Gaṇitānanda: Selected Works of Radha Charan Gupta on History of Mathematics

621 Pages·2019·11.829 MB·English

by  K. Ramasubramanian

K. Ramasubramanian Editor
Gan. itānanda
Selected Works of Radha Charan Gupta
on History of Mathematics
ṇ ā
Ga it nanda
R.C.GuptareceivestheKennethO.MayPrize(2009)
K. Ramasubramanian
Editor
ṇ ā
Ga it nanda
Selected Works of Radha Charan Gupta
on History of Mathematics
123
Editor
K.Ramasubramanian
Cell for Indian ScienceandTechnology in Sanskrit,
Department of Humanities andSocial Sciences
Indian Institute of Technology Bombay
Mumbai,India
ISBN978-981-13-1228-1 ISBN978-981-13-1229-8 (eBook)
https://doi.org/10.1007/978-981-13-1229-8
LibraryofCongressControlNumber:2018945878
©SpringerNatureSingaporePteLtd.2019
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Many hitherto hidden facts about [Indian]
mathematics were brought to light by R. C. Gupta
through the light of his brilliant expositions. May the
sun[light]oftheseexpositionsblossomthelotusminds
of scholars. Having compiled these expositions, we
present them to the scholarly world with immense
pleasure and a deep sense of gratitude. May this
offering be gracefully accepted.
Foreword
It is a great pleasure as well as a privilege to be invited to write these few words
aboutthiscollectionoftheselectedworksofProf.RadhaCharanGupta,oneofthe
great Indian scholars on the history of Indic mathematics. Dr. Gupta began his
career as a mathematics teacher in a college and was inspired by Datta & Singh’s
book on the History of Hindu Mathematics, which he came across in 1963, to
pursue the history of Indic mathematics. He went on to complete his Ph.D. thesis
under the guidance of Prof. T. A. Sarasvati Amma, whose book on Geometry in
Ancient and Medieval India represents a landmark in Indic historical studies of
mathematics.
Dr. Gupta dedicated the rest of his life to carrying out a whole series of
meticulous studies on Indic works in mathematics—studies which have stood the
testoftimeandwonhimthe7thKennethO.MayPrizeintheyear2009,awarded
bytheInternationalCommissionontheHistoryofMathematics—thefirstIndianto
get the Prize. Among his most notable contributions are the analyses of
Parameśvara’s third-order series approximations for the sine, and the methods of
Govindasvāmin for interpolating in sine tables. He has contributed articles to
StudiesinHistoryofExactSciences,volumeinhonourofDavidPingree,editedby
Burnettetal.,andWritingtheHistoryofMathematics:ItsHistoricalDevelopment,
edited by Dauben and Scriba. He has over 500 publications and has served the
world of scholarship in many different ways.
Hispersonalqualitiesofsimplicity,modesty,frugalityandgenerositymatchthe
passion and extraordinary care with which he has pursued the history of mathe-
matics. He is at once both an outstanding scholar and a sage, in the classical Indic
tradition.IcongratulatetheeditorofthisvolumeProf.K.Ramasubramanianforhis
effort in producing a collection of selected works of Dr. Gupta. The volume is
appropriately calledGaṇitānanda (roughly theJoyofMathematics)—andIcannot
help recalling how the great Bhāskara promised that his algorithms will bring
ānanda to all gaṇakas. I am sure this book will do the same.
vii
viii Foreword
We need more of the kind of authentic papers that Dr. Gupta has written with
suchdedication.Suchpapersarerare,andaregenerallyscatteredoverthescholarly
literature, so it is convenient to collect them into a volume and make them easily
available. Prof. Ramasubramanian deserves our gratitude for his effort.
October 2015 Roddam Narasimha
Preface to the Second Edition
In the year 2015, the Annual Conference of the Indian Society for History of
Mathematics (ISHM) was held at IIT Bombay. As the 80th birthday of
Prof.R.C.Guptaalsohappenedtobeinthesameyear,therewasasuggestionfrom
the then Administrative Secretary S. L. Singh1 and the President of the Society
Prof.S.G.DanithatwecouldtaketheopportunitytofelicitateProf.R.C.Guptaon
thisoccasionfortheimmensecontributionshehasmadetothestudiesinthehistory
ofmathematicsaswellastothesociety.Fromthisgerminatedtheideaofbringing
out a volume containing selected works of Prof. Gupta. Since the time interval
between the emergence of this idea and the conference was hardly two months, it
was not possible to approach any professional publisher to bring out this volume.
Hence, the volume was brought out as a publication of ISHM, and only a few
copies were printed, primarily for the distribution among the participants of the
conference and a few others.
