Why did John Stuart Mill argue that mathematics is based on experience?

John Stuart Mill argued that mathematics is based on experience because he viewed all knowledge as ultimately empirical and inductive. In his view, mathematical truths are not a priori or necessary in the traditional sense; rather, they are empirical statements of extremely high generality.123

Mill contended that the apparent necessity of mathematical propositions—such as the belief that two straight lines cannot enclose a space—arises from the human mind's habit of thinking. This habit is formed through an unbroken, lifelong series of observations and experiences, such as seeing the edges of a table or the path of light beams. Consequently, he interpreted mathematical statements as generalizations derived from these repeated experiences.3

Furthermore, Mill proposed a physicalistic interpretation of mathematical operations. For example, he suggested that the proposition "2 + 3 = 5" is not a statement about abstract entities, but rather a description of physical reality: it asserts that whenever a pile of two objects is combined with a pile of three objects, the result is a pile of five objects.4