The Vedic era marked the beginning of a new era of advancement in science and technology. During the Vedic period, science emerged from the religious level. Vedic people influenced the development of Indian science. Natural phenomena in the framework of rainfall, the appearance of the sun, the moon, changes in season, and agriculture began with the study of natural phenomena in the context of rainfall, the appearance of the sun, the moon, changes in season, and agriculture. As a result, ideas about physical processes and natural forces evolved, which are today being investigated as specialized issues within a variety of branches of physical science.

Advances in mathematics, astronomy, astrology, medicine, surgery, and other fields were substantial in ancient India by any measure. 

• Bhaskara I was a Indian mathematician  who lived in the 7th century between 600–680 BC
• When evaluating an extraordinary rational approximation for the function of sine while noting on Aryabhata’s work, his employment of a circle for the zero in the Hindu-Arabic decimal system is considered quick and excellent
• There is very little information about Bhaskara’s life. He was born near Saurashtra in Gujarat and passed away in Ashmaka 
• He was educated by his father in astronomy. He was a follower of Aryabhata I and was considered to be one of the most renowned scholars of Aryabhata’s astronomical school
• Two treatises were written by him namely, the Mahabhaskariya and the Laghubhaskariya
• He also wrote commentaries on the work of Aryabhata I entitled Aryabhatiya Bhashya. The Mahabhaskariya contains eight sections managing numerical cosmology
• The topics that are dealt with in the book include the longitudes of the planets; the relationship of the planets with each other and also with the bright stars; the lunar crescent; sun oriented and lunar obscurations; and rising and setting of the planets
• Bhaskara I suggested a formula that gave an accurate value of Sin.  The formula is:  sin x = 16x (p – x)/[5p2 – 4x (p – x)]
• Bhaskara I wrote the Aryabhatiya Bhashya in 629, which is a commentary on the Aryabhatiya written by Aryabhata I
• Bhaskara I commented only on the 33 verses of Aryabhatiya which is about mathematical astronomy and discusses the problems of the first degree of indeterminate equations and trigonometric formulas
• While discussing Aryabhatiya he discussed cyclic quadrilaterals. He was one of the first mathematicians to discuss quadrilaterals with unequal sides and with none of the opposite sides parallel
• Bhaskara I did not accept pi value and believed that pi had an irrational value which later proved to be true
• Some of the major contributions that Bhaskara I made in the field of mathematics are: numbers and symbolism, the categorization of mathematics, the names and solution of the first degree equations, quadratic equations, cubic equations and equations having multiple unknown values, symbolic algebra, the algorithm method to solve linear indeterminate equations which were suggested by Euclid later, and formulated certain tables for solving equations that occurred in astronomy

Some important works of Bhaskara I

• Discovery of Circle for Zero, positional arithmetic, the approximation of sine
• The three treatises that were written by him on the works of Aryabhata (476–550 CE )

• The Mahabhaskariya (“Great Book of Bhaskara”)
• The Laghubhaskariya (“Small Book of Bhaskara”)
• The Aryabhatiyabhashya (629)

Zero, positional arithmetic, approximation of sine: 

• The depiction of numbers in a positional system is one of his most significant mathematical discoveries. Before Bhaskara I, Indian astronomers had known about the basic positional depictions for almost 500 years, but the numbers were recorded in words, images, or graphical renderings rather than figures
• For example, Use of moon to represent number 1, and pair of things representing number 2 and so on
• Bhaskara I clarified a number given in this framework, using the formula ankair api by repeatedly composing it with the initial nine Brahmi numerals,  wherein small circles were used as zeroes
• The Brahmi numerals system, which dates from the 3rd century B.C is an ancient system for writing numerals and is considered to be the direct graphic ancestor of the modern Indian and Hindu-Arabic numerals 
• Since 629, the decimal system has been known to Indian scientists. Although Bhaskara I did not invent it, he was the main individual to utilize the Brahmi numerals in a logical commitment in Sanskrit

The Mahabhaskariya (“Great Book of Bhaskara I”)

• The Mahabhaskariya is considered to be a work on Indian mathematical astronomy that consists of eight chapters dealing with mathematical astronomy
• The book deals with topics such as the longitudes of the planets; association of the planets with each other, conjunctions among the planet and the stars; the lunar crescent; also, lunar obscurations; and rising and setting of the planets
• This treatise also contains chapters that illustrate the sine approximation formula
• Both the treatises, Mahabhaskariya  and Laghubhaskariya”), are astronomical works in verse
• Interestingly enough, parts of Mahabhaskariya were later translated into Arabic

The Aryabhatiyabhashya (629)

• The Aryabhatiyabhashya is Bhaskara I’s analysis on the Aryabhatiya. The Aryabhatiya is a composition on cosmology written in Sanskrit. It is supposed to be the main surviving work of the fifth-century Indian mathematician Aryabhata. It is assessed that the book was composed around 510 B.C. Bhaskara I wrote the Aryabhatiya Bhashya in 629
• Bhaskara I’s comments critique the 33 verses in Aryabhatiya which is considered to be about mathematical astronomy
• He also explains the problems of indeterminate equations and trigonometric formulas. While discussing Aryabhatiya, he discussed cyclic quadrilaterals. He was one of the first mathematicians to discuss quadrilaterals whose sides were unequal and none of their opposite sides were parallel
• Bhaskara I explain in detail Aryabhata’s method of solving linear equations with illustrative examples. He stressed upon the need for providing mathematical rules

Conclusion

Bhaskara 1 was the first mathematician to use the Hindu decimal method to write numbers. He looked into Aryabhata’s work and worked on the Sine Function, giving a more accurate value for Sine.