# Before Newton, Kerala Was Already Taking Mathematics Toward Infinity Calculus Wasn’t Born in Europe Alone, The Kerala Mathematicians Who Were Solving the Sky Author: Sandesh · Published: 2026-08-25 · Updated: 2026-08-25 · Section: Blog · Category: Foundations · Reading time: 12 min · Publisher: Supastro (Quantum Karma), Bangalore, India _The Kerala School of Mathematics: When Better Astronomy Pushed Mathematics Toward Calculus_ --- I used to think of calculus as one of those subjects that appeared in history with Newton and Leibniz, complete with derivatives, equations and terrifying school textbooks. Then I discovered what happened in medieval Kerala. Between roughly the 14th and 16th centuries, a remarkable community of Indian mathematician-astronomers developed infinite series for π, sine, cosine and inverse tangent. Their work appeared centuries before comparable results were rediscovered in Europe. The mathematician most strongly associated with this breakthrough was **Madhava of Sangamagrama**, who lived around the late 14th and early 15th centuries. And here is the part that gets seriously interesting for anyone fascinated by Jyotish: A major driver of this mathematics was astronomy. Not astrology in the simplistic modern sense of "tell me whether my crush will text me." > Astronomy meant calculating the positions and movements of celestial bodies, including the Sun and Moon, and phenomena such as eclipses. Those calculations mattered to the broader Indian Jyotisha tradition, which had long connected astronomical computation with calendrical and astrological practice. So yes, there is a fascinating historical connection between the pursuit of more accurate celestial calculations and the development of mathematics that looks remarkably like early analysis. But I want to make one correction before the internet turns this into another viral half-truth: It would be inaccurate to say that calculus was literally invented solely to make better horoscopes. The Kerala School did not produce the complete modern calculus of Newton and Leibniz in the exact form we learn today. What it did produce was something extraordinary: mathematical techniques involving infinite series, limits, approximations and trigonometric functions that anticipated important elements of later calculus. Historians therefore debate exactly how far the label "calculus" should be pushed. And honestly, the historically accurate version is more impressive than the myth. --- ## So what actually happened in Kerala? Imagine trying to calculate the position of the Moon without a smartphone, astronomical software or a computer. You have observations. You have geometric models. You have trigonometry. You have numerical tables. And you need increasingly accurate answers. The Moon does not politely give you its coordinates. The sky is continuous, while your calculations are finite. That creates a problem. How do you squeeze greater precision out of limited arithmetic? This is where the Kerala mathematicians became seriously clever. Madhava developed infinite series equivalent to modern expansions for sin x, cos x and arctan x. He also developed series for π. Ranjan Roy's historical study published by Cambridge notes that Madhava's work appeared more than two and a half centuries before Newton's corresponding rediscoveries of these series in Europe. One famous result can be written in modern notation as: **π/4 = 1 − 1/3 + 1/5 − 1/7 + ...** That infinite process gives increasingly accurate approximations to π. Madhava also developed corrections that dramatically improved the efficiency of the calculation. Historical accounts attribute to the Kerala tradition an approximation of π accurate to many decimal places, including a famous value equivalent to **3.14159265359**. Think about that for a second. No calculator. No Python. No Excel. No GPU. No Google. Just mathematics, observation and an extraordinary ability to reason about infinity. --- ## Why did astronomy need this? Because celestial mechanics is basically a precision problem. If I want to know where the Moon will appear, I need angular calculations. If I want to understand an eclipse, I need relationships between celestial positions. If I want to construct astronomical tables, I need trigonometric calculations. And if my trigonometric approximations are poor, my astronomical predictions become poor. Cambridge's historical account notes that Madhava's surviving astronomical work included methods for determining the Moon's position at a particular time, while his student Paramesvara made systematic observations of solar and lunar eclipses between 1395 and 1432. > This is the key distinction I want to preserve: The mathematics was directly connected to astronomy. Astronomy, in the Indian intellectual environment, was deeply connected with Jyotisha and calendrical practice. That is much stronger historically than claiming that Madhava sat down and said, "I need calculus because someone's horoscope needs more accuracy." We simply do not have evidence for that specific story. --- ## And where does karma enter this? This is where I think the story becomes relevant to 2026. Karma is frequently reduced to: "Do good things and good things happen." Or worse: "Everything bad happening to you is because of your past karma." Neither is a sufficient representation of the philosophical idea. > In the Bhagavad Gita, karma fundamentally concerns action. One of the most famous teachings appears in 2.47, where Krishna tells Arjuna that his sphere of responsibility is action rather than possession of its results. For me, that creates a useful modern framework: Karma is not merely what happens to me. It is also what I repeatedly do. My decisions create consequences. My habits create tendencies. My reactions reinforce patterns. My choices affect other people. And those patterns can influence what happens next. That does not mean every event in life can be scientifically reduced to karma. It cannot. --- ## Three useful ways to understand karma ### 1. Sanchita karma Traditionally understood as accumulated karma: the larger store of past actions and their potential consequences. In modern language, I think of this carefully as the background of accumulated tendencies and consequences rather than a literal spreadsheet sitting somewhere in the universe. ### 2. Prarabdha karma This refers to that portion of