Book Reviews

A Selected Works of Gurugovinda Chakravarti onAncient and Medieval Indian Mathematics

Pradip Kumar Majumdar and Rajib Chakravarty (compiled and edited),Vivekananda Book Centre, Bankim Chatterjee Street,

Kolkata-700073, 2014, 214 pages, Price: Rs. 240/-.

The book contains reprints of sevenarticles of Gurugovinda Chakravarti, Editor’sviews & additional supplements of original verseswith notes (References), and Bibliography.Gurugovinda Chakravarti (1905-1938) appears tobe originally from Chittagong and was born in thesame year when Bengal was partitioned by theBritish Colonial Regime, and the nationalmovement against this partition was at its peak.In his short span of life of 33 years, Gurugovindashowed a tremendous national spirit not only as asuccessful advocate of Calcutta High Court afterhis graduation from St. Xaviars College, and Lawdegree from Calcutta, but also by his persistentzeal to bring-forth the achievements of earlyIndian mathematics in his spare time. He evensubmitted a thesis for the Griffith Memorial Prizeof the Calcutta University on Relation of Hinduand Chinese Mathematics, which still remainsunknown and unpublished. He prepared articlesbased on his studies of early Sanskrit sources andpublished them in journals like Bulletin of theCalcutta Mathematical Society, BhandarkarOriental Research Institute, Journal of theDepartment of Letters (Calcutta University). Thearticles are very informative, exhaustive & originalin nature, and show his scholarship in both archaicSanskrit language and Mathematics besides otherareas.

The articles are mainly based on Sanskritsources and maintain a period coverage roughly

from antiquity to 12th century AD. The first threearticles discuss on the progressive series, termsfor area, and geometrical methods of quadratureappearing in the Śulbasūtras, giving an ideamainly of A.P., G.P., their types, gradual evolutionalong with the rules for summation, including useof technical terms, and how the values of √2, and√10 are obtained by quadrature method. The fourthand fifth articles are on Surds and Fractions withdetails of their algebraic operations on addition,subtraction multiplication, division, and analysisof different methods of approximations. The sixthdeals with the methods of permutation and

combination, with application of ;

nCr + nCr+1= n+1Cr+1; . The last article on

‘Typical Problems’ is equally interesting, for itidentifies more than fifteen mathematicalproblems from Sanskrit sources and found theirparallels in other countries like Greece, China andLatin Europe. The solutions of these problemsinvolve summation of progressions, quadraticequations, solution of indeterminate equationswhich have however not been discussed. TheVedic Sahitās, Śulbasūtras, Jaina, Buddhistsources, besides the works of Āryabhaa, BhāskaraI, Brahmagupta, Bakhshāli Ms, Mahāvīra, Śrīpati,Bhāskara II were used in general. On the problemsof series, surd, permutations and combination,further extension has been made by Datta, as

Indian Journal of History of Science, 50.1 (2015) 154-155 DOI: 10.16943/ijhs/2015/v50i1/48118

BOOK REVIEWS 155

revised by Shukla (IJHS, 27.3-4, 1992-1993).Some of the rules of the Indian works foundsimilarities with those of al-Khwarizmi, al Bīrūnī,Fibonacci (1202 AD) and others have also beenhinted indicating the possibility of transmissionof knowledge.

The section on references, containing theoriginal quotations (both in Devnagari and Romanscripts) with English translation wherevernecessary, is supplied by the editors to supportthe merit and authenticity of the statements madein the original. The editors have done a marvelousjob and must be thanked for adding thissupplement. The notes added by the editors withquotations, and even diagrams with additionalmaterial in the form of rational have made thenotes quite interesting. Editors’s view on thepapers are short and equally meaningful.

There is a great need for similar such bookshaving compilations of earlier well knowncontributors. A few other Bengali scholars madegreat names for their active contributions onancient Indian sciences before and duringGurugovinda Chakravarti’s life time, they are:Acharya P.C. Ray (1861-1944) on chemicalsciences; Sir Brojendranath Seal (1864-1938 ) onpositive sciences; Prabodh Chandra Sengupta(1876-1962), Sukumar Ranjan Das, Sarada KantaGanguli, Jyotish Chandra Ray, on astronomy;Bibhuti Bhushan Datta (1888-1958), and N.K.Mazumdar on mathematics; and many others. Thefirst two scholars have published books of theirown. About 50 articles are published by Datta andSengupta separately on their own fields, lists ofwhich along with biographical details are alreadycompiled and published by R.C. Gupta (GaitaBhārati, 1, 1979, 31-35) and HistoriaMathematics, 7, 1980, 126-133 respectively).

What is urgently required is a similar suchcompilations/ volumes/website containing all thearticles of Senguta, Datta and others. Similar suchsurvey may be done for other areas. This willundoubtedly make a foundation in the studies ofhistory of science, besides avoiding of repetitionsof original materials again and again. This isimportant to encourage research in the field amongyounger generation of scholars and to search fornew materials. Apart from this, it will also be ofgreat help to train core groups engaged in earlyand medieval history of science engaged indifferent research centres and universities to buildup and coordinate further studies in the field. Thishas been rightly emphasized by the editors.

The book has however failed to supplyoriginal verses from sources like Bhaddevatā (edwith Eng tr by Macdonell, Harvard, 1904), Jainasources on Kalpasūtra (of Bhadrabāhu), AntagadaDasāo (ed by Barnett, 1907), Pthudaka’scommentary on the Brāhmasphua-siddhānta ofBrahmagupta and so on. Some spelling mistakesalso occur [Āghana, to be corrected as Aghana(non-cubic), p.7; ‘theese’, to be corrected as‘these’, p. 67, line 9 from top; nC4 to be correctedas nCr, p. 94 and so on]. We would expect thatthose lacuna could be met in case a second editionis planned. In spite of these small drawbacks, thisvolume will be an asset to any individualresearcher in the field or for any library interestedon original sources on early Indian mathematics.The Publisher is also to be thanked to keep theprinting font of the book quite attractive and theprice quite low.

A K BagEditor

Indian Journal of History of ScienceINSA, New Delhi-110002

Email: akbag99@gmail.com