• Prevent nuclear terror. Network analysis can contribute to this, as can cryptology, data mining, and other intelligence tools.
• Secure cyberspace. Requires advances in cryptography and theoretical computer science.
• Enhance virtual reality. Requires improved algorithms for scene rendering and simulation.
• Advance personalized learning. Requires advances in machine learning.
• Engineer the tools of scientific discovery. Requires advances to enable multiscale simulations, including improved algorithms, and improved methods of data analysis.
Engineering in general is dependent on the mathematical sciences, and that dependency is strengthening as engineers push toward ever greater precision. As just one illustration of the pervasiveness of the mathematical sciences in engineering, note the following examples of major improvements in manufacturing that were provided at the 2011 annual meeting of the National Academy of Engineering by Lawrence Burns, retired vice president for R&D and strategic planning at General Motors Corporation:
1. Simultaneous engineering,
2. Design for manufacturing,
3. Math-based design and engineering (computer-aided design),
4. Six-sigma quality,
5. Supply chain management,
6. The Toyota production system, and
7. Life-cycle analysis.7
It is striking that six of the seven items are inextricably linked with the mathematical sciences. While it is obvious that Item 3 depends on mathematical advances and Item 4 relies on statistical concepts and analyses, Items 1, 2, 5, and 7 are all dependent on advances in simulation capabilities that have enabled them to represent processes of ever-increasing complexity and fidelity. Research in the mathematical sciences is necessary in order to create those capabilities.
ILLUSTRATIVE DEMANDS FROM NETWORKING AND INFORMATION TECHNOLOGY
The 2010 report from the President’s Council of Advisors on Science and Technology (PCAST) Designing a Digital Future: Federally Funded