A Case Study of the Diversity and Optimization of Mathematical Definitions and Symbolization

Taking the idea of “reflective and critical optimization thinking”, this article first examines “the outlook on development of big mathematics” in International Mathematics Day in 2003 from the perspective of the history of mathematics. Then according to the requirements of mathematical core literacy and mathematical beauty, a deep analysis is conducted on the limitations of the teaching methods in the Turing mathematics and statistics series “Terence Tao Analysis”. The case study shows that (1) the sets, relations, functions and operations present a concentric circle relationship of layer-by-layer proper subsets; (2) rejecting mathematical notation damages the beauty of simplicity and learning efficiency; and (3) forcing the first mapping function to be a surjection unnecessarily limits the wider range of applications that composite functions can have, and it lacks the unified beauty of mathematical definitions. Finally, itemized strategies and suggestions for improvement and optimization are proposed.