History of Maths

Mathematics did not grow in isolation. Ideas about numbers, geometry, algorithms and infinite processes appeared in different cultures and were refined, translated and transmitted across centuries. This section of Brahmagyaan Math Academy gathers historical context and careful explanations so that students can see both what the results are and how they developed.

In-Depth Articles

Start with the published pages below. More topics will be added as they are prepared.

How Mathematicians Calculated π

From Archimedes’ polygons to Aryabhata, Zu Chongzhi and the Kerala school’s infinite series — the long effort to understand the ratio of a circle’s circumference to its diameter.

History & Proofs of the Pythagorean Theorem

Coming soon — early geometric statements (including in the Śulba-sūtras), classical Greek proofs, and later algebraic and geometric approaches.

Heron’s Formula — History and Derivation

Coming soon — the formula for the area of a triangle from its three sides, its classical background, and a clear modern derivation.

Zero, Place Value and the Decimal System

Coming soon — the development of zero as a number and the place-value system in the Indian mathematical tradition, and how these ideas travelled westward.

Knowledge from the Indian Subcontinent

Several foundational ideas of mathematics were developed and refined in the Indian subcontinent over a long period. Among the best-documented contributions are:

• Geometry in the Śulba-sūtras (roughly 800–200 BCE) — rules for constructing altars, approximations to √2, and geometric relationships that include early forms of the Pythagorean result for particular cases.
• Aryabhata (born 476 CE) — place-value notation, a sophisticated treatment of trigonometry (sine tables), and a value of π accurate to four decimal places (≈ 3.1416).
• Brahmagupta (7th century) — systematic rules for zero and negative numbers, and work on cyclic quadrilaterals and algebra.
• Bhāskara II (12th century) — further advances in algebra, trigonometry and calculus-like ideas (including the notion of the instantaneous rate of change in certain contexts).
• Kerala school (especially Mādhava of Saṅgamagrāma, c. 14th century, and his successors) — infinite series for π, sine and cosine, centuries before similar developments in Europe.

How this knowledge travelled

Mathematical ideas did not stay confined to one region. From the early medieval period onward, scholars in the Islamic world studied, translated and extended Indian works (along with Greek sources). Important figures such as al-Khwārizmī and al-Bīrūnī engaged with Indian astronomy and mathematics. Through Arabic texts, and later Latin translations, many of these ideas reached Europe.

A well-known example is the decimal place-value system and the use of zero. These reached Western Europe in a practical form through contacts with the Islamic world; Fibonacci’s Liber Abaci (1202) was one of the works that helped spread the “Indian numerals” (via Arabic intermediaries) among European merchants and scholars. Infinite series of the kind developed in Kerala became widely known in Europe only much later, after different lines of research had already produced related results in the 17th century.

This page will gradually add focused articles that present the historical evidence carefully and show the mathematical content in a form useful for students.

Why History Matters for Students

Seeing how results were discovered helps in two ways:

• It shows that mathematics is a human activity — ideas are refined over time, not handed down complete.
• It often reveals simpler or more intuitive routes to theorems that appear in school textbooks (for example, different proofs of the Pythagorean theorem or different ways of approaching π).

We aim for historical accuracy. Where dates or attributions remain uncertain among scholars, we will note the uncertainty rather than present a simplified story.