# Srinivasa Ramanujan

**Type:** Person  
**Domain:** Indian Mathematics  
**Born:** 22 December 1887, Erode, Tamil Nadu, India  
**Died:** 26 April 1920, Kumbakonam, India (aged 32)  
**Codex URL:** /mathematics/indian-mathematics/ramanujan/  
**Entry status:** Live — v1.0 (2026-05-27)

## Summary
Self-taught genius producing thousands of original results in number theory, infinite series, modular forms. Collaborated with G.H. Hardy at Cambridge (1914-1919). Died at 32.

## The 1913 letter
Sent ~120 unproven theorems to Hardy at Cambridge. Hardy: results "must be true, because if they were not true, no one would have the imagination to invent them."

## Key contributions
- Hardy-Ramanujan partition function asymptotic formula (circle method)
- Ramanujan tau function; Ramanujan conjecture proved by Deligne (1974, via Weil conjectures)
- Rapidly-converging π series (each term adds ~8 correct digits)
- Mock theta functions (1920 final letter) — explained by Zwegers (2002 thesis)
- Taxicab number: 1729 = 1³+12³ = 9³+10³

## The Lost Notebook
Discovered by George Andrews, 1976, in Trinity College Library — ~600 additional formulas from his final year.

## Sources
### Tier 1
- Berndt, B.C. (1985-1998). *Ramanujan's Notebooks*. Parts I-V. Springer.
- Hardy, G.H. (1940). *Ramanujan: Twelve Lectures*. Cambridge University Press.
### Tier 2
- Kanigel, R. (1991). *The Man Who Knew Infinity*. Scribner.
- Andrews, G.E. and Berndt, B.C. (2005-2018). *Ramanujan's Lost Notebook*. Parts I-V.

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