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 world is not a mere collection of sense data.
The human mind is capable of understanding infinite concepts.
Mathematics is not just a tool for science, but a way of understanding reality.
The universe has a purpose.
The concept of causality is fundamental to our understanding of the world.
The laws of nature are not arbitrary.
The human mind can transcend the limitations of formal systems.
The concept of number is not a human invention.
The concept of infinity is not a paradox.
The human mind has access to a realm of objective ideas.
The laws of mathematics are discovered, not invented.
The universe is intelligible.
The concept of certainty is attainable.
The human mind is not limited by its physical structure.
The concept of proof is fundamental to mathematics.
The universe is ordered.
The concept of knowledge is not relative.
The human mind has an innate capacity for reason.
The concept of truth in mathematics is objective.
I am convinced that there are such things as absolutely undecidable propositions.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).