Solved cryptogram
The diagonal of a square cannot be written as a fraction of its side, and the Greeks proved it.
Mathematics Facts, sourced to Wolfram MathWorld.
What it means
Assume it can, in lowest terms, and a short argument shows that both the top and the bottom of the fraction must be even, which contradicts the assumption. The discovery was a genuine shock to a school of thought built on the idea that all quantities are ratios of whole numbers, and the story that its discoverer was drowned at sea for it is almost certainly a later invention.
The claim comes from Wolfram MathWorld, and the page it comes from was read on 2026-08-27 to confirm it still says this.
This is not the kind of claim that goes out of date, which is why it was set as a puzzle rather than a fact with a shelf life.
Solve it yourself
This fact is a cryptogram here: 75 letters over 21 different ones, graded medium.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length75 letters, 21 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldhard, 65 letters
- Wolfram MathWorldmedium, 79 letters
- Wolfram MathWorldmedium, 81 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 70 letters
- Wolfram MathWorldmedium, 74 letters
- Wolfram MathWorldmedium, 76 letters
- Wolfram MathWorldhard, 75 letters