Math in History is a series in Medium that writes about brilliant rebels, daring ideas, and discoveries that reshaped civilizations, powered science, and quietly transformed the way we understand our world. Read and enjoy the journey through history!
Contents
- e: The Spark of Mathematics
- How Eratosthenes Measured the Earth
- How a Boy’s Walk to School Birthed the Bell Curve
- Leibniz: The Man Behind Calculus
- Square Root: A Manual Journey
- THE GOLDEN RATIO
- The Boy Who Outsmarted the World’s Greatest Minds
- The Bridges of Königsberg and Graph Theory
- The Divine Proportion: Mathematics of Beauty
- The Genius Who Solved Everything before Dying at 26
- The Man Who Defined Modern Mathematics
- The Man Who Solved the World’s Most Famous Math Problem
- The Man Who Tried to See the Universe Through Equations
- The Most Beautiful Equation
- The Most Dangerous Problem in Math
- The Number That Gives Scientists Headaches
- The Rule of 72
- The Simple Math Problem We Still Can’t Prove
- Who Invented Calculus?
- Why Minus Times Minus Makes Plus
- Why Was Logarithm Introduced?
- Levels of Mathematical Genius: From Ancient Cults to Midnight Duels
- Beauty of Truncatable and Deletable Prime Numbers
- Why Do We Use ‘X’ for the Unknown in Mathematics?
- An Infinite Gift with Finite Volume and Infinite Surface Area
- The Mystery of Fermat’s Last Theorem — from history to new mathematics
- Why 360 Degrees Rules the Circle
- Andrew Wiles and the Long-Awaited Ghost’s End
- The Simplest Problem Mathematics Can’t Prove
- The Multiple Choice Question That Breaks The Social Media
Math in History. “e: The Spark of Mathematics.” Medium, May 22, 2026. https://medium.com/@ganeshonline6/e-the-spark-of-mathematics-a7c6022e4f8b.
The number e is a relatively new discovery compared to its main rival, π (pi). While π has been known since ancient times, going all the way back to the Babylonians, e doesn’t carry that long historical baggage. Instead, e feels fresh and lively. What makes it special is that it naturally appears whenever something is growing. Whether it’s population, money, or physical processes, whenever growth is happening continuously, the number e is almost always involved.
Math in History. “How a Boy’s Walk to School Birthed the Bell Curve.” Medium, May 24, 2026. https://medium.com/@ganeshonline6/how-a-boys-walk-to-school-birthed-the-bell-curve-7a5c3ff4a20c.
People generally think great mathematics comes from complex, abstract ideas. But some of the deepest insights come from simple truths. The rule is straightforward: your result can’t be more precise than your least precise measurement. It seems like just a classroom guideline — but it carries a deeper meaning. Significant figures are about honesty. They remind us that no calculation can create accuracy that wasn’t in the original data. Precision without truth is meaningless. Beyond math, this idea applies everywhere. Whether in science or real-life decisions, your conclusions are only as reliable as your inputs. Sometimes, the most powerful mathematics isn’t complicated — it’s simply honest. But why does that make sense? Why can’t a physical measurement be entirely “accurate”? Why haven’t we simply engineered an instrument capable of making something absolutely “exact”? The intuition behind this limitation wasn’t discovered in a high-tech lab. It came from a young boy in the late 1780s.
Math in History. “How Eratosthenes Measured the Earth.” Medium, June 2, 2026. https://medium.com/@ganeshonline6/how-eratosthenes-measured-the-earth-0ebfeb3fc768.
Eratosthenes concluded that the Earth’s circumference was 250,000 stadia. While historians debate the exact modern equivalent of the Greek stadium he used, the most widely accepted conversion places his estimate at approximately 24,660 miles. Today, using advanced satellite technology, we know the Earth’s meridional circumference (measured from pole to pole) is about 24,860 miles. This means Eratosthenes’ calculation, made over two millennia ago with nothing but a stick, a shadow, and brilliant spatial reasoning, had an error margin of less than 2%. This historical triumph remains one of the most elegant examples of applied mathematics in human history. It demonstrates that profound scientific truths can often be uncovered not through complex technology, but through careful observation and the foundational rules of geometry.
