Mathematics as Known to The Vedic Samhitas (An Old Book)

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This book is written with the view to examine and ascertain whether the Vedas really contain any consideration on mathematics in the real sense. The study is purposefully limited to nine Vedic texts which go by the name Samhitas. The present study deals with the arithmetic’s only. As one goes through the Vedic samhitas and examines and interprets the mathematical data, one cannot but be impressed by the high stage of mathematical development in those ancient times. The books contains following chapters Introductory, Scope of the present work, The sequence or the-serial order of the numbers, Characteristic features of the Vedic number system, The methods of counting, The ordinal numbers, Numbers without Number-words, Number as adjectives, Types of Mathematical Operations, Signs and Sign words for Mathematical operations, The concept of sets or groups, Examples of addition, Examples of subtraction, Examples of multiplication, Examples of division, The concept of fractions, Squares, Square-roots, Cubes, Cube-roots, Arithmetic and Geometric progression, Zero, The base 10, The concept of position, The journey of Zero, Resume, Appendix-A, Appendix-B, Bibliography and Abbreviations and Subject Index.

Dr. M.D. Pandit is presently at the centre of Advanced Study in Sanskrit, University of Poona, Pune.

We encounter with mathematical numbers at the very outset when we start studying the Sanskrit language. Every student of Sanskrit language has to imbibe well first its syntax. Of all the four types of syntaxes found in the different languages of the world, viz. agglutinative, inflexional with the two varieties of internal and external inflection, positional or isolating and the polysynthetic or incorporating types of syntaxes, the Sanskrit language exhibits the inflexional-and there too the external inflection predominantly-type of syntax. The Sanskrit language thus, according to Schlegel, displays "an organic" character, "the words of which were built round modifiable roots by means of intimately linked inflection". The result of this highly rigid and complicated nature of the inflection of the Sanskrit words has been that besides the linguistic meaning they convey, they also convey the correct gender, number and mutual relations so accurately that there is practically no chance of any confusion in understanding the correct meanings of the words. Thus in Sanskrit, the inflexional category viz. what is called as the pratyaya in Pariini's grammar is a compulsory category. This is the most important principle, underlying the Papinian analysis of the Sanskrit language, as Patanjali in his bhasya on the Papinian sutra, 1.2.45. (arthavad adhatur apratyayah pratipadikam ) puts it; cf. Patafijali on 1.2.45: pratyayena nityasarhbandhat. nitya-sambandhiv etas, arthau prakrtih pratyaya iti. pratyayena nityasambandhat kevalasya prayogo na bhavisyati.

It can be seen, therefore, that of all the six grammatical categories called vyavasitas by Patafijali, viz. dhatu, pratyaya, agama, adega, pratipadika and nipata2, the category of pratyaya plays the most important role in building up the syntax of the language and thereby in conveying the correct meaning of the words. As Vaiyakarauabhusanasara puts it: prakrtipratyayau saha artham brutal); tayoh pratyayarthasya pradhanyam.

Because of the pivotal role that pratyaya plays in signifying the meaning, it is invested with different powers. It thus signifies the linga or gender, the vacana or the number, vibhakti or the mutual karaka-relations between words, the kala or the tense in the case of dhatus and lastly, the svara or the accent in the Vedic Sanskrit. In other words, all these meanings of gender, number, relations, tense and accent reside or dwell in the pratyayas', in the language and consequently in Panini's grammar. It is because of the different powers of signifying the meaning, which are invested in the category of pratyaya, that the use of single word like devau signifies the meanings of 'masculine, dual, nom or acc., and accent' simultaneously; it is because of this power of the pratyaya that the word gacchati signifies simultaneously the meanings of 'singular, 3rd person, present tense and its initial position in the beginning of the foot of a verse'. The inflectional nature of the Sanskrit language has made the syntax so rigid with a potential capacity of signifying the meaning as accurately as possible that there is no chance of misunderstanding a sentence, so far as the above-mentioned meanings are concerned.

We have great pleasure in associating ourselves with the publication of Mathematics As Known To The Vedic Sarhhitas by Dr. M.D. Pandit. The work is the culmination of author's concentrated efforts to investigate into Vedic Mathematics. A book on Vedic Mathematics is usually associated with fast mental calculations by the use of the Sutras. Sutras are not everything as Dr. Pandit points out. The author makes an earnest attempt to understand the scientific mind of the Vedic people. Mathematics is the Queen of all Sciences. An understanding of the mathematics of the Vedic people will, therefore, shed a light on their scientific temper. By restricting himself to the Saithitas the author has made some interesting and useful contributions to the study of mathematics. By a skilful employment of symbols of present day mathematics with Vedic words, the author has attempted to explain the Vedic Mathematics. Interestingly, the author points out how the Vedic people could have had two intrepretations of Zero - one as a number and the other as a "place value substituted for absence of rank". The idea of counting numbers in two different ways-ascending and descending orders as found in the Sarhhitas-has been well brought out. "The word nava-data (for 19) implies the starting point of count in data (10) and ascending is done by nine (nava) steps to arrive at 19. EkonavimSati or ekannavirhtati indicates counting from viridad (20) and going down by one step to 19". Taking advantage of the linguistic intrepretation of numbers, the author has also introduced the notion of simple and compound numbers. For example, 1 to 9 are simple while 10, 11, 12 etc., are compound numbers. This is perhaps typical of Sanskrit language. It seems there is still much scope for the study of Vedic Mathematics. Dr. Pandit has shown the way. With the recent awareness of the use of Sanskrit in general and Vedic Mathematics in particular in computer science, the present work is very valuable.

In a work like this one has to rely on the Vedic texts only, as Dr. Pandit himself points out; there is no way of testing the accuracy of the literary evidence provided by the Vedas.

Dr. M.D. Pandit is an extremely devoted scholar and is dedicated to the work on Vedic Mathematics. We have had many valuable discussions on the subject. His enthusiasm and self-confidence have overwhelmed us. He has restricted himself only to the arithmatical aspect of Vedic Mathematics. We hope, the other aspects, such as algebraic, geometric etc. will be considered by him in his later works.

**Contents and Sample Pages**