Aryabhatta was the Gupta Era's legendary mathematician. At the age of 23, he wrote Aryabhattiya and later Arya-Siddhanta. He worked on a 3.1416 approximation for pi. He concluded in trigonometry that the area of a triangle is the product of a perpendicular with the half-side. He also observed the motions of the solar system, determining that the solar year is 365.8586805 days long. Aryabhatta remained in Pataliputra's Kusumpur.

•    Aryabhatta was a mathematician, astronomer, astrologer, and physicist who lived in the fifth century.
•    He wrote Aryabhattiya, a description of his time's mathematics. It is divided into four parts. In the first part, he explains how to use alphabets to represent large decimal numbers.
•    In the second part, we'll find challenging questions on number theory, geometry, trigonometry, and algebra, among other topics in modern mathematics.
•    The final two parts of Aryabhattiya, also known as Khagol-shastra, are about astronomy (Khagol was the famous astronomical observatory at Nalanda, where Aryabhatta studied).
•    Zero and Aryabhatta: He demonstrated that zero is more than a number; it is also a symbol and a definition.
•    He measured the distance between the earth and the moon to the nearest millimetre.
•    Negative numbers gained a new dimension with the discovery of zero.
•    Because of the necessity of crossing oceans and deserts at night, astronomy knowledge, especially knowledge of the tides and stars, was of great importance in trade.
•    He rejected the notion that our world is "Achala" (immovable) and asserted that "the universe is round and rotates on its own axis."
•    By using illustrations, he demonstrated that the presence of the sun shifting from east to west is incorrect. One example is when an individual is in a boat and the trees on the shore seem to be moving in the opposite direction.UPSC Prelims 2024 dynamic test series
•    He also said that reflected sunlight shines on the moon and planets, which was later proven in modern times.
•    He also provided a theoretical explanation for solar and lunar eclipses, dispelling the myth that they were caused by Rahhu, Ketu, or another rakshasa (demon).
•    As a result, Aryabhatta is the name of India's first satellite launched into space.

He seems to attribute the apparent movements of the heavens to the Earth's rotation in some documents. He may have assumed the planet's orbits were elliptical instead of circular.
Contrary to popular belief at the time, Aryabhata correctly asserted that the earth rotates on its axis regular and that the visible movement of the stars is a relative motion induced by the rotation of the earth. This is hinted at in the first chapter of the Aryabhatiya, where he gives the number of earth rotations in a yuga, and explained in the gola chapter. The Sun and Moon are each borne by epicycles, according to Aryabhata's geocentric model of the solar system.
Eclipses: Aryabhata scientifically explained solar and lunar eclipses. According to him, the Moon and planets are illuminated by reflecting sunlight. He describes eclipses in terms of shadows cast by and falling on Earth, rather than the prevalent cosmogony in which eclipses are caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes). He goes into great detail about the scale and magnitude of the Earth's shadow (verses gola.38–48), and then explains how to calculate the size of the eclipsed portion during an eclipse.
Aryabhata determined the sidereal rotation (the rotation of the planet based on fixed stars) to be 23 hours, 56 minutes, and 4.1 seconds in modern English units of time; the modern meaning is 23:56:4.091. Similarly, his modern meaning for the duration of the sidereal year is 23:56:4.091, which is 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days). Similarly, his worth of 365 days, 6 hours, 12 minutes, and 30 seconds for the duration of the sidereal year (365.25858 days).

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