. January 17, Nature Accessed March 19, 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.