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Mathematical logic is a sub-branch of symbolic logic in which the foundations of the assumptions upon which rest mathematics itself are investigated and made rigorous.
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The roots of mathematical logic originate with the work of George Boole, who first made an attempt to formally define the rules of logic in mathematical terms.
Its development as a serious discipline was directly inspired by Hilbert's program, as an attempt to create a consistent and complete set of axioms that would render mathematics completely rigorous.
This did not go the way David Hilbert had planned, as Gödel's Incompleteness Theorems proved that there were always going to true statements in mathematics which could never be proved.
- 1951: Willard Van Orman Quine: Mathematical Logic (revised ed.) ... (next): Introduction
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $1$ The Nature of Logic
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $1$: Introduction: $\S 1.1$: The origins of mathematical logic
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): mathematical logic