Book Reviewed: The Origins of Mathematics by V. Lakshmikantham and S. Leela

Mathematics and astronomy in ancient India This is a short book of ninety-two pages that focuses on Indian mathematics and astronomy very briefly. The account is not complete; the work of well-known Kerala School of Mathematics is largely ignored. The title of the book is somewhat misleading, but I recommend the authors review the material and include all important aspects to point the superiority of Indian mathematicians over Greek and European mathematics. The dates of several historical events in Indian math and astronomy are overestimated and not supported by archeological and historical evidence. Chapters 5 and 6 show a significant trigonometry which could be confusing to an average reader interested in learning about significance of Indian contribution to mathematics, astronomy, physics, cosmology, philosophy, economics, and architecture. Mathematics in ancient India has a rich and remarkable history, characterized by profound discoveries and developments that influenced mathematics worldwide. Ancient Indian mathematicians made significant contributions to arithmetic, algebra, geometry, and astronomy. Some the highlights include the decimal number system, including the concept of zero as a numeral; the Aryabhatiya by Aryabhata (476 CE) introduced techniques for solving quadratic equations, trigonometry, and approximations of π (pi); Brahmagupta (7th century CE) formalized the rules for operations involving zero and negative numbers; the Sulba Sutras (800-500 BCE) that described astronomical rules for constructing fire altars using geometric principles; Bhaskara I (7th century CE) and Bhaskara II (12th century CE) expanded algebraic understanding, solving complex equations and introducing concepts like cyclic quadrilaterals; and Bhaskara II’s Bijaganita ("Seed Counting") was a pioneering text in algebra. Indian astronomers integrated mathematics into their study of planetary motion and eclipses. The Surya Siddhanta, an ancient astronomical text, contains advanced calculations for planetary orbits. The Kerala School of Mathematics (14th–16th centuries) led by Madhava of Sangamagrama made early advancements in calculus, including power series expansions for trigonometric functions. Their work predated European calculus by centuries. Ancient scriptures like Rigveda contain mathematical ideas presented in philosophical terms: the hymn of Creation (Nasadiya Sukta) – Rigveda 10.129; The Cosmic Order Hymn Rigveda 1.164; and Purusha Sukta - Rigveda 10.90. These are the earliest philosophical concepts found in the ancient Vedic scripture that later led to six schools of Hindu philosophy culminating in Vedanta. The physical reality described by theoretical physics and is identical to Advaita Vedanta. The most fundamental entity of the cosmos is the Pure Consciousness out of which matter, and energy appears in spacetime. Guided by the laws of physics cosmos and life evolve.