Annals of Mathematical Sciences and Applications

Volume 3 (2018)

Number 1

Special issue in honor of Professor David Mumford, dedicated to the memory of Jennifer Mumford

Guest Editors: Stuart Geman, David Gu, Stanley Osher, Chi-Wang Shu, Yang Wang, and Shing-Tung Yau

Accuracy of Ptolemy’s Almagest in predicting solar eclipses

Pages: 7 – 29



Jayant Shah (Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.)


Predicting eclipses, especially solar eclipses, was one of the important challenges in ancient and medieval astronomy. Using a statistical approach, David Mumford tested the accuracy of the Chinese algorithm for predicting solar eclipses as formulated in the Shoushihli. I carried out a similar analysis of the Indian Tantrasaṅgraha using his appoach. In this paper, I report on the accuracy of Ptolemy’s algorithm and compare it with the Shoushihli and the Tantrasaṅgraha.


Almagest, Ptolemy, ancient eclipse prediction, medieval Chinese astronomy, Shoushihli, medieval Indian astronomy, Tantrasaṅgraha

2010 Mathematics Subject Classification

Primary 85-03. Secondary 01A20, 01A25, 01A32.

I thank David Mumford for introducing me to this subject and making his computer code for eclipse prediction by modern and the Shoushihli’s algorithms available. The code was essential for carrying out the comparisons reported here. I also thank Lovy Singhal of the Tata Institute of Fundamental Research for his help with figures in this paper.

Received 6 March 2017

Published 27 March 2018