Soap bubbles, so easy to make, still cannot be fully explained mathematically.

It might be said that a major challenge in "variational problems" is to understand soap bubbles mathematically. For this seemingly simple problem, it was shown that "a soap bubble is mathematically realized as something that minimizes its surface area," an achievement honored with the first Fields Medal. Like the energy minimization problems in science and engineering and the optimization problems in economics, many phenomena are driven by the same variational principle as soap bubbles. In the academic pursuit of finding and abstracting the common essence within complex phenomena, the abstraction and freedom of the mathematical sciences are vast. Once a perspective is gained after overcoming numerous difficulties, the deep essence of things emerges, and its broad applicability can be recognized from examples like the advent of computers. Material science is a field at the forefront of scientific research, actively studied by brilliant minds from around the world. This field aims to create functional materials through molecular design, and its research awaits deep insights not only from computer calculations but also from mathematical analysis. Problems such as those involving liquid crystals and superconductivity, which are formulated as multivariable variational problems, involve the analysis of points (functions) that minimize the energy functional and its critical points (points where the derivative of these functionals is zero). In particular, the problem of general critical points is formidable, standing as a challenging and exciting peak to conquer. I encourage you to hold high aspirations, pursue the path of mathematical sciences to address problems in science, engineering, economics, and other fields, and take on the challenge of building new mathematical sciences that accompany it.