The Interrelationship between Mathematics, Physics, and Chemistry

The interrelationship between mathematics and physics has been a subject of deep interest since ancient times, engaging not only mathematicians and physicists but also, more recently, historians and educators. The evolution of mathematical sciences, physics, and chemistry has been extensive and continues to expand—particularly over the past two decades, where this growth has accelerated significantly. Much of this expansion is driven by the increasing reliance of scientific and engineering disciplines on computation and simulation—domains in which mathematical sciences naturally serve as the foundational language. Additionally, with the rapid advancement in data collection capabilities, mathematical sciences have become central in interpreting and extracting knowledge from large datasets. Nevertheless, there remains a pressing need to strengthen mechanisms that facilitate collaboration between mathematical scientists and researchers in other disciplines. The influence of research in mathematical sciences can be far-reaching. A novel mathematical insight can swiftly be incorporated into software and applications, bypassing the lengthy translation process typical in fields such as chemistry, where basic research may take years to influence practical pharmaceutical development. Mathematical innovations that improve data compression or analysis, financial modeling, signal processing, or simulation modeling in engineering can be adopted rapidly. As such, even sectors seemingly disconnected from the mathematical sciences—such as certain branches of government or industry—have a vested interest in maintaining a robust mathematical sciences community. Furthermore, since this community also supports the development of a well-trained workforce in STEM (Science, Technology, Engineering, and Mathematics), its vitality should be a matter of national concern. This chapter outlines how increasing interdisciplinary interactions have expanded the definition and scope of the mathematical sciences. It further highlights their importance across a wide range of disciplines—many of which identify mathematical problems as top research priorities.