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 human mind has an intuitive grasp of mathematical concepts.
The world is not meaningless.
My work has shown that Hilbert's program cannot be fully realized.
The concept of number is not merely a human invention.
The universe is not a machine.
The human mind can transcend its physical limitations.
The universe is not a closed system, but open to higher influences.
I don't believe in empirical science. I only believe in proof.
Mathematics is the science of the self-evident.
I am convinced that there are mathematical objects that are not constructible.
Logic is a tool for reasoning, not a substitute for it.
The unexamined life is not worth living, but the unexamined proof is not worth believing.
I have a great deal of difficulty with the word 'existence.'
The world is not a logical place, but it is a mathematical one.
One cannot prove everything.
The truth is out there, but it's not always provable.
I am a Platonist, but I don't believe in the existence of universals.
The only way to do great work is to love what you do. Or, in my case, to be obsessed with it.
Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.
The world is a comedy to those who think, a tragedy to those who feel. And a proof to those who are Gödel.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).