Kurt Gödel

Mathematics Austrian-American 1906 – 1978 527 quotes

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)

Creativity defies computation.

Lecture 1951

Life without meaning is empty.

Reflection

Undecidability is everywhere in logic.

Later work

I trust few, but seek truth.

Personal note 1960

The ontological argument can be formalized.

Proof 1970

Mathematics is poetry of logical thought.

Metaphorical

No last words recorded, but his silence spoke of caution.

Deathbed 1978

The speed of light is not the limit for thought.

Conversation

All truths are consistent, but not all provable.

Theorem 1931

I fled Europe for freedom.

Letter 1940

The mind's eye sees the unprovable.

Philosophy

Logic is the key to reality.

Belief

My proof took years of solitude.

Autobiography 1931

Humor in math? The absurdities of infinity.

Joke

Einstein said I was the greatest logician.

Recall 1950

The foundations are shaky, but beautiful.

Reflection

I believe in rational theology.

Work 1970

Politics? Only if logical.

View

Wisdom is knowing the limits.

Aphorism

My life was dedicated to truth.

Final reflection 1978