Skip to main content

Mathematics in Ancient India

The first appearance of evidence of the use of mathematics in the Indian subcontinent was in the Indus Valley Civilization, which dates back to around 3300 BC. Excavations at Harappa, Mohenjo-daro and the surrounding area of the Indus River, have uncovered much evidence of the use of basic mathematics. The mathematics used by this early Harappan civilization was very much for practical means, and was primarily concerned with weights and measuring scales.

By 1800 BC, Indian mathematicians were discussing the idea of infinity, pointing out that "if you remove a part from infinity or add a part to infinity, what remains is still infinity." By about 400 BC, Indian mathematicians were doing more work on the idea of infinity. The Surya Prajinapti defines five kinds of infinity: an infinite line beginning from an endpoint, an infinite line going directions, an infinite plane, an infinite universe, and the infinity of time.

Lot of progress was made in geometry as a result of interest in astronomy, and by 1300 BC the Indian astronomer Lagadha used geometry to write a book of rules for the apparent movement of the sun and moon.

Around 300 BC, Indian mathematicians began working on the mathematical idea of combinations. This is the study of how many combinations you can make out of the same group of things. They were working on how you could figure that out, and published their ideas in a book called the Bhagabati Sutra. Around the same time, Indian mathematicians worked out the first beginnings of our modern number system. By 100 AD, people in India were writing the numbers.

Indian mathematician’s biggest invention was the use of zero as a placeholder, to make it easier to add and multiply numbers. Our word "zero" comes from the Sanskrit word meaning "nothing." In 458 AD, Indian mathematicians wrote a book, the Lokavibhaaga, that uses zero in this way. In 628 AD, Brahmagupta wrote a book explaining how zero worked, with rules like "The sum of zero and zero is zero" and "The sum of a positive and a negative is their difference; or, if they are equal, zero.”

Algebraic theories, as also other mathematical concepts, which were in circulation in ancient India, were collected and further developed by Aryabhatta, an Indian mathematician, who lived in the 5th century. He has referred to Algebra as Bijaganitam in his treatise on mathematics named Aryabhattiya, composed in A.D. 499. He was first to treat Mathematics as a distinct subject and he dealt with evolution and involution, area and volume, progressions and algebraic identities, and intermediate equations of the first degree. He also arrived at a remarkably accurate value of PI ( 3.1416). Aryabhatta was also the first to hold that the earth was a sphere and rotated on its axis. He says, to a person traveling in a boat trees on the shore appear to move in opposite direction, similarly because earth is rotating on its axis towards east it appears to us as if the sun moves from east to west. He also explained that the eclipses were caused by the shadow of the earth falling on the moon. One of the most important features of Aryabhatta's mathematical system is his unique system of notation. It is based on the decimal place value system, now in use throughout the civilized world.

Another mathematician of the 12th century, Bhaskaracharya also authored several treatises on the subject ­ one of them, named Siddantha Shiromani has a chapter on algebra. He is known to have given a basic idea of the Rolle's theorum and was the first to conceive of differential calculus Bhaskaracharya's Leelavati translated to English in 1816 by James Taylor.

The 14th century Indian mathematician Madhava of Sangamagrama along with other mathematician’s of the Kerala School studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala School wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated only in seventeenth century Europe.

The credit for fine-tuning and internationalizing these mathematical concepts originated in India ­ goes to the Arabs and Persians. Al-Khawarizmi, a Persian mathematician, developed a technique of calculation that became known as "algorism." This was the seed from which modern arithmetic algorithms have developed. Al-Khwarizmi¹s work was translated into Latin under the title Algoritmi de numero Indorum, meaning The System of Indian Numerals. A mathematician in Arabic is called Hindsa which means from India. With the formation of the Islamic in 16 the century, the use of Indian Mathematics spread quickly from India to West Asia and Africa (by the 800's), and then more slowly to Christian Europe.

Will Durant, American historian, said that India was the mother of our philosophy of much of our mathematics. A. L. Basham, an Australian, writes in his book, "The Wonder That was India" says the world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. Albert Einstein says, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.”

Comments

  1. Nice blog and Algebra is the most important and simple topic in mathematics and I am here to share simple and clear definition of algebra that is ,Its a branch of mathematics that substitutes letters in place of numbers means letters represent numbers.

    ReplyDelete

Post a Comment

Your comments here.

Popular Posts

The Art of Love

Love is often described as a feeling. But love is more than an emotion. It’s an art form. Like a painter with a blank canvas or a poet wrestling with words, those who master the art of love approach it with creativity, vulnerability, and a willingness to evolve. Love is not a monolith. It wears countless unique interconnected faces. Romantic love often takes center stage in our cultural narratives. But love extends far beyond romance. Love is also the quiet devotion of a parent cradling a child and the unspoken loyalty between friends who weather life’s storms together. Philosopher Alain de Botton suggests that love is “a skill, not just an enthusiasm.” It’s not enough to feel love; we must learn to sustain it. This means cultivating empathy, practicing forgiveness, and embracing the imperfections of others. Romantic Love: A Dance of Intimacy and Independence Romantic love is immortalized in poetry, music, and art. It thrives on closeness but requires space; it demands vulnerabil...

Superior Man

The concept of a “superior man” comes from various philosophical, cultural, and historical contexts. Each offering a different perspective on what it means to embody excellence or virtue. In Confucianism, the term “superior man” (or junzi in Chinese) refers to an ideal person who embodies moral excellence, wisdom, and virtue. In the Analects, Confucius describes the junzi as someone who “cultivates themselves to bring peace to others” (Analects 14.42). The superior man is not born superior but becomes so through effort, discipline, and a commitment to virtue. In Stoic philosophy, particularly in the works of Marcus Aurelius or Seneca, the ideal person lives according to reason and virtue, mastering their emotions and focusing on what they can control. Traits like wisdom, courage, justice, and temperance align closely with the junzi, emphasizing self-discipline and ethical living. In Aristotle’s Nicomachean Ethics, the “great-souled man” is someone of exceptional virtue who achieves...

The Backwards Law

The Backwards Law is the idea that the more you pursue or cling to something, the less likely you are to get it. Whether it’s happiness, love, success, or even sleep, the act of striving can feel like chasing a mirage. Conversely, when you let go of your desperate need for it, you often create the conditions for it to come to you naturally. It’s a counterintuitive principle rooted in the interplay of desire, resistance, and acceptance. We live in a world that constantly tells us to strive, to push harder, and to never give up on our goals. We are taught that success, happiness, and love are things to be pursued with relentless effort. What if the very act of chasing something is what pushes it further out of reach? It’s the counterintuitive idea that when you desperately want something, you are subconsciously signaling to yourself that you don’t have it, thus reinforcing a feeling of lack. This feeling of lack often leads to behaviors that are counterproductive to achieving your des...

The Power of Discipline

Discipline is the ability to control your actions, emotions, and behaviors to align with your goals, even when you don’t feel like it. Discipline is the quiet, relentless force that turns dreams into realities, goals into accomplishments, and potential into action. In a world that glorifies instant gratification and quick fixes, discipline stands as a timeless virtue, demanding consistency, sacrifice, and an unwavering commitment to the long game. Discipline is often the unsung hero in the stories of great achievements. It’s not as glamorous as talent, not as fleeting as motivation, and not as celebrated as luck. Discipline is not about perfection; it’s about persistence. It’s the choice to show up, day after day, regardless of external circumstances or internal moods. Motivation might spark the desire to start, but discipline is what keeps you going when the spark fades. Discipline is the bridge between where you are and where you want to be. Without it, even the most brilliant ide...

The Pause Principle

The Pause Principle is the practice of intentionally stopping and reflecting before acting. Pausing is a deliberate and strategic act that enables clarity, awareness, and better choices. It is a simple concept with profound implications for leadership, learning, and life. In a world addicted to speed, the idea of slowing down can feel like a failure. We praise hustle. We reward reaction. We glorify multitasking and speed as if they were synonymous with effectiveness. But the best decisions, the most powerful conversations, and the most transformative moments don’t come from speeding up. The term was coined by Kevin Cashman, a leadership coach and author of The Pause Principle: Step Back to Lead Forward. The term captures the essence of a powerful paradox: slowing down can speed up your effectiveness. When we pause, we engage the prefrontal cortex, the part of the brain responsible for complex thinking, empathy, and decision-making. In contrast, reacting impulsively often activates t...

Nyaya Philosophy - The Art of Logical Thinking

Nyaya is one of the classical schools of Indian philosophy. At its core, Nyaya is a system of rational inquiry that explores things like: What is valid knowledge? How do we know what we know? How can we argue effectively, without falling into fallacies or confusion? Nyaya is a practical philosophy for clear thinking, careful dialogue, and living a life grounded in truth. The Foundations: Four Means of Knowledge Nyaya identifies four valid sources of knowledge (pramanas), a concept that sets it apart from many Western traditions. Perception (Pratyaksha) : What we directly observe with our senses. Inference (Anumana) : Logical reasoning from observation. Comparison/Analogy (Upamana) : Learning something by comparing it to something familiar. Verbal testimony (Shabda) : Trustworthy knowledge from a reliable authority, including scripture or an expert. These four pillars help define how Nyaya separates true knowledge from illusion, error, or blind belief. Logi...

Rules for Living Well: An Eastern Perspective

The Eastern perspective on living well is gentle yet powerful. These teachings prioritize inner peace, balance, and alignment with the natural rhythms of existence. It’s an approach that shifts the focus from external achievements to internal balance. The paths of Buddhism, Taoism, Hinduism, and Confucianism have their distinct characteristics. Let us explore key principles from these traditions for living well. Embrace Impermanence In Buddhist philosophy, the concept of “anicca” or impermanence is a cornerstone of understanding suffering. We cling to pleasure, youth, and success. We resist pain, loss, and change. Our emotions, relationships, possessions, and even our lives are transient. Clinging to things as if they are permanent leads to suffering (dukkha). We must accept the change to live well. Think of a river. It is constantly moving, changing course, and evolving. Trying and holding onto a single drop of water is futile. Similarly, our lives are a continuous flow of experi...

The Enneagram

The Enneagram is a personality framework that identifies nine core personality types, each with its worldview, patterns of thinking, emotional drivers, and habitual behaviors. Unlike many personality systems that focus solely on traits, the Enneagram offers a map to the deeper motivations, fears, and desires that shape how we think, feel, and behave. It reveals patterns of conditioning you’ve picked up over a lifetime and offers a pathway toward greater freedom and authenticity. The Nine Enneagram Types The Reformer (Type One) – Principled, purposeful, and self-controlled, with a deep drive for improvement and integrity. The Helper (Type Two) – Caring, empathetic, and generous, often motivated by a desire to be needed and appreciated. The Achiever (Type Three) – Success-oriented, adaptable, and image-conscious, thriving on accomplishment and recognition. The Individualist (Type Four) – Sensitive, expressive, and introspective, driven by a search for authenticity and identity....

Sharing : Lessons from the universe

In a world obsessed with ownership, boundaries, and individuality, it's easy to forget that life itself only exists because of sharing. Beneath every living cell, within every breath, and throughout every relationship in nature, sharing is not just an act of kindness. Sharing is a biological and spiritual necessity. The electrons in an atom to a vast interconnected web of ecosystems, nature teaches us one clear truth. Nothing exists in isolation. At every level of life, sharing is not optional. It is essential. Atoms are the building blocks of everything in the universe, including stars, rivers, skin, bones, and breath. But a single atom, on its own, is limited. When atoms share electrons through chemical bonds to form molecules. Water (H₂O), which sustains all life, exists because hydrogen and oxygen share electrons. DNA, the molecule that stores life’s genetic code, is a complex result of countless atoms sharing electrons in intricate patterns. Every structure in your body, fr...

Election Talks

The Election Commission of India announced the general election to the 15 th Lok Sabha on March 2, 2009. The elections will be held in 5 phases starting on April 26, 2009 and ending on May 13, 2009. The results of the election will be announced on May 16, 2009. Two phases are over by now. In democracy the election is opportunity to discuss about the future of the country. The state of economy, the current policies, the achievements and failures of the current government etc. should be part of that discussion. Unfortunately our politicians and main stream media seems not interested. Major parties published election manifestos as usual. It talk about subsidies, pensions and free stuff. Also some useless claims of secularism, stability and security. But all of them failed to provide a plan for the future of our country in this fast moving interconnected world. The major discussion points of our politicians are still around secularism. All of them favouring religious and communal elemen...