Math in History. “Leibniz: The Man Behind Calculus.” Medium, May 30, 2026. https://medium.com/@ganeshonline6/leibniz-the-man-behind-calculus-93e38bcaad8f.
Gottfried Wilhelm Leibniz was a universal genius who pursued a unified framework for all knowledge, a logical calculus to arrive at the truth, and a universal language for all sciences. During his life, he corresponded with over a thousand scholars, penning more than 20,000 letters, and became one of the most famous philosophers and scientists in Europe. Yet, when he died, his funeral was small, unofficial, and socially insignificant. Here is the story of how one of history’s greatest minds ended up buried in an unmarked grave for over fifty years.
Math in History. “The Boy Who Outsmarted the World’s Greatest Minds.” Medium, May 19, 2026. https://medium.com/@ganeshonline6/the-boy-who-outsmarted-the-worlds-greatest-minds-9f96b124cfab.
In July 1988, the International Mathematical Olympiad in Australia gathered the world’s brightest teens. Among them stood 13-year-old Terence Tao — small, quiet, and the youngest competitor. When Prime Minister Bob Hawke placed a gold medal around his neck, the crowd erupted. Tao had become the youngest gold medalist in the competition’s history, yet he remained calm, almost puzzled by the applause.
Math in History. “The Bridges of Königsberg and Graph Theory.” Medium, May 21, 2026. https://medium.com/@ganeshonline6/the-bridges-of-k%C3%B6nigsberg-and-graph-theory-c31273e7d8ec.
Occasionally, a simple puzzle gives rise to an entirely new area of mathematics. Such cases are rare, but they do occur. The most famous example is the problem of the Bridges of Königsberg, which led Leonhard Euler to found a branch of what is now known as graph theory in 1735.
Math in History. “The Divine Proportion: Mathematics of Beauty.” Medium, June 5, 2026. https://medium.com/@ganeshonline6/the-divine-proportion-mathematics-of-beauty-875364b8fc02.
Have you ever stopped to count the petals on a flower? If you look closely at an intact blossom, you will likely find that the number of petals is 3, 5, 8, 13, or 21. Look at your own hands: you have 2 hands, 5 fingers on each, and 3 segments per finger. These numbers are not a biological accident; they belong to a mathematical pattern known as the Fibonacci sequence. From the spirals of a pinecone to the grand architecture of the modern world, this series of numbers and its resulting geometric ratios govern the hidden structure of the universe.
Math in History. “The Genius Who Solved Everything before Dying at 26.” Medium, May 26, 2026. https://medium.com/@ganeshonline6/the-genius-who-solved-everything-before-dying-at-26-a4abb79834f4.
The history of mathematics is illuminated by brilliant minds, but few stories are as profoundly moving or tragically brief as that of Niels Henrik Abel (1802–1829). In a life spanning a mere twenty-six years, Abel transformed the landscape of algebra and mathematical analysis. Operating under the crushing weight of poverty, family responsibility, and terminal illness, he dismantled centuries-old problems and laid the groundwork for modern group theory and elliptic functions. His journey is a poignant reminder of how sublime intellectual triumph can coexist with devastating personal hardship.
Math in History. “THE GOLDEN RATIO.” Medium, May 12, 2026. https://medium.com/@ganeshonline6/the-golden-ratio-5aa36dd95bbe.
There is a number often described as “perfect”, a number people claim to see everywhere. It appears in discussions of sacred geometry, in patterns found in nature, and in ideas that suggest mathematics is somehow built into the fabric of the universe. This number is known as the golden ratio.
Math in History. “The Man Who Defined Modern Mathematics.” Medium, May 10, 2026. https://medium.com/@ganeshonline6/the-man-who-defined-modern-mathematics-1c20f99e132a.
This French genius revolutionized calculus and laid the foundations of modern mathematical analysis. But that’s not all. He was also a devout Catholic, deeply involved in the Society of Saint Vincent de Paul. He helped establish the Institut Catholique de Paris and even defended the Jesuits at a time when doing so was risky. From Fourier series to complex functions, his contributions are mind-blowing. So the next time you solve a complex problem, remember, you’re standing on the shoulders of a giant named Augustin-Louis Cauchy.
