[INDOLOGY] Help with 'Vedic' mathematics

McComas Taylor McComas.Taylor at anu.edu.au
Tue Jan 14 23:54:00 UTC 2020

Dear Colleagues,

An outstanding student of mine, Lila-manjari Dasi, has asked for help with decoding a manuscript on 'Vedic' mathematics. If you can help, please respond to Lila at:

lila.manjari.dasi.108 at gmail.com.

Thanks in advance,



Here is the message from Lila and her collaborator, Kenneth Williams:

Sri Bharati Krishna Tirthaji (1884 - 1960) was a Shankaracharya at Puri who in addition to his many other achievements reconstructed an ancient system of mathematics which he called 'Vedic Mathematics'. This system is extraordinary in its range and simplicity. The branches of mathematics are shown to be unified in unexpected ways and the system offers a new approach to mathematics education, being easy, natural and very much encouraging creativity.

Tirthaji write sixteen books expounding this system but these were somehow lost and we have only one introductory book which he wrote in his later life. He also wrote examples and notes in an old diary. Those of us researching this system are seeking to reconstruct his reconstruction, from the one book. But there are some intriguing notes in Sanskrit in the diary which could shed valuable light onto some of the things mentioned in the book but not explained.

We would like to ask for your assistance in translating these short sections of Sanskrit. There is no doubt that there are applications of Vedic mathematics yet to be discovered and Tirthaji's Sanskrit notes could be key to opening up these areas for research.

Please find attached four pages from the diary. The text is handwritten and rather unclear in places but even if you can only give the gist of the meaning or some words used it may help us to interpret what is being said.


More specifically, the text in need of translation is:
Page 133: The devanāgarī between the stamp and the equations
Page 146 (on spherical triangles): The two half lines devanāgarī above the equations at the bottom
Pages 139-140 (on astronomy): All the DN below the stamps

Another attachment is with the 16 VM sūtras:


In case there would be math terms among the scanned scribbles that you might not be familiar with, I thought you could use the sūtras as a reference - to help recognize the DN of some terms that might be found there as well (if that made sense).

Other Sanskrit maths terms used in Tīrtha's book are:
Apara - multiplier (P.36)
Purva - multiplicand (P.36)
Sunyam - zero
Anka - coefficient (P.157)
Dhwaja Ghata - power (P.157)
Purva - original index (P.191)
Caramanka - units digit (P.221)
Sahayak - auxiliary (fraction) (P.255)
Vestana - osculator (P.273)
Viparita - negative osculator (P.286)
Dwandwa Yoga - duplex (P.305)

McComas Taylor
Associate Professor
Reader in Sanskrit
College of Asia and the Pacific
The Australian National University
WSC Website<http://www.wsc2021.com.au>| McC Website<https://sites.google.com/site/mccomasanu/>
Tel: +61 2 6125 3179

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