The National Research Council has made available a pre-print of the forthcoming report of its Committee on The Mathematical Sciences in 2025, chaired by Caltech EE/applied physics professor Thomas Everhart. Like all NRC publications, it’s a long and dense document, but the summary remains fully accessible to the general reader. Though it makes all the usual pleas for funding of basic research without undue hope for immediate practical application, the report also starkly underlines what should now be obvious connections between mathematical knowledge and rapidly accumulating advances in a wide array of other disciplines and real-world applications. Even within mathematics itself, the report argues, boundaries between sub-disciplines are breaking down, and mathematicians who would formerly have seemed past their prime years of creativity can now still make important discoveries because it pays increasingly to have long experience of these interconnections.

What I found remarkable was how hard this committee came down on the core discipline itself, calling mathematicians generally “incognizant” (fighting word!) of the expanding role that the mathematical sciences now play in other realms of theory and practice. “It is easy,” the authors write, “to point to work in theoretical physics or theoretical computer science that is indistinguishable from research done by mathematicians, and similar overlap occurs with theoretical ecology, mathematical biology, bioinformatics, and an increasing number of fields.” By implication, the authors are calling their colleagues insufficiently appreciative of these connections. And in practical fields, it seems that everyone — biotechnologists, communication-system engineers, and financial-market “quants,” to take just a few examples — has proved more aware of these interdependencies than mathematicians themselves.
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If you’ve ever wondered why some city governments elaborate their own greenhouse-gas-reduction strategies – when it might seem odd to spend scarce resources fighting a global problem in exchange for such minor potential improvements in local environmental quality – then you may find much useful insight from Joan Fitzgerald’s Emerald Cities: Urban Sustainability and Economic Development (Oxford University Press).

An urban planner at Northeastern University, Fitzgerald traces the reasoning that leads cities to conclude that they can extract economic- and job-development benefits by positioning themselves as leaders in the new “green” industry sectors. These are the industries that draw their economic relevance from the reality of long-term trends in energy pricing and from the moral commitment of sufficiently well-off populations to lead more sustainable lives.

This book systematically explores the crossover between four aspects of sustainability – renewable energy, energy efficiency, waste management, and transportation – and three economic-development strategies that Fitzgerald calls “linking” (connecting populations to new employment opportunities based); “transformational” (taking hard-hit local manufacturing industries into new markets); and “leapfrogging” (building entirely new technology clusters).

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