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)
The human mind is capable of understanding the infinite.
I believe in the possibility of a universal mind.
Either mathematics is too large for the human mind or the human mind is too small for mathematics.
The more I think about it, the more I realize that the world is a very strange place.
There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.
My work on undecidability has shown that there are true mathematical statements that cannot be proven.
The existence of God is a consistent hypothesis.
I am convinced that there are objective mathematical truths.
The continuum hypothesis is undecidable.
The future is not predetermined.
Mathematics is a part of physics.
The world is not a closed system.
There are no contradictions in mathematics.
The human mind can grasp the infinite.
The universe is not absurd.
My incompleteness theorems show the limitations of formal systems.
Time travel is theoretically possible in some models of general relativity.
The foundations of mathematics are not purely formal.
The concept of truth is fundamental.
Mathematics reveals the structure of reality.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).