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)
There is a reality independent of our minds.
The world is intelligible.
The concept of truth is absolute.
Logic is the foundation of all knowledge.
The human intellect is capable of reaching beyond any formal system.
The incompleteness theorems show that mathematics is not a finite game.
The concept of number is fundamental.
The universe is governed by laws.
There is an order in the world.
The human mind is not limited by algorithms.
The foundations of mathematics are not arbitrary.
The concept of infinity is essential to mathematics.
The world is not a product of chance.
There is a purpose in the universe.
The human mind can transcend its own limitations.
The incompleteness theorems are a proof of the richness of mathematics.
The concept of proof is central to mathematics.
The universe is not chaotic.
There is meaning in existence.
The human mind is not a mere computer.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).