India had many mathematicians who made great contributions. Among them we can highlight:

*Aryabhata*

In 499 he published a work entitled “Aryabhatiya”. This publication is a short volume on astronomy and mathematics, similar to Euclid's "Elements," but eight centuries earlier. These are compilations of previous results. This work contains: name of the powers of ten to the tenth; measurement rules (many wrong); triangle area; pyramid volume (incorrect); circle area; sphere volume (incorrect) and quadrilateral areas (some incorrect). We also found calculations with time measurement and spherical trigonometry.

*Brahmagupta*

He lived in central India a little over a hundred years after Aryabhata. It has little in common with its predecessor who lived in eastern India. His most important work was to generalize Heron's formula to find the area of any quadrilateral. He also worked on solving negative root quadratic equations.

*Bhaskara*

Considered the most important mathematician of the twelfth century (1114 - 1185). He filled the gaps in Brahmagupta's work. This is his first plausible answer to division by zero. In his work "Vija-Ganita" he states that such quotient is infinite. His other work, “Lilavati”, presents topics on linear and quadratic equations, determinate and indeterminate, measurement, arithmetic and geometric progressions, radicals, Pythagorean triads, among others. His work represents the culmination of previous Hindu contributions.

*Ramanujan*

After Bhaskara, India spent several centuries without mathematicians of comparable importance. Srinivasa Ramanujan (1887-1920) is considered the Hindu genius in arithmetic and algebra of the twentieth century.

Introducing a notation for an empty position, the symbol for zero, was the second step in our modern numbering system. It is not known whether the number zero (other than the symbol for the empty position) came along with the nine Hindu numerals. It is quite possible that zero originates from the Greek world, perhaps from Alexandria. Possibly it was transmitted to India after the positional system was already established there. It is interesting to note that the Mayans of the Yucatan (Mexico), prior to Columbus, used positional notation, with notation for the “empty position”. With the introduction, in Hindu notation, of the tenth numeral, a goose egg to zero, our modern integer numbering system was complete.

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The new numbering, commonly called Hindu-Arabic, is a new combination of the three basic principles, all of ancient origin:

i) decimal base

ii) positional notation

iii) encrypted form for each of the ten numerals

None of these were originally due to the Hindus, but it was because of them that the three were first linked to form our numbering system.

Another important contribution of the Hindus was the introduction of an equivalent of the sine function in trigonometry to replace the string table of the Greeks. Hindu trigonometry was a useful and accurate instrument for astronomy.

**BIBLIOGRAPHY**

BARBEIRO, Herodotus. Et alli. **History**. Ed. Scipione. 2005

BERUTTI, Flavio. **History**. Ed. Saraiva. 2004

BOYER, Carl B. **Math history**. 2nd ed. SP. Edgard Blucher, 2003.

EVES, Howard.** Introduction to the history of mathematics**. 2nd ed. UNICAMP, 2002.

LINTZ, Rubens G. **Math history**. FURB 1999

STRUIK, **Concise History of Mathematics**. Gradient 1989

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