From mathematical study to mechanical experiments
Hua studied Chinese mathematical books and developed a close working relationship with Xu Shou. Visits to Shanghai brought them into contact with Li Shanlan and translated scientific works. They acquired instruments and conducted experiments concerning optics, projectiles and mechanical motion, bringing calculation and physical observation together.
At the Anqing arsenal, Hua worked with Xu Shou, Xu Jianyin and others on steam machinery and experimental boats, later moving into the Jiangnan Arsenal network. Calculations, drawings and collaboration with manufacturing workers formed parts of this practical work. Producing an operating machine required repeated adjustments beyond understanding its description in a book.
Probability and the calculation of uncertainty
Hua and John Fryer produced the ten-volume Jueyi shuxue, with Fryer interpreting and Hua composing the Chinese text. Jueyi, or resolving doubt, expressed their choice of terminology for probability. Alongside games of chance, the work treated life insurance, judicial calculations and regularities found in large numbers of observations.
Ding Fubao’s bibliographical account singled out lifespans, lawsuits, ships meeting storms and warehouses catching fire. Such examples connected probability with insurance, commerce and social administration. The account maintained by Huazhong University of Science and Technology also describes material on the law of large numbers, the normal distribution and least squares, extending well beyond gambling puzzles.
Research, translation and teaching
Hua wrote on root extraction, number-theoretical questions, recurring decimals and finite differences, collecting part of this work in Xingsuxuan suangao. His translations with foreign collaborators ranged across mineralogy, geology, algebra, trigonometry and calculus. Technical understanding mattered when oral explanations had to become reliable Chinese prose.
He taught at institutions including Shanghai’s Gezhi Academy, the Tianjin military school and the Lianghu Academy in Wuchang. He also prepared introductory material such as Xuesuan bitan. Research methods, translated theories and graded classroom instruction offered different routes through the material, linking his work as a practical investigator with the preparation of books and the education of students.