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)
I don't believe in the empirical method. I believe in a priori knowledge.
The world is rational.
Mathematics is the science of the a priori.
The human mind is not a machine.
Either mathematics is too hard for man or man is too hard for mathematics.
The true reason for the incompleteness of mathematics is that the human mind is not a machine.
The concept of set is a primitive concept, not definable in terms of other concepts.
The continuum hypothesis is undecidable from the axioms of set theory.
The development of mathematics is not a mechanical process.
The axioms of set theory are true.
The universe is not a random collection of events.
There are absolute truths.
The world is not absurd.
The existence of God is a matter of pure reason.
Time travel is possible in certain cosmological models.
The future is not determined.
The human mind can grasp infinite concepts.
The limits of formal systems are inherent.
Mathematics is an objective reality.
The universe is not a closed system.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).