This is the first book covering original information on the mathematical science of such the artifacts as 3M&I-body system, in which “3M” means human, material/machine, money, and “I” means the information/method in nature versus artifacts. This book is the product of industrial engineering versus Wiener’s cybernetics challenge for a half-century. For 3M&I-body, there are two approaches of artificial intelligence/IoT (internet of things) and Matsui's matrix/3D to systemization and control. The former is the analogical and visual approach to real entity. The latter is the digital and logical approach to system decision and is applied to the robotics of bodies. The mathematical science of a body is well constructed from the algebra, geometry, analysis, and control on Matsui’s equation, toward the sandwich and balancing propositions of bodies. The sandwich issues propose the squeeze or pinching theorem in mathematics at the 3M&I-body, and the balancing issues propose the principle of balancing and invisible collaboration of bodies, beginning from the work of Archimedes. This book contributes to the integration of knowledge and intelligence in science and facilitate the realization of the cyber/real-world , such as the enterprise robot, cloud-coordinated supply-chain management (SCM), and smart cities in the near future.