Math in History. “The Man Who Tried to See the Universe Through Equations.” Medium, May 8, 2026. https://medium.com/@ganeshonline6/the-man-who-tried-to-see-the-universe-through-equations-94694b9d5c95.
Before computers, one man tried to calculate everything. He transformed celestial mechanics, showing that the motion of the solar system could be understood through careful mathematics rather than divine intervention. He introduced an important transform, a powerful tool that turns difficult equations into solvable ones, forming a foundation of modern engineering, physics, and signal processing. In probability, He demonstrated how mathematics could be used to measure belief, helping shape what we now call Bayesian thinking. Pierre-Simon Laplace is known as the man who tried to see the universe through equations.
Math in History. “The Man Who Solved the World’s Most Famous Math Problem.” Medium, February 11, 2026. https://medium.com/@ganeshonline6/the-man-who-solved-the-worlds-most-famous-math-problem-a9c60af2d787.
In 1994, Andrew Wiles solved a mystery that had stumped mathematicians for 357 years. He later reflected, “Having solved this problem, there’s certainly a sense of loss, but at the same time there is this tremendous sense of freedom. That particular odyssey is now over. My mind is at rest.”
Math in History. “The Most Beautiful Equation.” Medium, May 3, 2026. https://medium.com/@ganeshonline6/the-most-beautiful-equation-b0b05efb0a4c.
There is a famous equation in mathematics that many people, including professional mathematicians, consider the most beautiful ever discovered. Yes, mathematicians really do debate and even vote on such things, and this equation consistently stands above the rest. It looks almost too simple: eiπ + 1 = 0.
Math in History. “The Most Dangerous Problem in Math.” Medium, May 11, 2026. https://medium.com/@ganeshonline6/the-most-dangerous-problem-in-math-1d1e0a8c685e.
This article is about a math problem that is famously so simple that even elementary school children can understand it — yet no one knows the proof. Many world-class mathematicians have spent decades trying to solve it. In fact, Paul Erdős once said that the mathematics we currently know is still not powerful enough for this problem. There is even a reward of more than 25 million Thai baht for anyone who can solve it. What’s even crazier is that many leading mathematicians around the world say that only “crazy people” would spend their time working on this problem.
Math in History. “The Number That Gives Scientists Headaches.” Medium, June 9, 2026. https://medium.com/@ganeshonline6/the-number-that-gives-scientists-headaches-702ab7fbdf87.
Physicists are paid to worry about numbers, but there is one specific number that has caused more existential dread and obsession than any other. That number is 0.00729735256 — which is approximately 1/137. To close with Richard Feynman’s poetic summary, alpha is “one of the greatest damn mysteries of physics,” musing that “the hand of God wrote that number, and we don’t know how He pushed the pencil.” It remains a tantalizing hint that to build a universe, perhaps only one ultimate number needs to be decided, and from it, all of reality naturally follows.
Math in History. “The Rule of 72.” Medium, May 18, 2026. https://medium.com/@ganeshonline6/the-rule-of-72-7c3751b6a91c.
These days, schools don’t focus on compound interest as much as they used to. Still, there’s a neat little trick called the “Rule of 72” that’s both useful and a bit surprising. It works quite well, and once you see it, it might even make you curious to understand the actual compound interest formula behind it.
Math in History. “The Simple Math Problem We Still Can’t Prove.” Medium, June 8, 2026. https://medium.com/@ganeshonline6/the-simple-math-problem-we-still-cant-prove-ec3e76c1ac31.
Mathematics is often viewed as a rigid discipline of absolute truths and finalized proofs. Yet, it is also a landscape filled with hidden curiosities that appear to act like magic. One of the most famous examples is a seemingly simple number puzzle that has baffled the greatest mathematical minds for nearly a century. Even today, nobody knows definitively why it works. This puzzle is known as the Collatz Conjecture, or the “3n + 1 problem.” It is a wonderful exercise to share with students and enthusiasts alike, proving that you do not need advanced calculus to encounter the frontiers of unknown mathematics.
