How did Galileo’s mathematization of nature figure in Husserl’s critique of modern science?

In his final work, The Crisis of European Sciences and Transcendental Phenomenology, Edmund Husserl utilized Galileo’s mathematization of nature to illustrate a fundamental critique of modern science. Husserl argued that by replacing the qualitative, immediately experienced world—the life-world—with a world of mathematical symbols and idealizations, science effectively "forgot" the human subject who performs these scientific acts.1

Husserl contended that this process led to a dangerous "objectivistic-physicalist" outlook that ignored the subjective foundations of all knowledge. Because the life-world is the primary, pre-scientific ground of all experience, treating mathematical constructs as the only "true" reality creates a crisis where the scientist and the subjective life-world are excluded from the scientific thematization. By failing to reflect on the founding acts of consciousness that make scientific knowledge possible, modern science became fragmented and alienated from its own origins. Husserl’s phenomenology sought to overcome this by "questioning back" to these foundations, asserting that the life-world is not an inferior truth but the essential, presupposed basis for all scientific meaning.1