Kurt Gödel 1931
To every w-consistent recursive class k of
formulae there correspond recursive class-signs R,
such that neither v Gen r, nor Neg(v Gen r)
belongs to Flg(k) (where v is the free variable of r).
Gödel Incompleteness Theorem.
Translation:
Any consistent axiomatic system does include
propositions whose truth is undecidable within that
system and its consistency is, hence,
not provable within that system.
Translation of a translation:
Either mathematics is too big for the human mind or
the human mind is more than a machine.
Any formal system is either inconsistent or incomplete.
in a universe where knowledge defeats us,
what can we do but be what we are?
I don't believe in natural science.
[Said to physicist John Bahcall.]
Bei mir gibt es nicht viel Neues;
ich hatte in letzter Zeit eine Menge mit Behörden zu tun.
Kurt Gödel, when being called to the Nazi's military service.