AI requires numerical representations of the world and phenomena so that it can perform mathematical operations that lead to actions, decisions, reasoning, or discovery. Mathematics is the language that underpins machine intelligence and offers us the tools to understand existing capabilities and guide the development of new technologies. Rather than assume a one-size fits all (or one model to rule them all), I believe that there are multiple ways to build operational AI systems rooted in optimization against different, interconnected design dimensions: Testing, Resources, Assurance, Data, and Expressivity (TRADE). Developing the ability to effectively assess TRADE considerations of existing AI technology to identify gaps, limitations, and applicability is how we can accelerate scientific discovery and create architectural blueprints for models and systems that are robust, reliable, and operational by design.