Vedic Sources of the "Vedic Mathematics" – Part II
Summary
The article "Vedic Sources of the 'Vedic Mathematics' – Part II" examines the mathematical concepts present in Vedic texts and compares them with the system presented in the modern book "Vedic Mathematics." The author, Dr. N. M. Kansara Sambodi, argues that while the book "Vedic Mathematics" by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaj (BKTM) is not directly derived from the Vedas, it is based on a traditional interpretation of the Sulba-sutras. The Sulba-sutras, which are part of the Kalpa Vedanga and Brahmanic geometrical manuals for constructing sacrificial altars, contain valid proofs of the Pythagorean theorem. The author notes that the names of the altars are as old as the Taittiriya Samhita and even the Rigveda. The article discusses the evidence of various mathematical operations found in Vedic sources. The Yajurveda mentions fractions, while the Shatapatha Brahmana details fraction operations. The Vedic hymns reference arithmetic principles, such as the consecutivity of numbers from 1 to 10 in the Atharvaveda, and the addition of numbers with multiples of 10. The author also highlights that the Sulba-sutras show the beginnings of algebraic notions, including the use of the Quadratic Equation for altar enlargement or reduction, and operations with surds. Furthermore, the Vedic Hindus were interested in permutations and combinations, which was activated by the considerations of Vedic meters, with Pingala's Chandah-sutras (200 B.C.) containing a method called meru-prastara, which is the same as Pascal's triangle. The author then compares the terminology of medieval mathematicians like Aryabhata I, Brahmagupta, Bhaskara I, Mahavira, Aryabhata II, Sridhara, Sripati, Bhaskara II, and Narayana with that of the "Vedic Mathematics" book. The medieval mathematicians composed works such as the Aryabhatiya, Brahmasphuta-siddhanta, Mahabhashya, Laghubhashkarya, Ganita-sara-samgraha, Mahasiddhanta, Patiganita, and Tripatika. The article lists twenty operations (parikarma) and eight determinations (vyavahara) in calculation, including addition, subtraction, multiplication, division, square, square-root, cube, and cube-root. Finally, the article addresses the claims made in the "Vedic Mathematics" book. The author notes that the word "all" in the title "Sixteen Simple Mathematical Formulae from the Vedas, to all mathematical problems" has led to a great deal of confusion. The book deals with arithmetic and computation, but it should not be confused with pure mathematics. The author argues that to be a great mathematician is not just to be a rapid computer, but to possess the intellectual effort of analyzing the solution. The book deals only with a small aspect of mathematics and its claim to give one-line answers to all mathematical problems is false. The author suggests that BKTM may have come across some Sulba-sutra traditionally associated with the Atharvaveda, picked up some sixteen sutras initially, and later on some other thirteen or more sutras, worked on it for eight years from a mathematical point of view, and discovered the mathematical application of the sutras. The author concludes that the book has its own mathematical excellence and intrinsic importance, and its novelty has inspired several scholars to delve into the new area of research created by it.
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Conclusion
The article demonstrates that Vedic texts contain foundational mathematical concepts, including fractions, arithmetic operations, geometry, and algebra, which predate medieval scholars. The Sulba-sutras, in particular, reveal advanced geometrical rules, such as the Pythagorean theorem and the squaring of the circle, alongside early algebraic notions and the concept of irrational numbers. While the modern "Vedic Mathematics" system is not directly derived from these ancient sources, it represents a novel, intuitive mathematical interpretation of traditional sutras. The author concludes that although the system lacks rigorous proof and is often criticized for its historical claims, its intrinsic mathematical value and the new research it has inspired highlight the enduring intellectual legacy of ancient Indian exact sciences.