Solved cryptogram
Any set of rules big enough to do arithmetic will contain truths it can never prove.
Mathematics Facts, sourced to MacTutor History of Mathematics.
Solve it yourself
This fact is a cryptogram here: 68 letters over 21 different ones, graded hard.
Or go to the puzzle’s own page first.
What it means
Goedel's 1931 result ended a program that had run for a hundred years, the hope that all of mathematics could be reduced to a finite set of axioms and mechanical steps. His method was to encode statements about proofs as statements about numbers, then build a sentence that says of itself that it has no proof. If the system is consistent, that sentence is true and unprovable inside it. Adding it as a new axiom only produces another one.
The claim comes from MacTutor History of Mathematics.
- SourceMacTutor History of Mathematics
- CollectionMathematics Facts
- Difficultyhard
- Length68 letters, 21 of them different
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