Draṣṭā // Course

History of Hindu Mathematics

This course explores the rich tradition of Hindu mathematics, highlighting its foundational contributions to various branches of mathematics, its transmission to the West, and the historical erasure and misattribution of its achievements.

18 Mar - 01 Apr 2024 Completed
About the Course Takeaways and Audience Know your Instructor

Overview

It is usually not known that India had a thriving tradition of mathematics. Today it is a common belief that mathematics arose in ancient Greece and Europe. Many key results of mathematics credited after Europeans, such as the “Pythagoras Theorem”, Taylor series, etc. were in fact developed in the Hindu civilization much earlier than they were known in the West. These ideas were transmitted to the West and later attributed to Western sources.

The history of Hindu mathematics is also the history of how and why it was erased from mainstream historical accounts. In particular, why are so many Hindu innovations named after Western scholars? Why are the names of prominent mathematicians such as Brahmagupta, Bhaskara etc, all but absent in mainstream accounts? Why is Hindu mathematics reduced to an unimportant footnote in historical accounts? This aspect forms another important part of the course. The attitudes of Western scholars towards Hindu mathematics such as Cantor, Rousse-Ball, Heath etc., and the attendant misrepresentations and distortions will be addressed.



Intent

This course will give an account of Hindu mathematics and seek to show how so many of the foundational branches of mathematics such as arithmetic, algebra, combinatorics, trigonometry, linguistics, prosody, calculus, and other fields were developed in the Hindu civilization. Ideas from Hindu mathematics, especially from linguistics and prosody, have also influenced the development of computer science in modern times. The main works and results of prominent Hindu mathematicians will be discussed. The transmission of Hindu mathematical ideas, especially to the Arab world and the West will also form an important part of the course.

Another important aspect the course addresses is the close connection of mathematical knowledge with the deeper philosophical, metaphysical and epistemological framework of the Hindu civilization. It will address issues such as how this knowledge spontaneously arose in the Indian civilization, and how the deeper framework and philosophical foundation made it possible for this knowledge to arise.

Contents

Day 1

Introduction :

Is mathematics “universal” or “secular”? Why the term “Hindu Mathematics”? Framework of knowledge in the Hindu civilization. How it is different from the Western framework? Overview of Hindu mathematics and mathematicians.

Day 2

The Śulbasūtras :

- Altar construction in the Śulbasūtras. - Some geometric constructions from the Śulbasūtras. - The “Pythagoras theorem”: An Exercise in Mythmaking. - Introduction to the West and reception by Western historians. - The role of Babylonia in Western history.

Day 3

Arithmetic and Algebra :

- Bhūtasaṃkhyā and Kaṭapayādi notation. - Hindu number system. - Kuṭṭaka and Cakravāla algorithms. - Transmission to the Arab world and Europe.

Day 4

Linguistics and Prosody :

- Pāṇini’s Aṣṭādhyāyī. - Pingala’s Chanda śāstra. - Binary numbers of Pingala. - Virahaṃkā-Hemacandra numbers. - Meruprastāra, combinatorics, binomial coefficients, and other topics. - Modern computer science and linguistics.

Day 5

Trigonometry, Calculus, and Astronomy :

Trigonometric conventions and results. Applications to astronomy. History of calculus: from Āryabhaṭṭa to Jyeṣṭhadeva.

Day 6

Transmission of Hindu Mathematics :

- Possible transmission of Śulbasūtra geometry. - Contacts between Greece and India; similarities in philosophy. - Transmission of mathematics and astronomy to the Arabs. - Transmission via Arabs to Europe. - Transmission of calculus to Europe via Jesuit priests in Kerala: motivation and evidence.

Day 7

The Attempted Erasure of Hindu Mathematics from History :

- The case of the Śulbasūtras: A Recap - Historiography of Kerala mathematics (based on the article by M. D. Srinivas in bhavana.org.in) - Reasons behind the attempted erasure - The Myth of Greek Mathematics

Key Takeaways

Bust myths:

After attending this course, the participant will be able to counter commonly accepted but false claims about the history of mathematics from a deeper perspective.

Gain perspective:

The participant will be better informed about the role of Hindu philosophical and spiritual thought in the history of Hindu mathematics.

Think critically:

The course will help to cultivate the ability to think independently and beyond second hand opinions built on consensus and authority. The focus in this case is mathematics, but it is hoped the participant will be able to extrapolate this to other areas of life as well.

Who is this course for?

  • - Students: Get deeply connected with mathematics by learning about the Hindu way of doing mathematics. - History Enthusiasts: Learn the history of transmission of Hindu thought from East to West and its erasure. - Mathematicians: Compare and contrast the ancient and modern methods of mathematics and incorporate beauty into the modern methods. - IKS Researchers: Join to know how colonialism shaped the commonly accepted history of mathematics.

Know your Instructor

Bhaskar Kamble

Bhaskar Kamble

Bhaskar Kamble is an author, theoretical physicist and data scientist. He obtained his Ph.D. in theoretical condensed matter physics in 2010 from the Indian Institute of Technology Kanpur, India. Thereafter, he worked as a researcher for several years at the Ruhr University Bochum, Germany, the University of Kaiserslautern, Germany, and at the Asia Pacific Center for Theoretical Physics in Pohang, South Korea, specializing in the fields of unconventional superconductivity, quantum phase transitions, and many-particle physics. Currently, he works as a data scientist in Berlin. He has a deep interest in the history of mathematics in the Hindu civilization and in Hindu philosophy. He is the author of the best-selling book The Imperishable Seed: How Hindu Mathematics Changed the World and Why This History Was Erased (2022).

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