Mathematics, 200 B.C.-600 A.D. (Max Dehn)
N. Ganesan
Mathematics, 200 B.C.-600 A.D.
The American Mathematical Monthly, Vol. 51, No. 3 (Mar., 1944), pp. 149-157
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12. Mathematics in India. We can give only a very short review of mathematical
activities in India during this period. The outstanding mathematicians
of this country were primarily astronomers; we mention only Aryabhatta (about
500 A.D.) and Brahmagupta (about 600 A.D.). Whereas Diophantus treated
problems of finding rational values for algebraic relations of second and higher
degree, the mathematicians of India treated the problem of finding integers
satisfying linear relations. One recognizes that such problems are indeed of interest in astronomical investigations. It is probable that the Indians were depending on the research work of Babylonian astronomers.
Probably the Indians, in their development of a new symbolism for the
writing of integers, were also indebted to the Babylonians. They determined
the integer by expanding it into a power series with 10 as basic number:
n = [sum of a series]
(a_i <10). Then they represented the integer by the symbol a_m***a_2a_la_o. The old Babyloniansh ad already represented integers in this way, using 60 as the basic number. But their representation was ambiguous because
they did not use symbols for those coefficients which are equal to zero.
We find our sign 0 already in the astronomical tables of Ptolemy, and we also
find it used as abbreviation for "nothing" (ouden) 
in Heron's writings. But the systematic use of the symbol 0 came from India to the Arabs and through them to Europe, and had an inestimable influence upon all kinds of scientific and practical computations.
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