we look at previous centuries, but the same phenomenon is providing opportunities and challenges today.

There is a long list of ways mathematics is now being used, and the types of fundamental mathematics that are needed spans almost every field of core mathematics—algebra, geometry, analysis, combinatorics, logic. A sampling of these uses, described in nontechnical language, can be found in the companion volume to this report, Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century.

Whether or not one gets directly involved in these developments, it would be very useful to the profession if core mathematicians were to increase their level of awareness of what is going on out there. As educators, professors want to continue to instill in their students the clarity and rigor that characterizes core mathematics. But they must do this cognizant of the fact that what students need to learn has vastly expanded, and multiple educational paths must be available to them. There is, of course, some intellectual investment for core mathematicians involved in teaching these courses, but in the end they will have a wider and more varied range of choices of what to teach, and they will be enlarging the number of ecological niches available to mathematicians in both the academic world and the outside world.

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