Master lecture: the enlightenment of scientific progress and interdisciplinary integration -- from backward stochastic differential equations

On the afternoon of November 27, the research center for mathematics and interdisciplinary sciences (hereinafter referred to as the "center") held a master lecture. Professor Peng Shige, academician of the Chinese academy of sciences and director of the center, gave a report entitled "the enlightenment of scientific progress and interdisciplinary integration -- from backward to stochastic differential equations". All the teachers and students in the center listened to the report.

In the report, academician Peng pointed out that mathematical crossover is the integration of multiple disciplines, which is the need of the development and the cradle of major academic achievements. Therefore, it is a very urgent task to attach importance to promoting the communication and crossover between different disciplines. In addition, he also shared some insights on interdisciplinary studies. Taking Alpha go as an example, he explained that most of the early stages of interdisciplinary studies were controversial. He encouraged students to learn to persist and not to give up. And he stressed that doing a good job in interdisciplinary science is not to weaken mathematics, but to lay a good foundation for mathematics. Only through a thorough understanding of mathematical theory can we draw parallels with other disciplines. In order to encourage students to join the cross-science research, and to do scientific research more firmly, academician Peng shared the typical case of cross-science research -- the development process of stochastic differential equations. He explained that with the development and progress of the society, the uncertainty of the problem increases. The original ordinary differential equations are not enough to describe the problem itself, so more scientific models are needed to describe the uncertainty of things themselves, such as probabilistic statistical models. In probabilistic statistical models, the axiomatic Kolmogoroff equation (the axiom of probability) was first proposed, and later the ITO equation was developed, leading to the final black-scholes formula. This is a typical example of cross-discipline, which greatly promotes the development of uncertainty research and has great practical significance. During the discussion session, academician Peng encouraged the students to listen to the report more and speak more actively. He also encouraged them to cultivate and exercise their language skills, so as to "understand and speak clearly". He also warned that research should be done with an open mind, focusing on innovation and cross-disciplinary cooperation, organizing research interest groups, taking full advantage of the center's favorable conditions, and more exchanges and collisions.

Author: Yang Yuan

Photography: Shan Ang

(Editor in Charge: Lei Hao)