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)
Creativity defies computation.
Life without meaning is empty.
Undecidability is everywhere in logic.
I trust few, but seek truth.
The ontological argument can be formalized.
Mathematics is poetry of logical thought.
No last words recorded, but his silence spoke of caution.
The speed of light is not the limit for thought.
All truths are consistent, but not all provable.
I fled Europe for freedom.
The mind's eye sees the unprovable.
Logic is the key to reality.
My proof took years of solitude.
Humor in math? The absurdities of infinity.
Einstein said I was the greatest logician.
The foundations are shaky, but beautiful.
I believe in rational theology.
Politics? Only if logical.
Wisdom is knowing the limits.
My life was dedicated to truth.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).