Which book was the first systematic treatment applying a mathematical method to logical thinking?

The book that represents the first systematic treatment applying a mathematical method to logical thinking is George Boole's "Laws of Thought." In this groundbreaking work, Boole introduced what is now known as Boolean algebra, which provides a way to represent logical statements and operations in mathematical form. This approach laid the foundation for the development of modern digital logic and computer science, as it allows for the manipulation of logical variables using mathematical principles.

Boole's work fundamentally transformed the field of logic by demonstrating how mathematical methods could be applied to logical reasoning, paving the way for the formal analysis of logical circuits and systems. This integration of logic and mathematics was pivotal, influencing future developments in various domains, including philosophy, mathematics, and computer science. The significance of "Laws of Thought" lies in its role in establishing a systematic framework for understanding and processing logical propositions, making it a cornerstone in both logical theory and digital electronics.