Uploaded April 2025 | Updated September 2026, 2 weeks ago
Mathematics is a pillar of national security.
A decision-maker’s ability to synchronize military activities across five domains (i.e., air, land, maritime, space, and cyberspace), and adapt to rapidly changing threat landscapes hinges on robust mathematical frameworks and effective problem formulations that fully encapsulate the complexities of real-world operational environments.
Unfortunately, mathematical approaches in defense often rely on “good-enough” approximations, resulting in fragile solutions that severely limit our nation’s ability to address these evolving challenges in future conflicts. In contrast, establishing robust mathematical frameworks and properly formulating problems can yield profound and wide-reaching results.
To excel in increasingly complex, dynamic, and uncertain operational environments, military decision-makers need richer mathematical frameworks that fully capture the intricacies of these challenges. Emerging fields in mathematics offer the potential to provide these frameworks, but realizing their full potential requires innovative problem formulations.
DARPA recently announced an Advanced Research Concepts (ARC) topic called COMPASS — short for Critical Orientation of Mathematics to Produce Advancements in Science and Security.
COMPASS aims to answer this question: How can new mathematical frameworks enable paradigm shifting problem formulations that better characterize complex systems, stochastic processes, and random geometric structure
Program: COMPASS: https://www.darpa.mil/research/programs/compass?utm_source=youtube&utm_medium=social&utm_campaign=programs-ar&utm_term=compass&utm_content=compass
ARC topics: https://www.darpa.mil/research/opportunities/arc?utm_source=youtube&utm_medium=social&utm_campaign=programs-arc&utm_term=compass&utm_content=compass
Mathematics is a pillar of national security.
A decision-maker’s ability to synchronize military activities across five domains (i.e., air, land, maritime, space, and cyberspace), and adapt to rapidly changing threat landscapes hinges on robust mathematical frameworks and effective problem formulations that fully encapsulate the complexities of real-world operational environments.
Unfortunately, mathematical approaches in defense often rely on “good-enough” approximations, resulting in fragile solutions that severely limit our nation’s ability to address these evolving challenges in future conflicts. In contrast, establishing robust mathematical frameworks and properly formulating problems can yield profound and wide-reaching results.
To excel in increasingly complex, dynamic, and uncertain operational environments, military decision-makers need richer mathematical frameworks that fully capture the intricacies of these challenges. Emerging fields in mathematics offer the potential to provide these frameworks, but realizing their full potential requires innovative problem formulations.
DARPA recently announced an Advanced Research Concepts (ARC) topic called COMPASS — short for Critical Orientation of Mathematics to Produce Advancements in Science and Security.
COMPASS aims to answer this question: How can new mathematical frameworks enable paradigm shifting problem formulations that better characterize complex systems, stochastic processes, and random geometric structure
Program: COMPASS: https://www.darpa.mil/research/programs/compass?utm_source=youtube&utm_medium=social&utm_campaign=programs-ar&utm_term=compass&utm_content=compass
ARC topics: https://www.darpa.mil/research/opportunities/arc?utm_source=youtube&utm_medium=social&utm_campaign=programs-arc&utm_term=compass&utm_content=compass
