# Mādhava of Saṅgamagrāma

**Type:** Person  
**Domain:** Indian Mathematics  
**Active:** c. 1340 – c. 1425 CE  
**Location:** Saṅgamagrāma, Kerala, India  
**Codex URL:** /mathematics/indian-mathematics/madhava/  
**Entry status:** Live — v1.0 (2026-05-27)

## Summary
Founded the Kerala School of Astronomy and Mathematics. Discovered infinite series for π, sine, cosine roughly 250 years before Gregory/Leibniz/Newton. No original writings survive; known through successors (Nīlakaṇṭha Somayājī, Jyeṣṭhadeva).

## Key contributions
- **Mādhava-Leibniz series:** π/4 = 1−1/3+1/5−1/7+... (~1400 CE; Europe: Gregory 1671, Leibniz 1673)
- **Mādhava-Gregory series:** arctan(x) = x−x³/3+x⁵/5−...
- **Sine/cosine series:** equivalent to Taylor series (Taylor, 1715, Europe)
- **π to 11 decimal places** using accelerated convergence techniques

## How we know his work
No original manuscript survives. Known via Nīlakaṇṭha's *Tantrasaṅgraha* (c.1500) and Jyeṣṭhadeva's *Yuktibhāṣā* (c.1530, written in Malayalam), which explicitly credit Mādhava and provide detailed derivations.

## The calculus debate
Raju (2007) argues Kerala School developed functional calculus equivalent. Mainstream historians (Plofker, Katz, Bressoud) acknowledge sophistication but argue a general, unifying theory (with Fundamental Theorem) is absent from surviving texts — active scholarly debate, not settled.

## Transmission question
Speculative claims (Raju) of Jesuit transmission to Europe are not accepted by mainstream historians; European rediscoveries regarded as independent.

## Sources
### Tier 1
- Plofker, K. (2009). *Mathematics in India*. Princeton University Press. pp. 217-253.
- Sarma, K.V. (ed./transl.) (2008). *Gaṇita-Yukti-Bhāṣā of Jyeṣṭhadeva*. Springer.
### Tier 2
- Katz, V.J. (1995). Ideas of calculus in Islam and India. *Mathematics Magazine*.
- Bressoud, D. (2002). Was calculus invented in India? *College Mathematics Journal*.
### Tier 3
- Joseph, G.G. (2011). *The Crest of the Peacock*. 3rd ed.

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*Mathematics Codex entry v1.0 — added 2026-05-27 — thecodex.expert/mathematics/*