Speaking of the #Entscheidungsproblem, I feel a bit of Schadenfreude for (one of) its author(s), David Hilbert, who was absolutely convinced that mathematics was complete and provable from its own axioms. Hilbert famously has the phrase “Wir müssen wissen—wir werden wissen!” (we must know—we will know!) engraved as his epitaph, as a defiant cry against the phrase “ignorabus et ignorabimus” (we do not know, and we will not know).

Alan #Turing (in addition to Gödel) put the last nail in Hilbert’s hopes by proving that it was impossible to decide the answer to certain classes of computation problems, and therefore mathematics must be incomplete.

Ignorabus et ignorabimus. Deal with it. https://mastodon.social/@mcnees/110594075888924099

Douglas R. Hofstaedter:
#Goedel, #Escher #Bach?

#AlanTuring kennt ja jeder, aber who the f*** is #KurtGödel und das Entscheidungsproblem in:

#Turing (1937): On #Computeable #Numbers with an Application to the #Entscheidungsproblem
https://doi.org/10.1112/plms/s2-42.1.230

„Wir müssen wissen, und wir werden wissen.“ ... Alles, was #wahr ist, wäre auch #beweisbar.
Kurt Gödels #Unvollständigkeitssatz erschütterte in den 1930er Jahren die #Fundamente der mathematischen Überzeugungen.

https://www.youtube.com/watch?v=eUywVvl_1oE