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 foundations of mathematics are not arbitrary inventions of man.
The concept of set is not a mere human invention.
The world is not a mere collection of data.
There is an objective reality to mathematical objects.
The human mind can grasp the meaning of existence.
The incompleteness theorems are a profound statement about the limits of formalization.
The concept of truth is not a matter of opinion.
The universe is not a chaotic mess.
There is a rational order to the universe.
The human mind is not a mere information processor.
The foundations of mathematics are not arbitrary human constructs.
The concept of number is not a mere symbol.
The world is not a random collection of facts.
There is an objective reality to mathematical concepts.
The human mind can grasp the absolute.
The incompleteness theorems are a profound statement about the nature of mathematical truth.
The concept of proof is not a mere mental exercise.
The universe is not a meaningless void of space and time.
There is a spiritual reality to the universe.
The human mind is not a mere biological accident.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).