Mathematics could be likened to an inextinguishable light that illuminates dark or unclear regions in our extremely sophisticated modern societies. Galileo Galilei once wrote that “nature is written in the language of mathematics,” and needless to say, Descartes and Newton are also followed this tradition. Even now, mathematics continues to be the common language of science. Furthermore, even more than in the past, mathematics today plays the role of a compass by indicating the directions that research in science and technology should follow. Without mathematics, progress in all fields could only be made by blind exploration. In fact, we find mathematics at the heart of nearly all the advanced technologies that drive modern society, including information security, networks, medical technology such as CT scans and MRIs, control in chemical plants, blast furnaces, and nuclear reactors, the development of airplanes and automobiles, design in robotics, scheduling in transportation, logistics in industries, finance and insurance, risk management, searching for resources, weather and earthquake prediction, and entertainment, etc. No matter how different these fields are in appearance, many of them have identical structures in terms of their mathematics. This is frequently acknowledged as “the universality and the general applicability of mathematics.” They are major characteristics of mathematics. For example, while it is a fact that the designs of CT scanners, MRI, and the control of blast furnaces for manufacturing iron each entail difficulties unique to their respective fields, mathematically, each involves the same activity—the solution of an inverse problem.