What are the core theoretical foundations driving advancements in chemical engineering, shaping the design and optimization of processes across industries? Explore pivotal theories like thermodynamics, kinetics, transport phenomena, and process control, elucidating their roles in understanding and manipulating chemical reactions, mass transfer, and energy conversion. Additionally, examine the significance of mathematical modeling and simulation in predicting system behavior and guiding decision$-$making. How do these theories empower engineers to address complex challenges and drive innovation in sustainable technology development?