• What is Practice-Grounded Mathematical Science?

Practice-Grounded Mathematical Science is the foundational philosophy of our laboratory. It represents a new paradigm for how mathematical science can interact with the complexity of the real world. Instead of applying existing mathematical tools unidirectionally to practical problems, we begin with the specific, diverse, and often conflicting constraints that characterize real-world systems—nonlinearity, large-scale structure, heterogeneity, uncertainty, physical and information constraints, operational limitations, environmental demands, and societal goals.

By abstracting from these unique "personalities" of real-world systems, and then projecting refined mathematical understanding back into practice, we aim to generate a bidirectional flow between theory and application. This forms a spiral of mutual growth that advances both academic knowledge and practical capability.

• Why It Matters in a Changing World

In today’s rapidly evolving society, conventional approaches that seek only universal or general mathematical principles are often ill-suited for complex, domain-specific problems. Many real-world systems—especially infrastructure systems—exhibit structural peculiarities that are often dismissed as “special cases” by traditional mathematics. However, we believe that it is precisely these specificities that should form the foundation for new mathematical discoveries.

Our approach acknowledges that "universality" and "specificity" in mathematical modeling are not mutually exclusive, but rather complementary. Real-world specificity, when properly understood, can reveal deeper structures that traditional abstraction overlooks. This philosophy underscores the importance of developing new mathematics "from" practice, rather than merely "for" practice.

• Application Domains: Energy and Communication Systems

We are applying this philosophy to critical infrastructure systems such as power systems and information and communication systems. For example, our research on smart inverters aims to mathematically guarantee frequency stability and voltage distribution from high-voltage to low-voltage power systems, which are becoming increasingly complex with the rise of renewable energy. 

Such infrastructure systems are becoming more decentralized, uncertain, and interconnected. As such, designing their future requires not just technological expertise or policy frameworks, but a scientific understanding grounded in physical laws and mathematical structures.

• Our Mission: Connecting Science, Technology, and Society

Through Practice-Grounded Mathematical Science, we aim to bridge the gaps between theory and application, science and technology, and individual disciplines and societal needs. We seek to offer a new form of scientific knowledge that can guide the design of sustainable, resilient, and intelligent social infrastructures.

Mathematics is not merely a descriptive tool—it is a language for envisioning the future. Our mission is to use this language not only to solve problems, but to imagine new systems, shape policy discourse, and cultivate the intellectual foundations for transformative societal change.