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 empirical science. I believe in a priori truth.
The more I think about it, the more I am convinced that the continuum hypothesis is undecidable.
My work on undecidable propositions has shown that there are limits to what can be known by formal systems.
I am very much interested in the problem of the existence of God.
The world is not a machine.
I have found a new proof of the existence of God.
I am convinced that there is an objective reality independent of our minds.
The human mind is not a computer.
I believe in the possibility of an afterlife.
The world is full of mysteries.
I am very much interested in the problem of time travel.
The universe is not a random collection of atoms.
I am convinced that there are other intelligent beings in the universe.
The human mind is capable of understanding the universe.
I believe in the possibility of miracles.
The world is a beautiful place.
I am very much interested in the problem of free will.
I am convinced that there is a purpose to life.
The human mind is not limited by the laws of physics.
I believe in the possibility of telepathy.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).