The Mathematical Sciences in 2025 (2013) / Chapter Skim
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The list of exciting accomplishments includes among many others surprising proofs of the long-standing Poincaré conjecture and the "fundamental lemma"; progress in quantifying the uncertainties in complex models; new methods for modeling and analyzing complex systems such as social networks and for extracting knowledge from massive amounts of data from biology, astronomy, the Internet, and elsewhere; and the development of compressed sensing. As more and more areas of science, engineering, medicine, business, and national defense rely on complex computer simulations and the analysis of expanding amounts of data, the mathematical sciences inevitably play a bigger role, because they provide the fundamental language for computational simulation and data analysis.
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Many mathematical scientists remain unaware of the expanding role for their field, and this incognizance will limit the community's ability to produce broadly trained students and to attract more of them. A community-wide effort to rethink the mathematical sciences curriculum at universities is needed.
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In order to move in these directions, the following will need attention: • The culture within the mathematical sciences should evolve to encourage development of the characteristics listed in the Conclu sion above. • The education of future generations of mathematical scientists, and of all who take mathematical sciences coursework as part of their preparation for science, engineering, and teaching careers, should be reassessed in light of the emerging interplay between the math ematical sciences and many other disciplines.
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One aspect of the mathematical sciences involves unearthing and understanding deep relationships among these abstract structures. Another aspect involves capturing certain features of the world by abstract structures through the process of modeling, performing formal reasoning on the abstract structures or using them as a framework for computation, and then reconnecting back to make predictions about the world.
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And the expanding connections between the mathematical sciences and so many areas of science, engineering, medicine, and business make it ever more important to have a strong mathematical sciences community through which ideas can flow. As stated in a recent review of the mathematical sciences enterprise in the United Kingdom, "Major contributions to the health and prosperity of society arise from insights, results and algorithms created by the entire sweep of the mathematical sciences, ranging across the purest of the pure, theory inspired by applications, hands-on applications, statistics of every form, and the blend of theory and practice embodied in operational research."1 The committee members -- like many others who have examined the mathematical sciences -- believe that it is critical to consider the mathematical sciences as a unified whole.
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The health and vitality of the mathematical sciences enterprise is maximized if knowledge and people are able to flow easily throughout that large set of endeavors. The "mathematical sciences" must be defined very inclusively: The discipline encompasses a broad range of diverse activities whether or not the people carrying out the activity identify themselves specifically as mathematical scientists.
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DMS in particular works to varying degrees with other NSF units, through formal mechanisms such as shared funding programs and informal mechanisms such as program officers redirecting proposals from one division to another, divisions helping one another in identifying reviewers, and so on. For the mathematical sciences community to have a more complete understanding of its reach and to help funding agencies best target their programs, the committee recommends that a modest amount of data be collected more methodically than heretofore.
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These institutes now play an important role in helping mathematical scientists at various career stages learn new areas and nucleate new collaborations. Some of the institutes create linkages between the mathematical sciences and other fields, and some have important roles to play in outreach to industry and the general public.
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Beyond this, because computation is often the means by which the mathematical sciences are applied in other fields and is also the driver of many new applications of the mathematical sciences, it is important that most mathematical scientists have a basic understanding of it. Academic departments may consider seminars or other processes to make it easy for mathematical scientists to learn about the rapidly evolving frontiers of computation.
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It is critical that the mathematical sciences community actively engage with STEM discussions going on outside their own community and not be marginalized in efforts to improve STEM education, especially since the r esults of those efforts would greatly affect the responsibilities of mathematics and statistics faculty members. The need to create a truly compelling menu of creatively taught lower-division courses in the mathematical sciences tailored to the needs of twenty-first century students is pressing, and partnerships with mathematics-intensive disciplines in designing such courses are eminently worth pursuing.
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This suggests that graduate education in the mathematical sciences needs to be rethought in light of the changing landscape in which students may now work. At the least, mathematics and statistics departments should take steps to ensure that their graduate students have a broad and up-to-date understanding of the expansive reach of the mathematical sciences.
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The policy of encouraging the growth of the U.S.-born mathematical sciences talent pool should continue, but it needs to be supplemented by programs to attract and retain mathematical scientists from around the world, beginning in graduate school and continuing through an expedited visa process for those with strong credentials in the mathematical sciences who seek to establish permanent residence. The underrepresentation of women and ethnic minorities in mathe matics has been a persistent problem for the field.
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The committee foresees a more difficult period for the mathematical sciences on the horizon because of this changing business model for universities. Because of their important role in teaching service courses, the mathematical sciences will be disproportionately affected by these changes.
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Recommendation: Academic departments in mathematics and statistics should begin the process of rethinking and adapting their programs to keep pace with the evolving academic environment, and be sure they have a seat at the table as online content and other innovations in the delivery of mathematical science coursework are created. The profes sional societies have important roles to play in mobilizing the com munity in these matters, through mechanisms such as opinion articles, online discussion groups, policy monitoring, and conferences.
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