Math: TIMELINE

• BCE: Aristotle, the roots of formalised logic

• 4 BCE Euclid "Elements" aximatic system of geometry

• 1860s Hermann Grassmann showed that many facts in arithmetic could be derived from more basic facts about the successor operation and induction.

• 1879: Frege's Begriffsschrift introduces propositional and predicate calculus

• 1881, C.S.Peirce provided Axiomatization of Natural Number Arithmetic (ANNA)

• 1884: Frege's Foundations of Arithmetic, math in formal logic

• 1888: Richard Dedekind another proposal for ANNA

• 1889: G.Peano published a simplified version of Dedekind's ANNA proposal as a collection of axioms in his book, The Principles of Arithmetic Presented by a New Method.

• 1900: At the International Congress of Mathematicians in Paris David Hilbert sets a plan to formalize math and establish completness, consistency and decidability, presents 23 math problems.

• 1903: Frege's Begriffsschrift reprint with Russell's paradox

• 1906: Bertrand Russell The Theory of Implication: gave a different complete axiomatization of propositional logic

• 1908: E.Zermelo proposes the first axiomatic set theory, Zermelo set theory

• 1909: Truth tables appear explicitly in writings by Eugen Müller

• 1912: C.I.Lewis, traces of modal propositional logic

• 1913: Principia Mathematica by Russell and Whitehead

• 1913: H.M.Sheffer, define all logic operators in terms of one (NAND)

• 1917: Jean Nicod, axiomatize propositional logic using the Sheffer stroke and only a single axiom schema and single inference rule.

• 1917: Jan Łukasiewicz, three-valued propositional logic

• 1921: Emil Post uses truth tables extensively

• 1921: Ludwig Wittgenstein Tractatus Logico-Philosophicus, in which truth tables and truth-functionality are prominently featured.

• 1926: Ernst Mally, deontic logic

• 1927: Second edition of Principia Mathematica, deriving math truth using axioms, inference rules of formal logic

• 1920: Löwenheim-Skolem theorem

• 1930: Herbrand universe, Herbrand interpretation, reduction of FOL's SAT formulas to propositional SAT problems.

• 1929: K.Gödel's Completeness theorem. Presburger: theory of natural numbers is decidable, algorithm to determine proposition's truth value

• 1930: D.Hilbert in Konigsberg: "Wir müssen wissen, wir werden wissen"

• 1931: K.Gödel's Incompleteness theorem, Entscheidungsproblem

• 1936: A.Church, lambda calculus, Church-Rosser theorem proved

• 1936: A.Church and A.Turing independently showed that a general solution to the decision problem is impossible.

• 1942: joint paper and introduction of Category theory by Saunders Mac Lane and Samuel Eilenberg.

• 1946: ENIAC computer

• 1960: Jaakko Hintikka, first systematic treatment of epistemic logic

• 1970s: A.R.Anderson, N.D.Belnap, relevance propositional logic

• 1970-80: N.C.A.da Costa, Graham Priest, paraconsistent logic