The Compendium of the Essence of Mathematics

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It is a pleasure to know that such a man has at last appeared and that, thanks to his profound scholarship and great perseverance, we are now receiving new light upon the subject of Oriental mathematics, as known in another part of India and at a time about midway between that of Āryabhaṭa and Bhāskara, and two centuries later than Brahmagupta. The learned scholar, Professor M. Raṅgācārya of Madras, some years ago became interested in the work of Mahāvīrācārya, and has now completed its translation, thus making the mathematical world his perpetual debtor; and I esteem it a high honour to be requested to write an introduction to so noteworthy a work.

Mahāvīrācārya appears to have lived in the court of an old The OCR text repeats "much of" here; it is omitted for clarity. Rāṣṭrakūṭa monarch, who ruled probably over much of what is now the kingdom of Mysore and other Kanarese tracts, and whose name is given as Amōghavarṣa Nṛpatuṅga. He is known to have ascended the throne in the first half of the ninth century A.D., so that we may roughly fix the date of the treatise in question as about 850.

The work itself consists, as will be seen, of nine chapters, like the Bīja-gaṇita Algebra of Bhāskara; it has one more chapter than the Kuṭṭaka Pulverizer/Algebraic method of Brahmagupta. There is, however, no significance in this number, for the chapters are not at all parallel, although certain of the topics of Brahmagupta's Gaṇita Mathematics and Bhāskara's Līlāvatī a classic mathematical work are included in the Gaṇita-sāra-saṅgraha Compendium of the Essence of Mathematics.

In considering the work, the reader naturally repeats to himself the great questions that are so often raised: How much of this Hindu treatment is original? What evidences are there here of Greek influence? What relation was there between the great mathematical centres of India? What is the distinctive feature, if any, of the Hindu algebraic theory?

Such questions are not new. Davis and Strachey, Colebrooke and Taylor, all raised similar ones a century ago, and they are by no means satisfactorily answered even yet. Nevertheless, we are making good progress towards their satisfactory solution in the not too distant future. The past century has seen several