Timeline of mathematical logic

A timeline of mathematical logic. See also History of logic.

19th century

• 1847 – George Boole formalizes symbolic logic in The Mathematical Analysis of Logic, defining what is now called Boolean algebra.
• 1874 – Georg Cantor proves that the set of all real numbers is uncountably infinite but the set of all real algebraic numbers is countably infinite. His proof does not use his famous diagonal argument, which he published in 1891.
• 1895 – Georg Cantor publishes a book about set theory containing the arithmetic of infinite cardinal numbers and the continuum hypothesis.
• 1899 – Georg Cantor discovers a contradiction in his set theory.

20th century

• 1908 – Ernst Zermelo axiomatizes set theory, thus avoiding Cantor's contradictions.
• 1931 – Kurt Gödel proves his incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent.
• 1940 – Kurt Gödel shows that neither the continuum hypothesis nor the axiom of choice can be disproven from the standard axioms of set theory.
• 1961 – Abraham Robinson creates non-standard analysis.
• 1963 – Paul Cohen uses his technique of forcing to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory.