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Talk 01 — Vinod Ghale (D Y Patil International Univeresity, Pune, India) — [computing…]Local time: click here to view in your time zoneTitle: From Vedic Altars to Digital Signatures: Baudhayana, Brahmagupta and Two Paths to Modern Cryptography
Abstract
The Baudhayana Sulbasutra (c. 800 BCE) records the earliest known Pythagorean triples. From these triples emerges the congruent number problem – which integers can be the area of a rational right triangle? – a question still open, yet now known to be equivalent to finding rational points on elliptic curves. Elliptic curves today form the bedrock of secure digital communication. Separately, Brahmagupta’s Bh¯avan¯a (628 CE) gives a composition law for solv- ing Pell’s equation, a method that directly inspires modern cryptosystems based on Pell hyperbolas. This talk traces both threads – from altar geometry and classical algebra – to the mathematics that protects our digital world.
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Talk 02 — Pabitra Narayan Mandal (Siksha O Anusandhan University, Institute of Technical Education and Research) — [computing…]Local time: click here to view in your time zoneTitle: Turagagati on Kachhaputa
Abstract
This talk explores a striking method from Indian mathematics, due to Nārāyaṇa Paṇḍita, for constructing magic squares (kachhaputa) using horse-like movement (turagagati). We describe this method as a systematic algorithm and show how it generates symmetric numerical structures.
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Talk 03 — Mahesh Sahebrao Wavare (Rajarshi Shahu Mahavidyalaya, Latur, India) — [computing…]Local time: click here to view in your time zoneTitle: Ancient Indian Mathematics: An Integrated View of Numeral Systems, Geometry, and Number Theory within the IKS Framework
Abstract
Ancient Indian mathematics reflects a rich and evolving intellectual tradition that forms an essential part of the Indian Knowledge Systems (IKS). It developed through a close connection with disciplines such as astronomy, architecture, language, and philosophy, resulting in both practical techniques and deep theoretical insights. One of its most influential contributions is the decimal place-value system along with the concept of zero, which transformed numerical representation and simplified computation across the world. This talk presents an integrated overview of key mathematical ideas emerging from classical Indian sources. It discusses distinctive approaches to representing numbers, including systems that encode numerical values through words and syllables, demonstrating an elegant fusion of mathematics and linguistic structure. The session also briefly highlights geometric knowledge from early texts, where construction techniques were applied to solve problems related to measurement and design. The central focus of the talk is on number-theoretic methods developed by Indian mathematicians. In particular, it examines systematic procedures for solving linear and quadratic indeterminate equations, which reveal an advanced understanding of algorithms and iterative reasoning. These methods not only addressed practical problems in astronomy and calendrical calculations but also anticipated ideas that are now fundamental in modern mathematics and computation. By bringing together historical developments and contemporary perspectives, this talk aims to emphasize the continued relevance of ancient Indian mathematical ideas in present-day teaching, research, and interdisciplinary studies.
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Talk 04 — Anita Tomar (Pt. L. M.S.Campus, Sridev Suman Uttarakhand University, Rishikesh, India) — [computing…]Local time: click here to view in your time zoneTitle: From Pingala’s Prosody to the Fibonacci Sequence and its Modern Applications
Abstract
The Fibonacci sequence is widely recognized for its mathematical elegance and diverse applications across science and technology. While it is commonly attributed to Leonardo of Pisa, known as Fibonacci, its conceptual foundations can be traced back to ancient India. This paper explores the contributions of Pingala, whose work Chandashastra presents a combinatorial analysis of poetic meters that exhibits recurrence relations equivalent to the Fibonacci sequence. By examining Pingala’s treatment of long and short syllables, this study highlights the early emergence of recursive structures in Indian mathematics. The paper further connects these historical insights to modern applications of the Fibonacci sequence in areas such as computer science, biological modeling, financial analysis, and art. Through this interdisciplinary approach, the study emphasizes the continuity of mathematical ideas from ancient traditions to contemporary scientific practices.
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Talk 05 — Rakesh Bhatia (Shiksha Sanskriti Utthan Nyas New Delhi, India) — [computing…]Local time: click here to view in your time zoneTitle: Application of Baudhayan Numbers in Trigonometry
Abstract
Students frequently struggle with trigonometric identities because they are expected to memorize a large number of formulas. This heavy reliance on memorization often creates confusion, reduces confidence and makes it difficult for learners to apply concepts effectively in different types of problems. Traditional teaching methods in trigonometry can be time-consuming and may not always promote deep understanding, leading to mechanical learning rather than conceptual clarity. Vedic Mathematics provides a more intuitive and efficient alternative to address these challenges. It introduces simplified techniques that reduce dependency on rote learning and encourage logical thinking. This lecture highlights the application of Baudhayan Numbers as a powerful tool to derive trigonometric identities in a systematic and meaningful way. By using this approach, students can understand the relationships between different trigonometric ratios rather than memorizing them in isolation. Additionally, this method proves highly effective in solving problems related to height and distance with minimal calculation. It reduces the need for lengthy, paper-based procedures and promotes mental computation. Overall, the Vedic approach enhances conceptual understanding, improves speed and accuracy and makes the learning of trigonometry more engaging and accessible for students.
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Talk 06 — Purnima Satapathy (Visvesvaraya National Institute of Technology, Nagpur, India) — [computing…]Local time: click here to view in your time zoneTitle: From Zero to Infinity: Ancient era to Modern India’s Mathematical Revolution
Abstract
The evolution of the number system in ancient India marks a profound journey from concrete counting to abstract mathematical thought. Early scholars developed a place value system that transformed how numbers were represented and calculated. The introduction of zero as both a placeholder and a number by Brahmagupta revolutionized arithmetic operations. This innovation enabled the systematic use of large numbers and efficient computation. Indian mathematicians further extended numerical ideas through algebraic methods and problem-solving techniques. Their work influenced global mathematical development through transmission to other civilizations. From zero to infinity, this evolution laid the foundation for modern mathematics and scientific advancement.
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Talk 07 — V. KANNAN (Retired from University of Hyderabad and from SRM University Andhra Pradesh, India) — [computing…]Local time: click here to view in your time zoneTitle: One area-formula in many ways in old Samskruta books.
Abstract
When the three sides of a triangle are given, the area of the triangle can be calculated by using a well-known formula. This formla is neatly written using symbols, as follows. The square root of s (s-a)(s -b)(s-c). But Brahmagupta states it concisely without symbols. Half of a verse in Arya meter suffices. Namely "Bhuja yogaardha chatushtaya bhujona ghaataat padam suukshmam ||" We first explain the meaning and then show that this sumbol-less formula is more brief than Heron's formula. Next we pass on to some later books (In Samskrutam) that re-describe the same formula in other ways. We notice that some words change, the meter changes, but the content does not change. More importantly, the formula is always given in the verse form. This helps in memorization and retention. We next make a mutual comparison of these various versions and discuss their advantages and disadvantages. Lastly, we see how some historians appreciate these formulae, and also how some others choose to ignore these.
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Talk 08 — Nidhi Handa (Gurukul Kangri (deemed to be) University, Haridwar, Uttarakhand, India) — [computing…]Local time: click here to view in your time zoneTitle: Rediscover the Mathematical Achievements in Vedic Scriptures
Abstract
A vast corpus of works dealing with astronomy, mathematics, linguistics, logic, and philosophy has been produced by the mathematical tradition of ancient and medieval India. It needs to be emphasised that the development of modern mathematics (Calculus, Abstract Algebra, Graph Theory, etc.) in India was not sudden; rather, its development shows a historical continuity right from the time of Aryabhata and many more years back. The beginnings of algebra are to be traced to the constructive geometry of the Vedic priests preserved in the Sulbasūtras. In later periods also algebra must have leaned on geometry. Vedic mathematics generally refers to the geometry contained in the Vedic scriptures called Sulbasutras (c. later 800-500 BCE). Sulbasutras are associated with Yajurved, and these are also regarded as appendices to the Yajurved.
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Talk 09 — Prajakti Aditya Gokhale (Founder and Director (Vedicly Ltd. Education Startup Israel and India)) — [computing…]Local time: click here to view in your time zoneTitle: The Poetic Logic of Lilavati: Perspectives on a 12th-Century Mathematical Masterpiece
Abstract
The Lilavati, authored by the legendary mathematician and astronomer Bhaskaracharya II in 1150 CE, stands as a cornerstone of the Indian mathematical tradition. Named after his daughter, the text is not merely a collection of rules but a unique synthesis of advanced mathematics and lyrical Sanskrit poetry. This lecture explores the Lilavati as a primer that bridged the gap between abstract calculation and everyday life, serving as a standard textbook for nearly 800 years. A central focus will be the pedagogical brilliance of Bhaskaracharya’s "word problems." By framing challenges through the lens of broken necklaces and swarms of bees, he transformed rigid logic into an engaging, conversational art form. These problems reflect a sophisticated understanding of mathematics that, in many instances, pre-dated similar Western discoveries by centuries—such as visual proofs of the Pythagorean theorem and precursors to infinitesimal calculus. Beyond the technicalities, the lecture will discuss the "Lilavati Perspective": an integrated approach to knowledge where Vidya (knowledge) is inseparable from aesthetic beauty and practical application. By revisiting this ancient treatise, we gain insights into a time when mathematics was perceived as a living language, essential for both astronomical precision and commercial prosperity. This session aims to re-evaluate how the Lilavati’s innovative teaching methods can inspire modern mathematical education to be more intuitive, holistic, and intellectually vibrant.
