Short answers, pulled from the story.
The dynasty's founder was Sri Gupta, an independent monarch ruling in the Magadha region during the late third century CE. Evidence from silver coins discovered in the Hajipur, Muzaffarpur region of Bihar confirms his existence and sovereign authority.
Samudragupta succeeded his father around 335 or 350 CE and transformed the regional power into a vast empire through relentless military campaigns. He uprooted eight kings of Aryavarta, subjugated kings of the forest region, and defeated twelve rulers of Dakshinapatha, advancing as far as the Pallava kingdom.
Chandragupta II, known as Vikramaditya, ruled from 375 until 415 and presided over the high point of the empire. His reign featured the Navaratna group of nine literary geniuses including Kalidasa, and the Chinese scholar Faxian visited India between 399 CE and 405 CE to describe a prosperous society.
The decline began with the rise of the Kidarites, also known as the White Huns, who invaded from the northwest around 455 CE. The empire disintegrated under attacks by Toramana and his successor Mihirakula, with the Alchon Huns overrunning much of the empire by 500.
King Vishnugupta was the tail end recognized ruler of the dynasty's main line, reigning from 540 to 550. The last known inscription by a Gupta emperor is the Damudarpur copper-plate inscription from 542 or 543 CE, made during his reign.
Indian mathematics flourished with the creation of the first positional base 10 numeral systems in the world, originating from Gupta India. The astronomer Aryabhata wrote the Aryabhatiya, developing a place value system and approximating pi to four decimal places, while Varahamihira developed formulas relating sine and cosine functions.