World Wars and the AtomScience & Math Gödel's incompleteness theorems 1931Major Any consistent system of mathematics strong enough for arithmetic contains truths it cannot prove. ▲ MattersSaveShareTrace roots Longest chain: The Big Bang → First stars ignite → Supernovae seed heavy elements → The Sun forms → Earth forms → First oceans → First life → Photosynthesis evolves → Great Oxidation Event → Complex cells (eukaryotes) → Multicellular life → First animals → Cambrian Explosion → First vertebrates → Jawed fish → Fish walk onto land → The amniotic egg → The Great Dying → Dinosaurs appear → Asteroid ends the dinosaurs → Early primates → Apes split from monkeys → Human line splits from chimpanzees → Walking upright → First stone tools → Genus Homo appears → Homo erectus → Control of fire → Habitual fire and cooking → Homo sapiens appears → Complex language → Natufian villages → Oldest known bread → Agriculture begins → Irrigation → Uruk and the first cities → Cylinder seals → Writing (cuneiform) → Babylonian mathematics → Babylonian astronomical diaries → Thales and natural philosophy → Trial and death of Socrates → Plato's Academy → Aristotle's Lyceum → Alexander's conquests → Alexandria founded → Library of Alexandria → House of Wisdom → Al-Khwarizmi and algebra → Descartes and analytic geometry → Calculus → Binary arithmetic → Boolean logic → Gödel's incompleteness theorems Community notesLoading notes… Learn more ranked by votesDocumentplato.stanford.eduGödel's incompleteness theorems (Stanford Encyclopedia of Philosophy) ↗Editor's pickBookErnest Nagel and James R. NewmanGödel's Proof ↗Editor's pickBookRebecca GoldsteinIncompleteness: The Proof and Paradox of Kurt Gödel ↗Editor's pickVideoSearch on YouTubeGödel's incompleteness theorems explained ↗Editor's pick