Irrationality of the square root of 2
Irracionalidad de la raíz de 2 (inconmensurabilidad)
- Date
- c. 450 BCE · confidence low
- Place
- Metapontum, Magna Graecia, Italy
- Credited to
- Hippasus of Metapontum (Pythagorean tradition)
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
The diagonal and side of a square share no common measure: there is no fraction whose square is 2. The first crisis of foundations, which separated number from geometric magnitude.
The legend of Hippasus's drowning for revealing the secret is a late addition; the proof by parity appears in Aristotle.
What it led to
- Eudoxus's theory of proportions
- proof by contradiction
- Dedekind's real numbers
Built on
- Pythagorean theoremc. 530 BCE
- arithmetic of odd and even numbers