Chapter 1: The Early Years

The remarkable journey of Xu Ruiyun, China's pioneering female mathematician, began in Shanghai on June 15, 1915. As the youngest daughter in a prosperous family—her father a businessman and her mother a devoted Buddhist—Xu Ruiyun was cherished and nurtured in an environment that fostered her academic aspirations.

Her fascination with mathematics emerged at a young age, leading her to dream of becoming a teacher. In February 1927, she gained admission to the Shanghai Public Wuben Girls' High School, where she graduated in 1932. Fueled by her passion for the subject, she enrolled in the Mathematics Department at National Zhejiang University that same year, becoming one of the few female students in the field. Under the guidance of esteemed educators like Qian Baocong, Chen Jiangong, and Su Buqing, Xu graduated with honors in July 1936 and continued as a teaching assistant.

Chapter 2: Pursuing Excellence in Germany

In February 1937, Xu Ruiyun married Jiang Ximing, an assistant professor in Biology at Zhejiang University. Just a few months later, the couple received a Humbert Scholarship to study in Germany. Xu focused her research on trigonometric series theory and, despite her doctoral supervisor, Caracy Odori, initially hesitating to accept new students, he recognized her determination and impressive academic record. Thus, she became his final student, often referred to as his "closed disciple."

By the end of 1940, Xu Ruiyun proudly obtained her doctorate, marking her as the first woman in China to achieve this distinction in mathematics. Her dissertation, "On the Fourier Expansion of Singular Functions in Lebesg’s Decomposition," was published in the renowned German journal Mathematical Times in 1941.

Chapter 3: A Legacy of Teaching and Research

Upon her return to China in April 1941, Xu Ruiyun became an associate professor at Zhejiang University. Following a departmental restructuring in 1952, she took on the role of head of the mathematics teaching and research group. Later, she transitioned to lead the mathematics department at Zhejiang Normal University (now Hangzhou University). Throughout her career, Xu actively engaged with various organizations, including the Zhejiang Mathematical Society and the Zhejiang Association for the Popularization of Science and Technology, significantly contributing to the advancement of mathematics in the region.

Chapter 4: The Tragic End

Tragically, in January 1969, Xu Ruiyun took her own life at the age of 53, unable to cope with the persecution she faced during the Cultural Revolution. Her life story is a testament to her dedication and passion for mathematics, as well as her role as an educator and academic leader. Despite the societal challenges she confronted, Xu made significant strides in mathematical research, particularly in analytical mathematics and trigonometric series theory. Her legacy, marked by both her achievements and the profound hardships she endured, remains a powerful narrative in the history of mathematics.