With this contribution of von Neumann, the axiomatic system of the theory of sets became fully satisfactory, and the next question was whether or not it was also definitive, and not subject to improvement. A strongly negative answer arrived in September 1930 at the historic mathematical Congress of Königsberg, in which Kurt Gödel announced his first theorem of incompleteness: the usual axiomatic systems are incomplete, in the sense that they cannot prove every truth which is expressible in their language. This result was sufficiently innovative as to confound the majority of mathematicians of the time.
యాక్సియోమాటిక్ వ్యవస్థ పూర్తి కాదని గోడెల్ ప్రకటన యొక్క కేంద్ర ఇతివృత్తం ఏమిటి?
they cannot prove every truth which is expressible in their language