The Precise Calculation of Pi
In his work Aryabhata gave the approximate value of pi as 3.1416, precise to four decimal places, and explicitly noted that this was an "approximation" and not an exact value — this clear awareness of the approximate nature of mathematics was quite rare in the world mathematical history of the time, and his calculation was thereafter spread through the Indian mathematical tradition to the Arab world and, further, influenced the development of medieval European mathematics.
The Bold Conjecture of the Earth’s Rotation
Aryabhata proposed that the apparent motion of the sun, moon, and stars rising in the east and setting in the west that we observe is in fact an illusion caused by the earth rotating once daily on its own axis, rather than the heavenly bodies truly revolving around a stationary earth — an astronomical insight some thousand years before Copernicus’s heliocentrism, though it did not provoke a fundamental overturning of the overall geocentric cosmology in the Indian astronomical tradition of the time.