In the

*Brahmasphutasiddhanta* (Opening of the Universe, also seen as

*Brahmasiddhanta*) of 628, Brahmagupta introduces

zero and

negative numbers. It is not know whether he

pioneered the concepts or whether they were known in

Indian

mathematics before that. This is the first major advance on

Greek mathematics.

He called positive numbers fortunes and negative numbers debts, defined them and zero, and introduced rules of arithmetic for them all, correct apart from an attempt to define division by zero: he set 0/0 = 0.

Brahmagupta was head of the leading astronomical observatory of India, at Ujjain, which might have been his birthplace (in 598).

The *Brahmasphutasiddhanta* is in 25 chapters. The first ten discuss "mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; the moon's shadow; conjunctions of the planets with each other; and conjunctions of the planets with the fixed stars." The remaining 15 are additions and summaries plus more on gnomons and other instruments.

At the age of 67, in 665, he wrote the *Khandakhadyaka*, a work in eight chapters covering similar astronomical topics.