Why did Gottlob Frege consider mathematics and philosophy closely connected?

Gottlob Frege viewed mathematics and philosophy as deeply intertwined because he believed that all of mathematics could be derived from, or reduced to, fundamental logical laws. This foundational position, known as logicism, posits that mathematics is essentially an extension of logic, requiring no independent mathematical concepts like numbers or sets to function.123

Frege’s interest in this connection was further driven by his efforts to create a rigorous logical notation capable of formalizing mathematical reasoning. In developing this system, he treated predicates as functions—a concept borrowed from mathematics—to analyze the structure of language and thought. By doing so, he sought to establish a "conceptual notation" (Begriffsschrift) that could serve as a foundation for both mathematics and science, moving away from psychological or empirical interpretations of meaning toward a purely logical, intensional framework. Consequently, his work in mathematical logic became the basis for his groundbreaking contributions to the philosophy of language.421