Catalan numbers (Mingantu's original use)
Números de Catalan (uso original de Minggatu)
- Date
- c. 1730 · confidence low
- Place
- Beijing, China
- Credited to
- Mingantu (Ming Antu); rediscovered in Europe by Leonhard Euler (1751) and named after Eugène Catalan
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Around 1730 the Mongol mathematician and astronomer at the Qing court, Mingantu, used this number sequence to express the series expansion of sin(2α) and sin(4α), in a work his student Chen Jixin completed in 1774 and which was not published until the 1830s. In Europe, Euler independently arrived at the same sequence in 1751 while studying polygon triangulation, and the definitive name came a century and a half later with Eugène Catalan.
Mingantu's work remained unknown in the West, which attributed the sequence to Euler (1751) and the name to Catalan; Wikidata flags a date inconsistency with the person, likely due to the uncertain chronology of Mingantu's life (d. 1763) and the late publication (1774-1830) of his work.
What it led to
- European rediscovery by Euler (1751)
- Definitive naming by Eugène Catalan (19th century)
- 66 combinatorial interpretations documented by Richard Stanley
Built on
- Trigonometric infinite series brought to China by Pierre Jartoux in the early 18th century