Indian Mathematicians and Astronomers

The decimal system, including the concept of zero and place-value notation, was invented and developed by ancient Indian mathematicians. Scholars like Aryabhata (5th century CE) and Brahmagupta (7th century CE) made significant contributions. This system was later transmitted to the Islamic world and then to Europe, where it revolutionized mathematics.

Aryabhata (476-550 CE) was a pioneering Indian mathematician and astronomer who made significant contributions to algebra. His work 'Aryabhatiya' included solutions to linear and quadratic equations, place-value system, and astronomical calculations. While the term 'algebra' comes from Arabic (Al-Jabr by Al-Khwarizmi), Aryabhata's contributions to algebraic concepts predate Islamic mathematics and were foundational.

Brahmagupta (598-668 CE) was the first mathematician to treat zero as a number and define its operations. In his work Brahmasphutasiddhanta (628 CE), he established rules for arithmetic with zero, including that zero multiplied by any number equals zero. Earlier mathematicians like Aryabhata used the place value system but Brahmagupta formalized zero as a number.

Correct answer is (2). 

Bhaskaracharya II (also known as Bhaskara II) was the 12th-century Indian mathematician who, in his work Lilavati, discussed division by zero and stated that a quantity divided by zero results in an infinite quantity (khahara). While earlier mathematicians like Brahmagupta had worked with zero, it was Bhaskara II who explicitly made this statement about division by zero yielding infinity.

Brahmagupta (7th century CE) was the first to treat zero as a number and establish rules for arithmetic operations with zero in his Brahmasphutasiddhanta (628 CE). He defined zero as a number (not just a placeholder) and explained operations like addition, subtraction, multiplication, and division involving zero. While Aryabhatta used zero as a placeholder, Brahmagupta was the first to treat it as an actual number with mathematical properties.

Bhaskaracharya II (Bhaskara II) wrote Siddhanta Shiromani in the 12th century, which included concepts of differential calculus and Rolle's theorem, centuries before Newton and Leibniz formalized calculus in Europe.

Aryabhatta (476-550 CE) composed the Aryabhatiya, a groundbreaking astronomical treatise that introduced revolutionary concepts like the rotation of Earth and accurate pi calculations. He is definitively associated with the Aryabhatiya. While the Surya Siddhanta is an ancient astronomical text that Aryabhatta referenced and built upon, it was an earlier work revised over centuries rather than written by him. However, among the options, Aryabhatta is clearly correct as the primary author of the Aryabhatiya and is associated with both texts in historical tradition.

Brahmagupta, the 7th-century Indian mathematician and astronomer, operated an observatory at Ujjain - one of ancient India's leading astronomical centers. While Varahmihir also worked in Ujjain during the earlier Gupta period, Brahmagupta is more specifically associated with establishing and using the observatory there for his astronomical calculations.

Isaac Newton developed calculus in the mid-17th century (around the same time as Leibniz independently). His work on fluxions formed the foundation of differential and integral calculus.

Aryabhatta (5th century CE) was the first ancient Indian scholar to systematically treat mathematics as a distinct discipline, making groundbreaking contributions to number systems, trigonometry, and astronomical calculations.

Aryabhatta (476-550 CE) lived during the reign of Chandragupta Vikramaditya of the Gupta Empire. This period is considered the Golden Age of Indian mathematics and astronomy, and Aryabhatta made pioneering contributions to both fields.

 Zero was invented by an unknown indian.