Bhāratīya Gaṇita is the documented tradition of mathematics and astronomy that grew up in India — the home of zero as a number and the decimal place-value system the whole world now uses. From the altar-geometry of the Shulba Sutras to the infinite series of the Kerala school, it is a record of real, well-attested achievement. This page sticks to what is genuinely evidenced in the texts.
Zero, place-value & the numerals
The single most influential Indian contribution to mathematics is the way numbers are written: ten digits, a positional base-ten layout, and a genuine zero that is both a place-holder and a number you can calculate with. This is the foundation everything else rests on.
Shunya — zero as a number
Indian mathematics treated shunya (zero) not merely as an empty space but as a number in its own right, with rules for how it behaves under addition, subtraction and multiplication. This is one of the most consequential ideas in the history of mathematics — without a true zero, the modern number system cannot work.
The decimal place-value system
In the Indian system the value of a digit depends on its position — units, tens, hundreds, thousands — so that just ten symbols can write any number however large. This positional, base-ten notation, combined with zero as a place-holder and a number, is the system the entire world now uses.
Brahmi numerals
The digits evolved from the ancient Brahmi numerals attested in Indian inscriptions. Over centuries these forms developed into the numerals used across India, and the same lineage gave rise to the digit shapes used worldwide today.
How it reached the world
The decimal place-value system with zero passed from India to the medieval Islamic world, where scholars such as al-Khwarizmi (early 9th century) wrote on “Hindu reckoning.” From there it entered Europe — which is why these digits are still called “Arabic numerals,” though the Arabs themselves called them “Indian numerals” (al-arqam al-hindiyya).
The great mathematician-astronomers
Indian mathematics and astronomy were closely bound together — the same scholars who worked out trigonometry and algebra also computed the motions of the planets. Here are some of the figures whose contributions are securely documented, with their real, specific achievements.
Aryabhatab. 476 CE
In his Aryabhatiya he gave a table of sine differences (the jya values from which our word “sine” ultimately derives), an approximation of pi as 3.1416 (62832/20000), methods for areas and volumes, and the bold proposal that the apparent daily motion of the stars is caused by the rotation of the Earth on its own axis. He also gave methods for solving certain indeterminate equations.
Varahamihira6th century CE
A leading astronomer-astrologer whose Pancha-Siddhantika summarises five earlier astronomical schools, and whose encyclopaedic Brihat Samhita gathers material on astronomy, the calendar, weather, architecture, gemmology and much else — an important window into the science and learning of the period.
Brahmaguptab. 598 CE
In the Brahmasphutasiddhanta he gave, for the first time in a surviving text, systematic arithmetic rules for zero and for negative numbers (which he described as “debts” as opposed to “fortunes”), a general solution method for quadratic equations, and his celebrated formula for the area of a cyclic quadrilateral. His rule that division by zero is problematic was a remarkably early engagement with the question.
Bhaskara I7th century CE
A close follower of Aryabhata who wrote the earliest known prose commentary on the Aryabhatiya, helped establish the place-value notation in his writing, and gave a remarkably accurate rational approximation for the sine function.
Bhaskara II (Bhaskaracharya)b. 1114 CE
Author of the Siddhanta Shiromani, whose famous sections Lilavati (arithmetic and mensuration) and Bijaganita (algebra) were studied for centuries. He worked with the place-value system, indeterminate equations (the so-called Pell’s equation via the chakravala cyclic method), and showed early intuitions pointing toward the calculus — including ideas about instantaneous motion and a result equivalent to the derivative of the sine.
Madhava of Sangamagrama & the Kerala schoolc. 1340–1425 CE
Madhava founded the Kerala school of astronomy and mathematics, which developed infinite series expansions for pi and for the sine and cosine (and the arctangent) — results equivalent to what are now called the Taylor and Maclaurin series, arrived at centuries before Newton and Leibniz. The work survives through his successors such as Nilakantha Somayaji and in the Yuktibhasha, and is among the most significant achievements in pre-modern mathematics.
Altar geometry & encoding numbers in words
Two distinctive strands of the tradition: the earliest geometry, preserved in the ritual Shulba Sutras, and the ingenious schemes that let an oral culture pack precise numbers into verse so they could be memorised and transmitted.
Shulba Sutras — geometry of the altar
The Shulba Sutras (appendices to the Kalpa texts, the oldest among the surviving mathematical writings of India) give the geometry needed to lay out fire-altars of precise shape and area. They contain constructions for squares, rectangles and circles of equal area, an accurate approximation for the square root of 2, and an early statement of the relation we now call the Pythagorean theorem — that the square on the diagonal of a rectangle equals the sum of the squares on its two sides.
Katapayadi — numbers as syllables
Katapayadi is a system for encoding numbers as consonants, so that a number can be hidden inside a pronounceable, memorable word or verse. It was widely used by astronomers and musicians to record numerical data (such as astronomical constants or the ordering of melodic scales) in a form easy to memorise.
Bhutasankhya — words that stand for numbers
In the Bhutasankhya (“object-numbers”) system, common words are used in place of digits because of a fixed association — for example “eye” or “hand” for 2, “fire” for 3, “Veda” for 4, “sense” for 5, and “sky” or “void” for 0. Read in place-value order, these words let numbers be woven into metrical Sanskrit verse — a practical aid for an oral tradition.
Educational overview, presented on an evidence-based footing. The dates and attributions above follow the mainstream history of mathematics; this page deliberately avoids romantic or pseudo-historical claims and states only what the surviving texts genuinely support. For the source material, consult the Aryabhatiya, the Brahmasphutasiddhanta, the Lilavati and Bijaganita, the Shulba Sutras, and modern scholarship on the Kerala school.