Application of Generic Programming to Unsolved Mathematical Problems

This study proposes a method to solve unsolved mathematical games using generic programming. Although AI can replace humans in some jobs, it also can help humans by enhancing their abilities. In this study, generic programming allows humans to find mathematical formulas that are beyond the imagination of humans, and this is a new method to enhance the mathematics ability of humans. For this purpose, the Python generic programming package “gplearn” was customized by implementing new features, such as conditional branching, a new common error metric, and a few discrete functions selected for the study. In this paper, they had four experiments on using gplearn under different conditions. First, they demonstrated how the formula with the least error size would be selected. After that, the authors compared the effectiveness of the default fitness function and the customized percentage fitness function and discovered that the percentage fitness function is better for a specific type of data. They also tried to use integers instead of real numbers in generic programming. They implemented conditional branching and found out that conditional branching is very powerful for a specific type of data. In the last section, the authors got a new theorem that is a counter-example to a well-known conjecture. The research result shows the possibility of generic programming in combinatorial games and widens the scope of the research on symbolic regression.