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)
God exists as a necessary being.
Shortage of time is the main reason for my not having done more work.
I am convinced that the search for truth is the highest goal of human endeavor.
Logic is the beginning of wisdom, not the end.
In mathematics, nothing is taken for granted; everything must be proven.
The incompleteness theorem shows the limits of formalization.
We cannot mechanize the creative process of mathematics.
The mind is not a machine.
Truth in mathematics transcends any formal system.
Gödel numbering allows us to encode statements as numbers.
The second incompleteness theorem applies to any system capable of expressing basic arithmetic.
I believe in the reality of mathematical objects.
The continuum hypothesis is independent of the standard axioms.
Mathematics is discovered, not invented.
The limits of reason are the beginning of faith.
Every consistent theory has consequences which are not provable within it.
Set theory is the foundation of mathematics.
Intuition plays a crucial role in mathematical discovery.
The universe is rational.
Proofs are the currency of mathematics.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).