Ancient-education/Philosophers and Scholars/Sridhara

(Wikipedia contributors, n.d.)

Sridhara

Sridhara, also known as Sridharacharya, was an Indian mathematician. For many centuries, students and teachers have read and used his work extensively. He lived in the later first millennium and is best known for short, practical books that teach rules for arithmetic and algebra. He became well-known for his easy-to-follow rules about numbers, shapes, and equations that made life easier for people. His main books, Patiganita and Trisatika (or Patiganitasara), teach easy ways to solve maths problems like interest, buying goods, and land measures.

Early Life and Background

Very little is known about Sridhara’s personal life, as his surviving works provide no details about his family, teachers, or birthplace. Scholars think he came from either Bengal or South India, and his writings suggest he was a Shaivite Hindu. References by Bhaskara II, Govindasvamin, and Mahavira indicate he lived in the 8th or early 9th century. He is sometimes confused with other scholars named Śridhara.(Wikipedia contributors, n.d.)

Sridhara lived in a time when Indian maths grew strong after greats like Brahmagupta. He was a Hindu scholar who wrote practical mathematical treatises, works meant to help people with everyday arithmetic and algebra. (Sinha, n.d.)

Major works of Sridhara

Sridhara was an important early Indian mathematician whose works dealt with practical arithmetic, measurements, and algebra. His writings provided rules for everyday calculations, from basic arithmetic to mensuration and quadratic equations. Despite the loss or incompleteness of many of his works, his surviving books shaped mathematical learning and influenced later mathematicians.

Patiganita

This is considered Sridhara’s main work on arithmetic and measurement. It is written in verse to help memory and teaching. The book begins with tables of money and measurement units. It includes rules for adding, subtracting, multiplying, dividing, calculating squares and cubes, square roots, cube roots, and working with fractions.

Patiganita also contains practical problems used in daily life, such as mixtures, proportion, barter, wages, interest and measurement of land, volume and building structures like cisterns. Only a part of the original text survives today. The original had about nine hundred verses, but only two hundred and fifty-one are available now. (Śrīdhara, n.d.)

Trishatika

Trishatika, also known as Patiganita-Sara, is a shorter version of Patiganita. Trishatika's name implies approximately three hundred verses, likely designed to facilitate easy learning of its main rules.

This work covers important topics in practical arithmetic: natural numbers, the idea of zero, multiplication, division, fractions, squares, cubes, the rule of three for proportion, interest, partnership in business, and mensuration of areas and volumes.

Because it is shorter and more direct, Trishatika is useful for students, merchants, and teachers who need a simple handbook of rules rather than a long text.(Śrīdhara & Sudyumna Acharya, n.d.)

Other attributed works

Some later writers mention other works related to Sridhara, such as Bijaganita, Navasati, and Brihat Pati.

Bijaganita was said to be his work on algebra and equations, though it does not survive. Later mathematicians quoted from it. Navasati and Brihat Pati may have been earlier or larger forms of Patiganita.

Many historians doubt that Sridhara truly wrote the present form of Ganita pancavimsi, another work often associated with him. (Wikipedia contributors, n.d.)

Sridhara’s rules

Sridhara’s style is practical. He wrote short rules (often in verse) that students could learn and repeat. The rules cover:

• The rules cover simple arithmetic operations and how to work with them effectively.
• The rules also cover fractions and how to create a common denominator. He wrote steps to add, subtract and combine fractions that matched other Indian authors of his time.
• He provided concise methods for measurements commonly used in trade and daily life.
• He composed elementary algebraic rules, which included a method for solving certain quadratic problems.

Teachers liked these books because they are concise and straightforward. Later authors who taught mathematics often referred to these small rulebooks as useful classroom material. (Datta & Singh, n.d.)

The quadratic rule

One reason Sridhara’s name still appears in modern school notes is a rule for solving quadratic equations. In simple terms, this is the familiar formula that determines the two solutions of a quadratic equation of the form ax² + bx + c = 0. The formula is usually written in modern books as:

x = [ −b ± √(b² − 4ac) ] / (2a)

In India, this rule is often taught under the name Sridharacharya (or Sridharacharya’s rule). Historical studies of Indian mathematics indicate that Sridhara was one of the early authors to set down this rule in a clear form for students. The name “Sridharacharya” subsequently became commonly used in school memory verses and teaching notes. (Datta & Singh, n.d.)

Style and influence

The Indian tradition at the time used short sutras (verses) to teach rules. Sridhara followed this pattern. He wrote in a compact way so that each line or verse carried a rule and a short example. Teachers then added explanations in class. Later scholars and historians of mathematics have used his short verses as evidence of the way arithmetic and algebra were taught in India. (Datta & Singh, n.d.)

Legacy

Sridhara may not have written long theoretical books, but his short, practical rules had a long life. His clear teaching style, especially the rule for solving quadratics, helped students learn arithmetic and algebra for centuries. His works, copied and republished, contributed to the strong Indian tradition of teaching maths through concise rules and practical examples. Today we can read his work again in scanned editions and see how mathematics was taught long ago. (Śrīdhara & Sudyumna Acharya, n.d.)

References

Wikipedia contributors. (n.d.). Sridhara. In Wikipedia, The Free Encyclopedia. Retrieved February 3, 2026, from https://en.wikipedia.org/wiki/Sridhara

Sinha, J. (n.d.). History of Indian Philosophy Vol 2 [PDF]. Internet Archive. https://ia800404.us.archive.org/21/items/HistoryOfIndianPhilosophyVol2ByJadunathSinha/History%20of%20Indian%20Philosophy%20Vol2%20by%20Jadunath%20Sinha_text.pdf

Śrīdhara. (n.d.). Patiganita [PDF]. Internet Archive. https://ia800806.us.archive.org/29/items/Patiganita/Patiganita.pdf

Śrīdhara, & Sudyumna Acharya. (n.d.). Trishatika of Sridhara – Hindi [PDF]. Internet Archive. https://dn790000.ca.archive.org/0/items/TrishatikaOfSridharaHindiSudyumnacharya/Trishatika%20of%20Sridhara%20-%20Hindi_Sudy