Math in History. “Square Root: A Manual Journey.” Medium, June 6, 2026. https://medium.com/@ganeshonline6/square-root-a-manual-journey-00ea0e14d49e.
By repeating this cycle of guessing, dividing, and averaging, we systematically close in on the exact value of the square root. While executing this algorithm by hand is undeniably cumbersome compared to relying on digital tools, it bridges the gap between rote memorization and true comprehension. Through the Newton-Raphson method, the abstract concept of a square root transforms into a logical, mechanical reality, granting students and math enthusiasts alike a much deeper appreciation for the numbers hidden within the math.
Math in History. “Who Invented Calculus?” Medium, June 4, 2026. https://medium.com/@ganeshonline6/who-invented-calculus-6a235691c778.
The Newton-Leibniz controversy was a clash of egos, national pride, and vastly different mathematical philosophies. Newton possessed a brilliant, intuitive grasp of how the physical universe moved, modeled beautifully through infinite series. Leibniz was a master of notation, logic, and pure mathematical structure, giving us the dx and dy symbols we still use today. While they fought bitterly in life over who was first, modern mathematics recognizes that we need the genius of both men to understand the universe.
Math in History. “Why Minus Times Minus Makes Plus.” Medium, June 7, 2026. https://medium.com/@ganeshonline6/why-minus-times-minus-makes-plus-12a2df64c3c0.
Putting all of this together, mathematical elegance leads us to define minus times minus to be plus. It is a conscious human convention, crafted to ensure that the rules of algebra remain consistent whether we are dealing with positive or negative values. We could have done it differently, but doing so would have unnecessarily complicated arithmetic and destroyed its logical structure. By choosing this convention, we keep arithmetic beautifully simple — and, as we saw with the debt example, we end up with a tool that accurately models important aspects of the real world.
Math in History. “Why Was Logarithm Introduced?” Medium, June 12, 2026. https://medium.com/@ganeshonline6/why-was-logarithm-introduced-fbf2060b7bba.
In the early 17th century, scientific progress was gridlocked by arithmetic. Astronomers charting planetary orbits and navigators guiding ships across vast oceans faced a paralyzing bottleneck: multiplying seven- or eight-digit numbers together by hand. A single misplaced digit could ruin months of meticulous work, threatening both scientific accuracy and lives at sea. In 1614, Scottish mathematician John Napier discovered a brilliant mathematical loophole that forever altered the course of science. By turning hours of complex multiplication into simple addition, he bypassed the computational limits of his era.
Math in History. “Levels of Mathematical Genius: From Ancient Cults to Midnight Duels.” Medium, June 13, 2026. https://medium.com/@ganeshonline6/levels-of-mathematical-genius-from-ancient-cults-to-midnight-duels-1bd4e5ee90eb.
The journey of mathematics is not just about numbers — it is about vision, rebellion, and raw human intensity. Each of these geniuses saw beyond the obvious, reshaping reality through patterns, logic, and imagination. Some sought recognition, while others rejected it, yet all left marks that continue to define modern thought. Mathematics, at its highest level, is not mere calculation — it is creativity within limits, truth beyond proof, and beauty hidden in abstraction. These stories remind us that true genius does not follow rules; it rewrites them, often at great personal cost.
Math in History. “Beauty of Truncatable and Deletable Prime Numbers.” Medium, June 25, 2026. https://medium.com/@ganeshonline6/beauty-of-truncatable-and-deletable-prime-numbers-52fed4447f5b.
It is easy to dismiss truncatable and deletable primes as simple novelties. However, unexpected mathematical explorations yield profound cognitive and scientific benefits:
New Mathematical Tools: Historically, solving “frivolous” puzzles has forced mathematicians to develop brand-new tools, algorithms, and branches of logic that later solve real-world problems in cryptography and computer science.
Cognitive Flexibility: Tackling problems that come completely out of left field forces the human brain to bypass rigid formulas learned in school, fostering lateral thinking and sharper problem-solving skills.
