In this seminar, I will discuss how mathematical and computational formalisms, ranging from differential geometry and optimization to data-driven methods, can be used to model, analyze, and solve problems arising in the design and physical realization of complex shapes. Examples will span a variety of scales, from small manufactured objects up to AI-assisted design of sustainable large-scale architectural structures. The goal of the seminar is to highlight how research in applied mathematics and computer science, coupled with Artificial Intelligence, can support new paradigms in design, fabrication, and sustainability.