Empowerment of Knowledge Rediscovery in the Cultivation of Top Mathematical Talents: Construction and Practice of the Undergraduate-Master-Doctoral Integrated Training Model

As the core pillar of basic disciplines, the cultivation of top innovative mathematical talents is a key measure to address the country’s core technological bottlenecks and support technological self-reliance and self-improvement. In the traditional mathematical talent training model, there are significant connection barriers between undergraduate and postgraduate stages. Problems such as fragmented scientific research training and delayed stimulation of innovative potential seriously restrict the growth of high-level top mathematical talents. Taking the major of Mathematics and Applied Mathematics in Qian Weichang College of Shanghai University as the practice carrier, and in conjunction with the Professional Committee of Educational Mathematics of the Chinese Society of Higher Education, this study takes the "knowledge rediscovery" concept as the core educational guidance, and systematically constructs and practices the "3+1+X" undergraduate-master-doctoral integrated training model. This model breaks the traditional linear teaching logic of "definition-theorem-proof-example", guides students to re-experience the generation process of mathematical knowledge as "quasi-researchers", and realizes the seamless connection of knowledge learning, scientific research training and thinking improvement between undergraduate and postgraduate stages through the whole-cycle training link of "foundation consolidation-scientific research connection-flexible further study". After 6 years of practical testing (2019-2025), the model has trained a total of 74 students, with an further study rate of 81\%. Students' scientific research capabilities and academic achievements have been significantly improved, and the training model has formed a good demonstration effect of on-campus promotion and off-campus radiation. This paper systematically explains the inherent compatibility between the "knowledge rediscovery" concept and the undergraduate-master-doctoral integrated cultivation of top mathematical talents, details the core design and key implementation measures of the "3+1+X" training model, summarizes the practical effects and core experiences, and puts forward the direction of future in-depth development, providing a replicable and promotable practical paradigm for the integrated cultivation of top innovative talents in mathematics and other basic disciplines in China.