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 universe has a rational structure.
Our intuition plays a crucial role in mathematical discovery.
Mathematical objects exist independently of our minds.
The human condition involves a striving for understanding.
There is a purpose to life.
The mind is not limited by the physical.
Beauty in mathematics is a sign of its truth.
The human being is more than a biological organism.
There is an order in the universe.
The human mind can transcend its limitations.
Truth is not relative.
The search for truth is a fundamental human endeavor.
Consciousness is not an illusion.
There is an ultimate reality.
The human spirit yearns for meaning.
The mind is not reducible to algorithms.
Mathematical truth is discovered, not invented.
The human quest for knowledge is boundless.
There is a deeper reality beyond the empirical.
The human mind possesses an inherent capacity for reason.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).