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 constructions.
The concept of set is not a mere convention.
The world is not a dream.
There is a reality beyond our perceptions.
The human mind can grasp abstract concepts.
The incompleteness theorems are not a limitation of mathematics, but a revelation of its depth.
The concept of truth is not relative.
The universe is not meaningless.
There is a higher order to things.
The human mind is capable of intuition.
The foundations of mathematics are not arbitrary conventions.
The concept of number is not a social construct.
The world is not a simulation.
There is an objective reality to mathematics.
The human mind can understand the infinite.
The incompleteness theorems are a testament to the power of human reason.
The concept of proof is not a mere game.
The universe is not a random accident.
There is a design in the universe.
The human mind is not reducible to physical processes.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).