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)
Proofs must be rigorous.
The world is not random; it's ordered.
Incompleteness implies humility in mathematics.
Cantor's paradise awaits the bold.
I proved what others thought impossible.
Systems are like cages for truth.
The choice axiom enables much of analysis.
Life is a search for consistency.
Mathematics is eternal.
My work on undecidability was inspired by the liar paradox.
The mind grasps absolutes.
Paranoia? No, just caution.
Truth is objective, even in math.
The end of Hilbert's program.
I enjoy Princeton's freedom.
Infinity is not a number, but a concept.
Reason leads to God.
Formal languages are powerful yet limited.
The universe's laws are logical.
My theorems are for the future.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).