This research delves into the innovative application of topological number theory to reform English language teaching methodologies in higher education. We introduce and assess a novel approach to English teaching in colleges and universities, inspired by the principles of topological number theory. Our methodology leverages a unique model for recognizing handwritten English based on visual topological cognition, applying the insights of topological cognition theory to enhance English language instruction. The empirical analysis reveals a low word error rate of just 9.42% for our model, outperforming traditional models like the CRNN, which exhibits a 15.12% error rate. In a 10-week instructional experiment, students taught using the topological approach demonstrated significant improvements across all dimensions of English learning compared to their peers in a control group. The findings underscore the substantial potential of topological number theory in elevating English language teaching in colleges, offering significant benefits in teaching effectiveness and student motivation.