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.