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)
I am not a philosopher; I am a logician.
The more I learn, the more I realize how much I don't know. It's a rather depressing thought, isn't it?
The greatest discovery of all time is that the universe is not logical.
I don't trust anything that can't be proven.
The only thing worse than a bad proof is a good proof that no one understands.
My work is not about proving things; it's about showing what cannot be proven.
The world is full of unprovable truths.
I am not a fan of paradoxes; they are merely contradictions in disguise.
The universe is a giant mathematical equation, and I'm just trying to solve for X.
If you can't explain it simply, you don't understand it well enough. Or it's inherently complex, like my theorems.
The only thing certain is uncertainty, especially in mathematics.
I often wonder if the universe understands my proofs.
To be a mathematician, you must be a little mad. Or perhaps, just very logical.
The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. And unprovable statements.
I prefer the company of numbers to the company of people; they are far more predictable.
My greatest fear is not that I will die, but that I will die before I prove everything.
The world is a theorem waiting to be proven, or perhaps, unproven.
I am not a genius; I am merely persistent.
The only true wisdom is in knowing you know nothing, and then proving it.
If I have seen further than others, it is by standing on the shoulders of giants, and then pointing out their logical inconsistencies.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).