The second-order optical nonlinearity σ⁽²⁾(ω) has been a focus of basic research and technological development for decades as it is both a probe of inversion symmetry breaking in media and the basis for generating coherent light from far-infrared to ultraviolet wavelengths. Here, we focus on the relation between band geometry and nonlinear optics. We measured second harmonic generation (SHG) with incident photon energy from 0.4 eV - 1.6 eV on a polar semimetal TaAs with a sharp resonant peak detected at 0.7 eV, that is larger than previously measured in any crystal. Our discovery of a giant anisotropic σ⁽²⁾(ω) in TaAs raises the following questions: what is special about TaAs and/or polar metals that accounts for large resonant optical nonlinearity, and, is there a fundamental upper bound on σ⁽²⁾(ω) in such inversion breaking crystals? I will describe in the Rice-Mele model based on the band-geometric theory of nonlinear optical response that addresses these questions.