The Ganitasarakaumudi was composed in the early fourteenth century at Delhi by the Jain Polymath thakkura Pheru who held a high position at the treasury of Ala al din Khalji, and contributed to the popularization of Science by producing six treatises in Apabhramsa verse on diverse scientific subjects.
The Ganitasarakaumudi extends the range of mathematics far beyond the traditional framework. The first three chapters are structured like the earlier Mathematical texts in Sanskrit and treat traditional topic like fundamental operations, fractions, series, proportion, plane and solid geometry and so on. The remaining two chapters contain supplementary material derived from diverse areas of contemporary life where numbers play a role such as mathematical riddles, conversion of dates from Vikrama era to Hijri era, magic squares, and most remarkably average yield per bigha of several kinds of grains and pulses – topics that were not touched upon in any mathematical text before.
The present volume offers, besides an introduction, a critically emended text, an English Translation, and a detailed mathematical commentary where efforts were made to interpret Pheru’s formulas and algorithms in modern notation. There are several appendices including a comprehensive glossary index.
Of the few scholars working on Sanskrit texts on astronomy and mathematics
today, the largest group is concentrated in Japan in the ancient city of Kyoto.
This group has the admirable habit of meeting once a week to study an original
text. One of the valuable fruits of this joint study is the Studies in Indian
Mathematics: Series, Pi and Trigonometry (Tokyo, 1997), which was awarded
the Publication Prize by the Mathematical Society of Japan in 2005.
When I spent a semester at Kyoto University as Visiting Professor of Indian
Science in 2002, I was invited to join the group, then consisting of Professors
Michio Yano, Takao Hayashi and Takanori Kusuba. I had met Professor Yano
for the first time in 1976 during the International Symposium on Aryabhata
in New Delhi; since then we have been meeting often in India and elsewhere.
Professor Kusuba and I were together at Brown University in the academic year
1992-93. I came to know Professor Hayashi in 1986 through his marvellous PhD
thesis on the Bakhshali Manuscript.
For our weekly meetings, we chose the Ganitasara-kaumudi of Thakkura
Pheru who held a high position in the treasury of Ala' aI-Din Khalji at Delhi.
This work is not only the first mathematical work to be composed in Middle
Indic, but it also extends the range of mathematics beyond the traditional frame-
work. In those six months, we translated the text and drafted a mathematical
commentary. It took, however, some time to prepare our work for publication,
as all of us were busy with various academic and administrative duties in the
intervening years. The work is now complete, thanks to the diligent efforts of
Professor Hayashi who acted as the editor of the team, put together our individual inputs and prepared the press copy in LATEX. It is also he who suggested
the name for our group.
The group name SaKHYa emphasizes the warm bond of friendship that developed among us during the past several years through the common interest in the history of science; it has an additional significance as well, for it was generated mathematically by the permutation of the initial letters of our names. Permutation and combination have been important elements in Indian mathematics; they also played a significant role in systems of classification in other sustras, Indeed, they were employed, for the very first time - in the classification of poetic metres - by Pingala Naga in his Chandahsutra, where he taught, among others, how to arrange the permutations in a tabular form called prastura. The initial letters of our four names produce a set of permutations
(caturaksara-prastara) consisting of 24 terms. From the fourteenth term of this
series is derived the group name SaKHYa.
SaKHYa is now pleased to offer to the historians of mathematics this edition, translation, mathematical commentary, and a detailed glossary-index of Thakkura Pheru's Ganitasara-kaumudi, 'The Moonlight of the Essence of Mathematics,' also known as Ganitasara, 'The Essence of Mathematics.'
As we complete this joint venture, we recall the memory of those scholars
who inspired us in this task in various ways. Sri Bhanwar Lal Nahata of Kolkata
discovered the writings of Thakkura Pheru in a single manuscript copy and published them in collaboration with Sri Agar Chand Nahata. When I brought out Thakkura Pheru's Rayanaparikkha with an English translation and commentary in 1984, Bhanwar Lal-ji sent me a warm letter of appreciation, which I greatly cherish, and shared with me his own notes on Pheru's other writings. The link between Bhanwar Lalji and me was Sri Hazari Mull Banthia of Kanpur from
whom I learnt much about contemporary Jainism.
We also remember fondly our mentor and friend Professor David Pingree; the four of us had the privilege of spending some time with him at Brown University; it is his monumental Census of the Exact Sciences in Sanskrit which
first introduced us to Thakkura Pheru's scientific writings. We dedicate our
book to the memory of Professor David Pingree.
We are highly indebted to Professor Irfan Habib who took a keen interest in
our work and very kindly translated for us relevant passages from lndo-Persian
sources, especially from the Dostur al-Albab fi ilm al-Hisab by Hajji Abd al-
Hamid Muharrir Ghaznavi.
Our sincere thanks are due to Mr Ramesh Jain of the Manohar Publishers
& Distributors for agreeing to bring out this work; he and his staff deserve all
praise for the fine production of the volume. Thakkura Pheru composed the
Ganitasura-kaumudi in Delhi; we are happy that our study of this work also is
being published from Delhi.
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