> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/math.timeline.md).

# 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.Göde**l'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