Ancient Indian Development of Mathematics

Curated by Vera Image 1

Geometry located within altar construction (Image 2)

How was it used?

The advancement of mathematics had many significant uses in Ancient India, such as using standardized measurements and decimals for exemplary city planning(Gonit Sora) and constructing altars for religious purposes(Schlagar), as well as efficiency and reliability while writing numbers and much more honest record keeping(Yates).

How was it made?

There was no specific time when mathematics was "made" or "created", rather it was the development and advancement of ideas that was added on to for centuries. Many different mathematicians made several different contributions, whether minor or major, that shaped their ideas of mathematics. The main reason it was developed was to fulfill the needs of the different civilizations as they came and went.

One of the many mathematicians that made significant contributions (Image 3)

A chart comparing the Ancient Indian number systems to our modern number system (Image 4)

How did it impact later civilizations?

There is no definite time that it was “created”, it was the advancement and refinement of different concepts that improved over time. Some ideas from Ancient Indian mathematics are still used in math today, such as giving us our number and decimal system, the concept of 0, evolved ideas of calculus, and even calculations for astronomy(Krantz).

Concept of 0

The development of the concept of 0 is one of the most memorable advancements, and it became a concept in 3rd - 2nd century B.C.. Many different mathematicians contributed to the development and added rules, such as Vahamihiras, who said that zero didn’t affect anything added or subtracted from it(Datta). Zero was originally used as a placeholder to differentiate 10 from 100, but only became a number in its own right in Ancient India(Yates). The word “Zero” came from the Sanskrit word for “nothing”, and it became much more widespread after India was invaded by the Arab and Turkish people(Gonit Sora).

Evidence of use of the concept of 0 as a placeholder (Image 5)

An excerpt from one of the 4 parts of the Siddhanta Shiromani, called the Lilavati (Image 6)

Algorithms to compute equations

Another significant advancement was the development of algorithms to compute equations. The mathematician Bhaskara I created formulas to calculate the sine of an acute angle without using a table(Gonit Sora). Bhaskara II, who was not related to Bhaskara I, used a method called the chakravala method to give solutions to the general form of Pell’s equation(Gonit Sora). Bhaskara II also wrote a book split into 4 parts, called the Siddhanta Shiromani, all of which gave early mathematical concepts (Gonit Sora), and one of those books is called the Lilavati which has been digitized and translated into English. One of the most memorable mathematicians, Brahmagupta, wrote the Brahmasphutasiddhanta, which gave a solution to a general linear equation(Sinha). Brahmagupta also developed a famous theorem on the diagonals of a cyclic quadrilateral (Gonit Sora).

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This video focuses mainly on the contributions and advancements of mathematicians from the Gupta Empire

(Video 1)

Informative Videos

This video not only showcases Ancient Indian mathematicians and their contributions but how those same contributions affected mathematicians over time

(Video 2)

Other Interesting Websites -

Lilavati - You may this website interesting because it leads to one of the 4 parts of the Siddhanta Shiromani, however it was translated into English and has notes added to make it more understandable.

https://vajiramandravi.com/upsc-exam/indian-mathematicians/ - You might find this website interesting because it gives a list of significant mathematicians along with their major contributions, as well as modern applications using those same contributions.

https://www.open.ac.uk/blogs/MathEd/index.php/2022/08/25/the-men-who-invented-zero/ - You might find this website interesting because it not only gives a written timeline of the development of zero but it also gives many different rules in different instances.

https://asiasociety.org/education/math-science-and-technology-india - You may find this website interesting because it not only touches on different contributions of mathematics, but also some other significant inventions of that time in Ancient India.