1795 10, Gauss left his hometown and went to the University of G? ttingen for further study. Soon, the rich math books there attracted him deeply. In his first year at the University of G? ttingen, Gauss solved the worldwide problem of drawing regular polygons with rulers and compasses for more than two thousand years by algebraic methods. At the same time, he also proved that it is impossible to make equilateral heptagons, equilateral nonagon, equilateral dodecagons, equilateral triangles and equilateral quadrilaterals with only compasses and rulers. In other words, Gaussian induction proves which regular polygons can be made with rulers and compasses and which cannot be made. His thought surpassed the methodological level of his time and was very creative. This mathematical thought of young Gauss brought the research of mathematical methodology into a new field.