☮ ♥ ♬ 🧑💻“Gödel presented his #CompletenessTheorem on 6 September 1930 at conference in Königsberg (today known as Kaliningrad in Russia). #Hilbert was at a different conference in Königsberg and gave a grand speech on 8 September, in which he famously rejected the idea that there are limits to human knowledge. “We must know. We will know,” he said – words that were eventually engraved on his tombstone.
There is just one problem with Hilbert’s rallying cry to mathematicians – Gödel had already destroyed all hope of it the day before. Not on 6 September, when he presented his completeness theorem, but on 7 September. During a discussion with fellow logicians that day, #Gödel let slip that he had identified the possibility of “undecidable” statements – ones that cannot be proven true given a certain set of axioms, but crucially cannot be proven false either. This was the genesis of an idea that would limit the horizons of #mathematics forever.”
#Proof / #MathematicalObjects / #JacobAron <https://newscientist.com/article/2522297-the-man-who-ruined-mathematics/> (paywall) / <https://archive.md/s18W0>
The man who ruined mathematics
The incompleteness theorem is accepted as part of the mathematical canon today, but columnist Jacob Aron says it was a bombshell when Kurt Gödel first introduced it. Gödel’s seminal work directly contradicted one of the great minds of mathematics and limited the field forever
Sakaé Fuchino 🔵
