How did Charles Sanders Peirce view the relationship between logic and mathematics?

Charles Sanders Peirce held a perspective on the relationship between logic and mathematics that contrasted with the views of contemporaries like Bertrand Russell and Gottlob Frege. While those thinkers argued that mathematics could be derived from logic, Peirce maintained the opposite position: he viewed logic as a branch of mathematics, rather than the other way around.1

Peirce’s work was deeply influenced by his father, Benjamin Peirce, a Harvard mathematics professor who introduced him to sophisticated conceptions of algebra. Throughout his career, Peirce sought to blend the algebraic tradition of George Boole with the study of quantified relational inferences. Although he made significant contributions to deductive, or mathematical, logic—including the development of the logic of relations and quantification theory—he remained primarily a student of the "logic of science," focusing on induction and abduction alongside deduction.21