Timeline of mathematical logic

A timeline of mathematical 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 shows that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his method was not his famous diagonal argument, which he published three years later. (Nor did he formulate set theory at this time.)
* 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 axiomizes 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.
* 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.