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Talk 10 — Satish Damodar Mohgaonkar (Retired Professor of Mathematics, Shri Ramdeobaba College of Engineering and Managemant, Nagpur) — [computing…]Local time: click here to view in your time zoneTitle: Geometry from śulbasūtras
Abstract
The Hindu geometry has its history since the days of construction of “altars” for the Vedic sacrifices of various kinds. Some of it were “Nitya” (indispensable) and some were “Kamya” (optional) sacrifices”. The ancient scriptures mention that each sacrifice must be made in altars of specific size and shape. It was also stressed that even a slight change in form and size would not only nullify the objectives of the whole ritual but might even lead to an adverse effect. Hence, there arose a need of geometry as well as arithmetic and algebra. Over a period of time this geometry developed from only the sacrificial importance to the more scientific one. This happened in Vedic age when different school of geometry were formed like Baudhāyana, Vādhūla, Mānava, Āpastamba, Varāha, Hiraṇyakeśin, Maitrāyaṇa and Kātyāyana. The knowledge was passed on with words of mouth for centuries. However, recognizing the need of manual which will help in construction of correct and desired altars, the vedic priests have composed a class of texts called “Sulva-sutras”. These texts, which are dated prior to 800 BC, form a part of Kalpasūtra. In this lecture, we will study śulbasūtras that includes • Kātyāyana’s method of drawing the East-West line • Kātyāyana’s method of drawing perpendicular bisector • Baudhāyana Theorem
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Talk 11 — Shivani Khare (Dr. Harisingh Gour Vishwavidyalaya, Sagar, Madhya Pradesh, India) — [computing…]Local time: click here to view in your time zoneTitle: Development and Contributions of Ancient Indian Mathematics
Abstract
Ancient Indian mathematics developed over three major periods—800 BCE–500 CE, 500–1250 CE, and 1250–1850 CE—showing a continuous growth of ideas and methods that contributed significantly to global mathematical knowledge. Early texts such as the Baudhyana Sulbasutra present important geometric results, including concepts similar to the Pythagorean theorem. The work of Pingala in the Chhanda Shastra introduces early ideas related to binary representation and combinatorial patterns. Indian mathematicians also created unique numeral systems for expressing numbers, including Bhutasankhya, Katapayadi, and the Aryabhatiya system, where numbers are represented through words and letters. These systems reflect both creativity and practical application in preserving and transmitting numerical information. Further developments include the study of magic squares, which highlight both mathematical structure and practical applications, as seen in works like Varahamihira’s Gandhayukti, where such arrangements were used in specific contexts. Indian scholars also made notable progress in approximating the value of π (pi), demonstrating strong computational skills and analytical thinking. These classical contributions form the foundation for later advancements, culminating in the work of Srinivasa Ramanujan, whose remarkable insights continue to influence modern mathematics. The presentation covers all these aspects, highlighting the richness, originality, and lasting impact of the Indian mathematical tradition.
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Talk 12 — Sumukha S (Central University of Karnataka, India) — [computing…]Local time: click here to view in your time zoneTitle: The Combinatorial Architecture of Ancient Indian Prosody
Abstract
The foundations of combinatorics emerged from the structural requirements of ancient Indian prosody, as documented in the Chandaśāstra of Piṅgala. The systematic arrangement of short (Laghu) and long (Guru) syllables provided the basis for the formal study of permutations and combinations. In this talk, we explore the combinatorial methods inherent in this system, including Prastāra, the procedure for listing all possible patterns, and Meru Prastāra. Furthermore, we examine how the study of mātrā-vṛtta (meters based on total beats) led to the discovery of the Virahāṅka-Hemacandra sequence. By focusing on these specific methods, the session illustrates how the architecture of Indian prosody gave rise to fundamental principles of number theory.
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Talk 13 — Margam Archana (SRR Government Arts and Science College (A), Karimnagar, India) — [computing…]Local time: click here to view in your time zoneTitle: The Antiquity of the Hypotenuse Theorem in India
Abstract
Hypotonuse theorem is known in this world as Pythagoras theorem. The well-known geometric theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its sides. When asked where the Pythogoras theorem originated, the answer is India. Because numerous nations were referenced in ancient times when discussing Pythogorean triplets, but not the precise formulation of the Hypotenuse theorem. In this paper we are proving that the theorem was existed 5000 years ago.