This paper aims to examine how the public perception of mathematics changed in England in the 19th century. As rapid industrial and social developments took place in the 19th century, the educational environment underwent great changes, and the value and public perception of mathematics also changed. Mathematics took a new position in the terrain of educational reform in the late 19th century. In this study, I analyzed the actual condition of mathematics education in elementary and secondary schools, popular educational institutions, and universities in England in the first half, middle, and second half of the 19th century, and compared what values and usefulness of mathematics education were justified in each institution. I also examined how satirical magazine Punch satirized the public understanding or view on mathematics at each period. It is to be hoped that this study will have significant implications for raising the public's positive perception of mathematics in modern society.