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Why did John Stuart Mill consider mathematics to be based on experience?

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Painting by Joseph Aubert of Saint Thomas Aquinas seated with a book, wearing a halo and black and white robes, surrounded by ornate patterns in St. Stephens Church, Jerusalem. — Western philosophy Painting of scholastic philosopher St. Thomas of Aquinas by Joseph Aubert, 1900.

John Stuart Mill, a prominent figure in 19th-century Western philosophy, held a thoroughly empiricist view, arguing that all knowledge—including mathematics—is derived from experience.1

Mill rejected the idea that mathematical truths are a priori or independent of observation. Instead, he proposed that the apparent necessity and certainty of mathematics result from the unique massiveness of its empirical confirmation. For Mill, mathematical statements are essentially generalizations based on our observations of the physical world.12

For example, he interpreted an arithmetical statement like "2 + 3 = 5" not as an abstract, analytic truth, but as 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. In this framework, all real knowledge is inductive and empirical, and Mill viewed deduction as sterile, as it does not produce new knowledge beyond what is already contained in the empirical premises.21