Wilson's theorem
Teorema de Wilson
- Date
- c. 1000 (Ibn al-Haytham) / 1771 (demostración de Lagrange) · confidence high
- Place
- Berlin, Prussia (present-day Germany)
- Credited to
- Joseph-Louis Lagrange (first proof); statement attributed to John Wilson and announced by Edward Waring in 1770
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
The theorem characterizing prime numbers — an integer p greater than 1 is prime if and only if (p-1)! + 1 is a multiple of p — was announced without proof by Edward Waring in 1770, crediting his former student John Wilson; Lagrange gave the first rigorous proof a year later at the Berlin Academy. Arab mathematician Ibn al-Haytham had already formulated it around the year 1000, unknown in Europe.
Ibn al-Haytham had essentially formulated the same result around the year 1000, centuries before Wilson and Waring, with no known connection to the European rediscovery.
What it led to
- Primality tests
- Algebraic number theory