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 is not only stranger than we imagine, it is stranger than we can imagine. And less provable.
I believe in the power of reason, even when reason itself is limited.
My life's work has been to show that some things are simply beyond our grasp, mathematically speaking.
The greatest joy in life is to discover something new, especially if it breaks all previous assumptions.
I am a man of few words, but many symbols.
The world would be a much simpler place if everything could be proven.
They say ignorance is bliss. I say ignorance is an unproven hypothesis.
I find human behavior far less logical than any mathematical system.
My theorems are not meant to be understood by everyone, only by those who truly appreciate the beauty of incompleteness.
The only thing I'm certain of is that nothing is certain, except my own existence, perhaps.
I have spent my life trying to find the limits of logic, and I believe I have succeeded.
There are objective truths in mathematics.
The mind is more than the brain.
Formal systems are incomplete.
The existence of undecidable propositions shows that the human mind infinitely surpasses any finite machine.
There is a reality independent of our constructions.
The world is not a chaos.
Mathematics is a science of objective reality.
There is a meaning to existence.
Truth is not merely a matter of convention.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).