This position paper proposes Brain-Forest Adaptive Intelligence (BFAI), a theoretical framework for energy-efficient AI that combines biomimetic design principles with mathematical structures from Srinivasa Ramanujan's work. The architecture features a dual-module system: a lightweight "Brain" for rapid query classification and a sparse "Forest" of heterogeneous experts for deep processing, connected via biologically-inspired routing. We explore how seven of Ramanujan's mathematical contributions, including Ramanujan Graphs, partition functions, and continued fractions, might provide theoretical grounding for specific architectural components. This paper presents a theoretical framework, not empirical results. Approximately 60% of proposed components build on established research, 30% represent novel combinations requiring validation, and 10% are speculative connections requiring significant formalization.