Sometimes, a mathematical concept doesn’t need an immediate commercial application to be valuable — sometimes, the joy of discovery and the mental exercise are more than enough.
Math in History. “Why Do We Use ‘X’ for the Unknown in Mathematics?” Medium, July 4, 2026. https://medium.com/@ganeshonline6/why-do-we-use-x-for-the-unknown-in-mathematics-e04ad8946a8a.
Since the 17th century, the letter x has transcended mathematics entirely. It has evolved into a universal symbol for the unknown, the mysterious, and the extraordinary in popular culture — giving us iconic names like the X-Files and the X-Men. Next time you are balancing an equation, remember that the symbol you are solving for is likely there simply because a French printer had a few extra metal blocks lying around!
Math in History. “An Infinite Gift with Finite Volume and Infinite Surface Area.” Gabriel’s Horn (also known as Torricelli’s Trumpet). Medium, July 7, 2026. https://medium.com/@ganeshonline6/an-infinite-gift-with-finite-volume-and-infinite-surface-area-8ddce5631f6d.
The paradox of the Infinite Gift leaves us with a profound realization: an object can possess an endless, infinite boundary while simultaneously containing a strictly limited, finite amount of space. In pure mathematics, these objects belong to a vital class of shapes that expand our understanding of geometry and calculus. However, if we look at this from a physics perspective, an infinite object like this cannot truly be constructed in the real world. As you descend further down the stack, the boxes would eventually become smaller than a single atom. At that microscopic scale, the smooth laws of classical geometry yield to quantum mechanics, making physical construction impossible. Nonetheless, as a thought experiment, the Infinite Gift remains a spectacular way to unwrap the beautiful complexities of mathematical infinity.
Math in History. “The Mystery of Fermat’s Last Theorem — from History to New Mathematics.” Medium, July 14, 2026. https://medium.com/@ganeshonline6/the-mystery-of-fermats-last-theorem-from-history-to-new-mathematics-b3101eb7af85.
For over 350 years, Fermat’s Last Theorem stood as a tantalizing unsolved mystery, driving major developments in algebraic number theory. It was finally put to rest in 1995 when Andrew Wiles published a rigorous, modern proof. While Fermat may not have had the tools to truly prove his own theorem, the centuries-long quest to solve his puzzle forever changed the landscape of mathematics.
Math in History. “Why 360 Degrees Rules the Circle.” Medium, August 2, 2026. https://medium.com/@ganeshonline6/why-360-degrees-rules-the-circle-00766cd8f3d4.
The idea of dividing a circle into 360 degrees comes from ancient Babylonian mathematicians. This system has been used for thousands of years, but it has also faced some challenges.
Math in History. “Andrew Wiles and the Long-Awaited Ghost’s End.” Medium, August 4, 2026. https://medium.com/@ganeshonline6/andrew-wiles-and-the-long-awaited-ghosts-end-7ea5e7296be2.
In mathematics, some problems are simple to solve, while others are very difficult. For more than 300 years, one equation puzzled and challenged many of the world’s best mathematicians. This is the story of Fermat’s Last Theorem and the mathematician who finally proved it.
Math in History. “The Simplest Problem Mathematics Can’t Prove.” Medium, August 5, 2026. https://medium.com/@ganeshonline6/the-simplest-problem-mathematics-cant-prove-49b8939e5b31.
The Collatz conjecture remains difficult to resolve. The rule is very simple, but its behavior is not fully understood. There are strong reasons to think it works for positive numbers, but similar reasoning also applies to negative numbers, where the rule does not lead to 1. After many years of study, it is still not clear what causes this difference.
Math in History. “The Multiple Choice Question That Breaks The Social Media.” Medium, August 9, 2026. https://medium.com/@ganeshonline6/the-multiple-choice-question-that-breaks-the-social-media-23958f019c6f.
Self-referential paradoxes often become popular on the internet because they look like simple questions that can be solved quickly. However, they may have no consistent answer. This difference between how simple the question looks and how difficult it is to resolve leads to many arguments online. People often believe they have found the obvious answer, while other people reach different conclusions. As a result, these questions can spread widely on social media and become popular again every few years.
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