History of Mathematics in American Mathematical Textbooks of the Late 19th and Early 20th Centuries

This paper investigated the usage of history of mathematics (HM) in 27 mathematical textbooks published between the late 19th century and the 1920s in the United States. The result shows that there are considerable HM materials in these textbooks, and their presentation forms can be divided into two categories: explicit and implicit. The explicit presentation includes famous quotations, mathematical characters, notes on specific topics, historical sketches of mathematical disciplines, as well as mathematical terminology, literature, problems, thoughts and methods in proving theorems; while the implicit presentation are involved in compiling mathematical exercises and introducing basic mathematical concepts. Among them, mathematical problems and historical notes on specific topics are most-used presentation forms. Then, five methods of approaching the HM materials in the textbooks were classified as: ornamentation, supplementation, duplication, accommodation, and reconstruction. The characteristics of the usage were also analyzed, and it is found that: the HM usage in a mathematical textbook is closely related to the HM knowledge at the time when the textbook published, the HM literacy of the editor of the textbook, as well as the value of HM and the scientific humanism ideological trend at that time. Compared with the textbooks one century ago, today’s Prentice Hall edition textbooks have made little significant progress in the HM usage.