Why did Gottlob Frege write Grundgesetze der Arithmetik?

Gottlob Frege wrote Grundgesetze der Arithmetik (The Basic Laws of Arithmetic) to provide a rigorous, formal development of his theory that all of mathematics could be derived from, or reduced to, pure logic.1

This project was the culmination of his long-standing research program, known as logicism, which sought to establish arithmetic on a foundation of logical laws rather than specifically mathematical concepts. In this work, Frege utilized a modified version of the symbolic system he had introduced in his earlier book, Begriffsschrift, to present his arguments with the precision and care that characterized his approach to the philosophy of mathematics.213