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 postulates.
The concept of set is not a mere mental construct.
The world is not a random collection of atoms.
There is an objective reality to numbers.
The human mind can perceive universal truths.
The incompleteness theorems are a profound insight into the nature of formal systems.
The concept of truth is not a social agreement.
The universe is not a meaningless accident.
There is a divine order.
The human mind is not a mere biological machine.
The foundations of mathematics are not arbitrary rules.
The concept of infinity is not a mere abstraction.
The world is not a random occurrence.
There is an objective reality to sets.
The human mind can grasp the infinite in a non-finite way.
The incompleteness theorems are a fundamental result in logic and mathematics.
The concept of proof is not a mere game of symbols.
The universe is not a product of blind forces.
There is a higher intelligence.
The human mind is not limited by its physical embodiment.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).