sciences talent and sophistication to bear on ill-posed problems so as to make a contribution to the solution of these problems. This requires different skills from the ones that they trained for during their graduate student days, and it suggests that the training of graduate students in the mathematical sciences needs to be rethought given 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.

Recommendation 5-1: Mathematics and statistics departments, in concert with their university administrations, should engage in a deep rethinking of the different types of students they are attracting and wish to attract and must identify the top priorities for educating these students. This should be done for bachelor’s, master’s, and Ph.D.-level curricula. In some cases, this rethinking should be carried out in consultation with faculty from other relevant disciplines.

Recommendation 5-2: In order to motivate students and show the full value of the material, it is essential that educators explain to their K-12 and undergraduate students how the mathematical science topics they are teaching are used and the careers that make use of them. Modest steps in this direction could lead to greater success in attracting and retaining students in mathematical sciences courses. Graduate students should be taught about the uses of the mathematical sciences so that they can pass this information along to students when they become faculty members. Mathematical science professional societies and funding agencies should play a role in developing programs to give faculty members the tools to teach in this way.

The mathematical science community collectively does not do a good job in its interface with the general public or even with the broader scientific community, and improving this would contribute to the goal of enlarging the STEM pipeline. Internet tools such as blogs and video lectures offer new pathways for this outreach, which may be appealing to both practicing and retired mathematical scientists. There is a special need to improve the general level of understanding about uncertainty, which relies on an understanding of probability and statistics.

Recommendation 5-3: More professional mathematical scientists should become involved in explaining the nature of the mathematical sciences enterprise and its extraordinary impact on society. Academic departments should find ways to reward such work. Professional societies



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