Sincethiswasalimitededition,subsequentlyitwasfeltthatitwouldbehighly
desirable to bring out the volume through a reputed publisher and make it com-
mercially available for various institutions and individuals to purchase and get
benefitedfromitscontents.ProfessorDanitooktheleadinthisdirectionandgotin
touch with Springer. They readily agreed to publish thevolume andrequested that
I, as an editor of the volume, should consider adding a few more articles to
thevolume.However,itoccurredtome,Ithoughtthatitwouldbemoreappropriate
to seek inputs from Prof. Gupta himself in this regard. When I approached him,
hegavealistofarticlesthatcouldbeconsideredtobeincludedinthisrevisedand
enlarged edition. From this list, ten articles have been typeset and included in this
volume.Theinclusionshavebeendoneinsuchawaythatwemayfindonearticle
addedperpartofthevolumeeitheratthebeginningorattheend,exceptforPartI
and Part VIII of the previous edition.
1ProfessorShyamLalSingh,bornonJanuary20,1942,tookhislastbreathattheageof75on
October2,2017.HisdedicationtothepromotionofstudiesinthehistoryofmathematicsinIndia
andhisselflessservicetothesocietycanneverbeoverstated.Formoredetails,seeGaṇitaBhāratī
39.1(2017).
ix
x PrefacetotheSecondEdition
WhilePartIofthepreviouseditionremainsunchanged,PartVIIIisincludedwith
two very interesting articles, one on Prof. P. C. Sengupta—a doyen among the
historians of Indian mathematics and astronomy—and the other on Prof. Augustus
DeMorgan,whowasabrilliantteacher,aprolificwriterandascholarparexcellence
onmathematics,logic,andphilosophy.Incidentally,duringoneoftheconversations
withProf.Gupta,IcametoknowthathetravelledallthewaytoCalcuttatomeetthe
directheirsofProf.Senguptainordertogetanauthenticbiographicalsketchabout
their father,whichhe has nicely written up inthe form of ashort article.
Another valuableaddition that hasbeenmade tothis volumeistheinclusionof
anup-to-datebibliographyofProf.Gupta.In1996,Prof.TakaoHayashiprepareda
bibliography of the writings of Prof. Gupta which was published in Historia
Scientiarum. Then again in 2011, he compiled an updated version of it which was
publishedinGaṇitaBhāratī.Thosetwoyearsincidentallyhappenedtobethe60th
and 75th birth anniversaries of Prof. Gupta. It was so kind of Prof. Gupta that he
gave us the necessary materials to further update and present an up-to-date
bibliography of his writings while working on this revised edition. This
bibliography is provided at the end of this volume.
While preparing this edition, as done in the earlier edition, much attention was
paidtoeliminatethetyposthathadinadvertentlycreptintotheearlierpublications,
particularly in the Sanskrit passages quoted by the author as well as in the
transliteration of Sanskrit terms. It is worth mentioning the suggestion from
Prof. Gupta that this volume be supplemented with an exhaustive index. Efforts
weretakeninthisdirection,andsignificantprogresswasalsomade.Butconsidering
the current trend of both the individuals and the institutions preferring to procure
digital versions of the texts, it was suggested by the publisher that efforts towards
preparinganindexmaynotbeworthwhile.Hence,theideaofaddinganindextothe
volume was dropped.
Finally,Iwouldliketoacknowledgeallthosewhocontributedinvariouswaysto
the production of this revised and enlarged edition of Gaṇitānanda. First, I would
like to thank Prof. Dani of ISHM and Mr. Shamim Ahmad of Springer for having
takeninterestinbringingoutthisrevisededition.WorkingwithShamimhasbeena
great pleasure as he has been very gentle, highly encouraging and extremely
cooperative. Secondly, I would like to thank all my project staff, namely
Ms.SushamaSonak,Ms.SreelekshmyRanjit,Ms.LalitaHotkar,Dr.DineshMohan
Joshi and Mr. G. Periasamy, for their editorial assistance. In particular, Sushama
needsaspecialmentionforbeingkindenoughtoworkquitelateintheeveningsona
few days inorder tomeet the deadline for thesubmission ofthe manuscript.
All these project staff are supported under the auspices of Science and Heritage
Initiative (SandHI) at IIT Bombay. But for the financial support made available, I
cannot imagine venturing into the task of producing this volume, as well as others
that were produced in the past, or are in the pipeline. In this connection, I would
like to express my sincere gratitude to Ms. Amita Sharma (former Additional
Secretary, MHRD) and Prof. Devang Khakhar (Director, IIT Bombay) for getting
thisprojectsanctionedandlettingmeworkwithitwithinthenormsofthesystemin
an unfettered system.