Improvements in mathematical notations in physics have provided not only practical benefits but also physical or geometrical insights. Especially, graphical notations such as Penrose notation, Feynman diagrams, and category-theoretical diagrams have found various applications in physics from quantum field theories to quantum computing. In this talk, I will introduce my own contributions to this stream of “notation engineering” works, from vector calculus to the symplectic geometry of thermodynamics. Then the underlying universal characteristic of good notations will be explicated. In the end, I will also briefly introduce some creative artworks of mine inspired by tensor graphs.