karma understood as already bearing fruit in the present life. The practical lesson is not "everything is predetermined." It is: Some conditions are given to me. My response to them is still part of my agency. ### 3. Kriyamana or Agami karma This points toward karma being generated through present action and its future consequences. And this is where 2026 becomes fascinating. Every day, I am effectively creating patterns. I doomscroll for hours. I procrastinate(or not). I stand for honest and fairness. I keep promises. I build something. I exercise. I learn. I help someone. I repeatedly choose the same toxic relationship pattern. Each action changes what becomes easier to do next. That is karma in a very practical sense. --- ## The astrology connection: don't confuse calculation with destiny This is where I think modern Jyotish needs a serious upgrade. A birth chart is a symbolic and computational representation based on astronomical positions at a particular time and place. The Kerala mathematicians remind me of something important: If the underlying astronomical calculation is sloppy, everything downstream becomes sloppy. That applies to modern astrology too. If planetary positions are wrong, divisional charts can be wrong. If the birth time is wrong, the Ascendant can change. If calculations are inconsistent, degrees, nakshatras, Vargas and other derived factors can become unreliable. Precision matters. But precision in calculation does not automatically prove that every astrological interpretation is scientifically validated. Those are two separate questions. The Kerala School gives us a history of extraordinary mathematical astronomy. It does not provide modern scientific proof that planetary positions causally determine human personality or destiny. I think intellectual honesty makes the story stronger, not weaker. --- ## What does this mean for me in 2026? I don't need to live as if my birth chart is a prison sentence. I can treat Jyotish as a framework for reflection, timing, symbolism and decision-making while remembering that my actions still matter. The Gita's teaching is particularly powerful here: act, but do not become psychologically enslaved to the outcome. So my modern karma practice is simple. **First, calculate carefully.** Before making a major decision, separate facts from assumptions. **Second, observe my patterns.** What do I repeatedly do even when I know it hurts me? **Third, identify my controllables.** I cannot control the economy, another person's choices or yesterday. I can control today's action. **Fourth, stop using karma as blame.** Someone suffering does not give me permission to say, "That's their karma." That is not wisdom. It is often just cruelty wearing spiritual vocabulary. **Fifth, use astrology as a mirror, not an excuse.** If a chart suggests a challenging period, I can ask: "What behaviour would help me navigate this intelligently?" Not: "Why bother? My destiny is already fixed." --- ## My DIY Karma Audit Tonight, I can take ten minutes and write five questions: 1. What pattern keeps repeating in my life? 2. What action of mine contributes to that pattern? 3. What part of this situation is genuinely outside my control? 4. What is one action I can take differently tomorrow? 5. If I repeated tomorrow's behaviour for one year, where would it take me? That last question is brutal. And useful. Because karma becomes much more understandable when I stop treating it as supernatural punishment and start examining the relationship between action, intention, habit and consequence. --- ## The bigger lesson from Kerala For me, the most inspiring part of this story isn't that India can claim a mathematical "gotcha" against Newton. History is not a schoolyard competition. Newton was extraordinary. Leibniz was extraordinary. So were Madhava, Paramesvara, Nilakantha Somayaji and Jyesthadeva. The real lesson is that human knowledge developed through multiple intellectual traditions, and some of those traditions were ignored, underestimated or poorly represented in older histories of mathematics. The Kerala School pushed mathematics toward infinity because astronomers wanted better ways to understand and calculate the heavens. Its mathematicians developed results that anticipated important pieces of later mathematical analysis, centuries before those results appeared independently in Europe. And that brings me back to where I started. I don't see this merely as an old story about π. I see a deeper lesson. When human beings become obsessed with asking better questions about the sky, they sometimes end up discovering better mathematics for understanding the world below it. And perhaps that is the most useful way for me to think about karma in 2026 too. I cannot control every condition I inherit. I cannot control every result. But I can improve the quality of the calculation. I can examine my patterns. I can make better decisions. And then I can act. That is where ancient mathematics, Jyotisha and the philosophy of karma unexpectedly meet: not in the promise that destiny is fixed, but in the discipline of understanding what I can know, what I cannot know, and what I choose to do next. --- _Sources_ - [_MacTutor: Madhava of Sangamagrama_](https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/?utm_source=chatgpt.com) - [_Cambridge University Press: Power Series in Fifteenth-Century Kerala_](https://www.cambridge.org/core/books/abs/sources-in-the-development-of-mathematics/power-series-in-fifteenthcentury-kerala/4B3570D4505BBADE0567CB23264C8C0A?utm_source=chatgpt.com) - [_Cambridge University Press: Spherical Trigonometry in the Astronomy of the Medieval Kerala School_](https://www.cambridge.org/core/journals/highlights-of-astronomy/article/spherical-trigonometry-in-the-astronomy-of-the-medieval-kerala-school/756B9796F3038E541C32C1905ECBA0CA?utm_source=chatgpt.com) - [_Gita Supersite, IIT Kanpur: Bhagavad Gita 2.47_](https://www.gitasupersite.iitk.ac.in/dv/bhagavadgita/2.47?utm_source=chatgpt.com) --- Canonical: https://supastro.com/blog/before-newton-kerala-was-already-taking-mathematics-toward-infinity · Supastro is an AI astrology platform for Vedic astrology (Jyotish), built as Vedic Super Intelligence (SI), by Quantum Karma, Bangalore, India. Chart positions are computed from NASA JPL ephemeris data on the Lahiri (Chitrapaksha) ayanamsa. 40 instruments are free to use.