Yuexin Liao

I am Yuexin Liao, a senior student at Caltech. I am passionate about creating new theories at the intersection of mathematics, computer science, and economics. My research concentrates on partial differential equations, dynamical systems, machine learning, and decision theory.

At the core of my work is a rigorous exploration and formulation of distribution laws—whether manifesting as intricate statistical patterns in data science, or analytical structures and abstract probabilistic frameworks within pure mathematics.

I perceive programming as a formal linguistic framework, language itself as a hierarchy of structural abstractions, and mathematics as the foundational syntax describing universal regularities. This integrated and generative perspective fuels my enthusiasm for theoretical elegance, structural unification, and deep explanatory power.

I am deeply committed to continually constructing and refining high-level theoretical frameworks and applying them rigorously to address meaningful real-world problems.

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