More meditations on mathematics and God and joyous amazement at hoo ancient Indian mathematicians combines math, verse and playful puns seamlessly. Lila anyone? Touches of mythological allegories enhance the charm of Bhāskarācārya’s Bījagaṇita. Whilediscussing properties of the mathematical infinity, Bhāskarācārya draws a parallel withLord Viṣnu who is referred to as Ananta (endless, boundless, eternal, ininite) and Acyuta (firm, solid, imperishable, permanent): During pralay (Cosmic Dissolution), beings merge in the Lord and during sṛṣti (Creation), beings emerge out of Him; but the Lord Himself — the Ananta, the Acyuta — remains unaffected. Likewise, nothing happens to the number ininity when any (other) number enters (i.e., is added to) or leaves (i.e., is subtracted from the infinity; it remains unchanged. The use of a mystic metaphor to explain the mathematical principle ∞ ± x =∞ reflects the vibrant culture of the bygone era. Perhaps the spiritual culture had prepared the Indian mind for, and probably suggested to it, the concept of the mathematical infinity (or zero!) with its curious properties. Again, in order to emphasize the importance, power and profundity of algebra, Bhāskarācāryabegins the treatise with an Invocation involving an interesting “pun” on the words Sāṁkhyāḥ (the Sāṁkhya philosophers as well as the experts in saṁkhyā, the science of numbers),Satpuruṣa (the Self-Existent Being as well as the wise mathematician), bīja (root/cause as well as algebra) and vyakta (the manifested universe as well as the revelation of an unknown quantity).Thus, through the opening verse, Bhāskarācārya venerates the Unmanifested — he Self-Existent Being of the Sāṁkhya philosophy — who is the originator of intelligence and the primal Cause of the known or manifested universe; and, through the very same words, Bhāskarācārya pays tribute to the wise mathematician who, using algebra, solves a problem (i.e., reveals or manifests an unknown quantity)! The importance of algebra is reiterated at the end of Bījagaṇita. Bhāskarācārya remarks that2algebra is the essence of all mathematics, is full of virtues and free from defects; and that cultivation of algebra will sharpen the intellect of children. He concludes with the exhortation “paṭha paṭha” (Learn it, learn it) for the development of intelligence. In this connection, I may mention here that one of our greatest contemporary mathematicians Shreeram S. Abhyankar (b. 1930) acknowledges the influence of Bhāskarācārya during his formative years. Abhyankar fondly recalls how his father (S.K. Abhyankar) used to teach him mathematics by reciting to him lines from Bhāskarācārya’s ext Līlāvatī and how he used to memorise them when he was around ten years of age. Bhāskarācārya’s Bījagaṇita not only makes us aware of the great advancements made by ancient Indian algebraists, it also gives us a feel for the charming atmosphere in which mathematical research and discourse — at both basic and advanced levels — used to take place in ancient times. While a study of Bījagaṇita will be enriching and inspiring for all cultured students of mathematics, a careful analysis of the treatise will also provide valuable insights to historians and scholars in general. The above excerpt is from an article by Prof Amartya Kumar Dutta was published in the magazine Prabuddha Bharata, in the Sept 2007 issue (pages 545–546). It is reproduced in the magazine At Right Angles published by Azim Premji Universityby kind permission of its editor, Swami Narasimhananda. For information on this publication, kindly refer to the website : advaitaashrama.org
Posted on: Sat, 03 Jan 2015 00:17:00 +0000
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