We propose a three-layered framework for mathematical specialization and research strategy in an era of rapidly advancing artificial intelligence. First, we introduce the "Diffraction Profile," a finite-resource cognitive model that uses a squared-sinc kernel to mathematically describe how deep specialization in a core domain generates non-monotonic, structurally resonant "side lobes" of secondary competence. Second, we provide a quantitative mapping of global mathematical research ecosystems, utilizing bibliometric data to estimate the approximate scales of various specialist communities. Finally, we outline a concrete T-shaped mathematical architecture featuring a vertical stem in algebraic topology, homotopy theory, and homological algebra, supported by high-transfer lateral engines like dynamical systems and category theory. Rather than attempting to identify an unstable "AI-proof" niche, our framework advocates for maximizing long-term cognitive compounding. The ultimate strategy is to combine deep human structural intuition and problem selection with aggressive AI augmentation for computational execution, proof search, and formal verification. ( direct link )