As early as 1666, Leibniz had conceived of logic as a universal system encompassing all principles. But this vision had remained a dead letter. Until the beginning of the 19th century, even the greatest scholars generally developed a mathematical theory to solve a concrete problem. Thus, Pierre-Simon de Laplace and Joseph-Louis Lagrange, among the most illustrious mathematicians of the late 18th century, drew inspiration from astronomy. Soon afterward, Jean-Baptiste Joseph Fourier drew inspiration from the propagation of heat.
Mathematics breaks free
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When Fourier died in 1830, the German mathematician Carl Gustav Jacobi wrote to Legendre in these terms: "Fourier held that the chief aim of mathematics was public utility and the explanation of natural phenomena; but a philosopher such as he should have known that the sole aim of science is the honor of the human mind, and that, in this regard, a question about numbers is worth as much as a question about the system of the world. "
This view naturally gave the German mathematician the freedom to pursue research without worrying about the "public utility" that results from it. More importantly, it implied that the foundations of mathematics did not lie in the sensory world but had to be constructed within a theoretical framework. At the time, however, the necessary tool—mathematical logic—was lacking.
Around 1850, the British mathematicians Augustus de Morgan and George Boole laid the foundations by developing an algebra of logic. Charles Peirce, whose father was the first renowned American mathematician, later disseminated Boole’s ideas and introduced propositional logic.
