- In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history.
Mathematicians of the era sought a solid foundation for mathematics: a set of basic mathematical facts, or axioms, that was both consistent — never leading to contradictions — and complete, serving as the building blocks of all mathematical truths.
But Gödel’s shocking incompleteness theorems, published when he was just 25, crushed that dream.
Hofstadter was too artistic, the Nagel and Newman book was too long, Wikipedia is too thorough or too simple. This presentation is just right; short enough to comprehend while including the important details.
Gödel’s Proof relies on the liar paradox, "this statement is false." Gregory Chaitin produced a similar result using the Berry paradox, demonstrated by the fifty-seven letter expression "the smallest positive integer not definable in under sixty letters."
Hagen von Eitzen expanded the predicate, giving two expressions of the Gödel sentence at the bottom of the page.
A TMI letter recipient noted that Nadir Dendoune, the first Algerian to summit Everest, was perhaps the least aptly-named person in history. I found a few more: Frank Beard James Cleverly (according to detractors) Dewey, Cheatem & Howe Rev. Jaime Sin, who became a cardinal
Indeed! Thanks for posting. I didn't spot it because Hubski search is Umlaut-sensitive.
are there known mathematical entities/subsystems about which people are searching for more information or certainty, where they are failing explicitly because of this idea of incompleteness? the general idea is that godel ruined the unified theory of math, but that's a vague statement. i'd understand this better if there was an example. (i mean beside his highly abstract proof.) i've been reading this, which seems like one: https://www.nature.com/news/paradox-at-the-heart-of-mathematics-makes-physics-problem-unanswerable-1.18983 but there's a missing link in the description of turing's work with undecidable algorithms. i guess that's the peril of science journalism: at some point you just need to learn the subject.