# Bhāskara II

**Type:** Person  
**Domain:** Indian Mathematics  
**Born:** 1114 CE, Vijjadavida, India  
**Died:** c. 1185 CE  
**Codex URL:** /mathematics/indian-mathematics/bhaskara-ii/  
**Entry status:** Live — v1.0 (2026-05-27)

## Summary
Head of astronomical observatory, Ujjain. Completed the chakravāla method for Pell's equation. Worked with concepts anticipating differential calculus. Wrote Līlāvatī and Bījagaṇita.

## Key contributions
- Completed chakravāla method (Pell's equation), predating Lagrange's 1766 European theory by ~600 years
- Showed a quantity's "differential" vanishes at a maximum — anticipates calculus concept
- Proposed a/0 = ∞ (khahara)
- Pythagorean theorem rearrangement proof ("Behold!")

## The Līlāvatī legend
Popular story that the book is named after his daughter is unverified in Bhāskara's own writing — treated as legendary by historians (Plofker, Hayashi).

## The calculus debate
Bhāskara's results are genuine and impressive but do not constitute the general, unifying theory Newton/Leibniz later developed (Katz 1995, Plofker 2009).

## Sources
### Tier 1
- Plofker, K. (2009). *Mathematics in India*. Princeton University Press. pp. 181-211.
- Colebrooke, H.T. (1817). *Algebra, with Arithmetic and Mensuration*.
### Tier 2
- Katz, V.J. (1995). Ideas of calculus in Islam and India. *Mathematics Magazine*.
### 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/*