The mathematical sciences and their interfaces in 2013.
National Academy of Sciences.

The mathematical sciences are part of almost every aspect of everyday life. Internet search, medical imaging, computer animation, numerical weather predictions and other computer simulations, digital communications of all types, optimization in business and the military, analyses of financial risks—average citizens all benefit from the mathematical science advances that underpin these capabilities, and the list goes on and on.

The opening years of the twenty-first century have been remarkable ones for the mathematical sciences. Major breakthroughs have been made on fundamental research problems. The ongoing trend for the mathematical sciences to play an essential role in the physical and biological sciences, engineering, medicine, economics, finance, and social science has expanded dramatically. The mathematical sciences have become integral to many emerging industries, and the increasing technological sophistication of our armed forces has made the mathematical sciences central to national defense. A striking feature of this expansion in the uses of the mathematical sciences has been a parallel expansion in the kinds of mathematical science ideas that are being used.

For the study that produced this report, the National Science Foundation’s (NSF’s) Division of Mathematical Sciences (DMS) and NRC’s Board on Mathematical Sciences and Their Applications (BMSA) chose a time horizon of 2025. It was felt that a strategic assessment of the mathematical sciences needed a target date and that the date should be sufficiently far in the future to enable thinking about changes that might correspond to a generational shift. Such changes might, for example, depend on changes in graduate education that may not yet be implemented.

To read more about their findings, you can read the full report here.