This articleneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Timeline of mathematical logic" – news ·newspapers ·books ·scholar ·JSTOR(October 2025) (Learn how and when to remove this message)

Atimeline ofmathematical logic; see alsohistory of logic.

• 1847 –George Boole proposes symbolic logic inThe Mathematical Analysis of Logic, defining what is now calledBoolean algebra.^[1]
• 1854 – George Boole perfects his ideas, with the publication ofAn Investigation of the Laws of Thought.
• 1874 –Georg Cantor proves that the set of allreal numbers isuncountably infinite but the set of all realalgebraic numbers iscountably infinite.His proof does not use his famousdiagonal argument, which he published in 1891.
• 1895 – Georg Cantor publishes a book about set theory containing the arithmetic of infinitecardinal numbers and thecontinuum hypothesis.
• 1899 – Georg Cantor discovers a contradiction in his set theory.

• 1904 -Edward Vermilye Huntington develops theback-and-forth method to prove Cantor's result that countable dense linear orders (without endpoints) are isomorphic.
• 1908 –Ernst Zermelo axiomatizesset theory, thus avoiding Cantor's contradictions.
• 1915 -Leopold Löwenheim publishes a proof of the (downward)Löwenheim-Skolem theorem, implicitly using theaxiom of choice.
• 1918 -C. I. Lewis writesA Survey of Symbolic Logic, introducing the modal logic system later called S3.
• 1920 -Thoralf Skolem proves the (downward)Löwenheim-Skolem theorem using theaxiom of choice explicitly.
• 1922 -Thoralf Skolem proves a weaker version of theLöwenheim-Skolem theorem without the axiom of choice.
• 1929 -Mojzesj Presburger introducesPresburger arithmetic and proving its decidability and completeness.
• 1928 -Hilbert andWilhelm Ackermann propose theEntscheidungsproblem: to determine, for a statement offirst-order logic whether it is universally valid (in all models).
• 1930 -Kurt Gödel proves thecompleteness andcountable compactness of first-order logic for countable languages.
• 1930 -Oskar Becker introduces the modal logic systems now called S4 and S5 as variations of Lewis's system.
• 1930 -Arend Heyting develops anintuitionistic propositional calculus.
• 1931 –Kurt Gödel proveshis incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent.
• 1932 -C. I. Lewis andC. H. Langford'sSymbolic Logic contains descriptions of themodal logic systems S1-5.
• 1933 - Kurt Gödel develops two interpretations of intuitionistic logic in terms of aprovability logic, which would become the standard axiomatization of S4.
• 1934 -Thoralf Skolem constructs anon-standard model of arithmetic.
• 1936 -Alonzo Church develops thelambda calculus.Alan Turing introduces theTuring machine model proves the existence ofuniversal Turing machines, and uses these results to settle theEntscheidungsproblem by proving it equivalent to (what is now called) thehalting problem.
• 1936 -Anatoly Maltsev proves the full compactness theorem for first-order logic, and the "upwards" version of theLöwenheim–Skolem theorem.
• 1940 – Kurt Gödel shows that neither thecontinuum hypothesis nor theaxiom of choice can be disproven from the standard axioms of set theory.
• 1943 -Stephen Kleene introduces the assertion he calls "Church's Thesis" asserting the identity ofgeneral recursive functions with effective calculable ones.
• 1944 -McKinsey andAlfred Tarski study the relationship betweentopological closure and Booleanclosure algebras.
• 1944 -Emil Leon Post introduces thepartial order of theTuring degrees, and also introduces Post's problem: to determine if there arecomputably enumerable degrees lying in between the degree of computable functions and the degree of the halting problem.
• 1947 -Andrey Markov Jr. andEmil Post independently prove the undecidability of theword problem for semigroups.
• 1948 -McKinsey andAlfred Tarski study closure algebras for S4 and intuitionistic logic.

• 1950 -Boris Trakhtenbrotproves that validity in all finite models (the finite-model version of the Entscheidungsproblem) is also undecidable; here validity corresponds to non-halting, rather than halting as in the usual case.
• 1952 - Kleene presents "Turing's Thesis", asserting the identity of computability in general with computability by Turing machines, as an equivalent form of Church's Thesis.
• 1954 -Jerzy Łoś andRobert Lawson Vaughtindependently proved that a first-order theory which has only infinite models and iscategorical in any infinite cardinal at least equal to the language cardinality iscomplete. Łoś further conjectures that, in the case where the language is countable, if the theory is categorical in an uncountable cardinal, it is categorical in all uncountable cardinals.
• 1955 -Jerzy Łoś uses theultraproduct construction to construct thehyperreals and prove thetransfer principle.
• 1955 -Pyotr Novikov finds a (finitely presented) group whoseword problem is undecidable.
• 1955 -Evertt William Beth developssemantic tableaux.
• 1958 -William Boone independently proves the undecidability of the uniform word problem for groups.
• 1959 -Saul Kripke develops a semantics for quantified S5 based on multiple models.
• 1959 -Stanley Tennenbaumproves that all countable nonstandard models ofPeano arithmetic are nonrecursive.
• 1960 -Ray Solomonoff develops the concept of what would come to be calledKolmogorov complexity as part of his theory ofSolomonoff induction.
• 1961 –Abraham Robinson createsnon-standard analysis.
• 1963 –Paul Cohen uses his technique offorcing to show that neither thecontinuum hypothesis nor theaxiom of choice can be proven from the standard axioms of set theory.
• 1963 -Saul Kripke extends his possible-world semantics tonormal modal logics.
• 1965 -Michael D. Morley introduces the beginnings ofstable theory in order to proveMorley's categoricity theorem confirming Łoś' conjecture.
• 1965 -Andrei Kolmogorov independently develops the theory ofKolmogorov complexity and uses it to analyze the concept of randomness.
• 1966 -Grothendieck proves theAx-Grothendieck theorem: any injective polynomial self-map ofalgebraic varieties over algebraically closed fields is bijective.
• 1968 -James Ax independently proves the Ax-Grothendieck theorem.
• 1969 -Saharon Shelah introduces the concept ofstable andsuperstable theories.
• 1970 -Yuri Matiyasevich proves that the existence of solutions toDiophantine equations isundecidable
• 1975 -Harvey Friedman introduces theReverse Mathematics program.

• History of logic
• History of mathematics
• Philosophy of mathematics
• Timeline of ancient Greek mathematicians
• Timeline of mathematics

• History of mathematics
• Mathematics timelines
• Mathematical logic

• Articles with short description
• Short description with empty Wikidata description
• Articles needing additional references from October 2025
• All articles needing additional references
• Use dmy dates from September 2020