Kurt Gödel
Proved incompleteness theorems transforming mathematical logic
Most quoted
"Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."
— from On Formally Undecidable Propositions of Principia Mathematica and Related Systems, 1931
"Either mathematics is incompletable in this sense, that its evident axioms can never be exhausted by a finite number of formal rules, or else there exist mathematical problems which are undecidable in principle."
— from On Formally Undecidable Propositions of Principia Mathematica and Related Systems I, 1931
"The incompleteness theorems are a profound statement about the limits of formal systems and the indispensable role of human intuition and insight in mathematics."
— from On Formally Undecidable Propositions of Principia Mathematica and Related Systems I, 1931
All quotes by Kurt Gödel (527)
Leibniz was right about a universal language.
The consistency of arithmetic cannot be proved arithmetically.
Life's meaning is in the pursuit of truth.
Set theory without choice is incomplete.
Mathematics requires creativity beyond algorithms.
The incompleteness is a feature, not a bug.
God has a plan for the universe, and it's mathematical.
Formalism fails where intuition succeeds.
My theorem changed the foundations forever.
Truth lies beyond the reach of proof in finite systems.
I am a Platonist in mathematics.
The axiom of reducibility is unnecessary.
Happiness comes from understanding the cosmos.
Undecidable propositions exist in every strong system.
Einstein and I walked to work discussing only physics and philosophy.
The generalized continuum hypothesis is consistent.
Logic alone cannot found mathematics.
Faith and reason are compatible.
My health prevents more discoveries.
The infinite fascinates me.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).