The Math Flow

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There’s a 3D shape that only has ONE side and ONE edge. It's the Möbius Strip. It completely breaks the rules of everyday geometry, and you can build one in your hands right now. The 5-Second Experiment: Cut a long strip of paper. Give one end a half-twist (180°). Tape the two ends together. Now, take a pen and draw a continuous line down the centre without lifting the tip. Eventually, your line will meet its exact starting point, and you’ll realise you just covered the entire surface of the paper without ever crossing an edge. There is no "inside" or "outside"!

The Greatest Dispute in the History of Science: Who Really Invented Calculus? 1. The Setup: Imagine inventing the most powerful mathematical tool in human history... and then keeping it a secret for 20 years. That’s exactly what happened in the 17th century, setting the stage for a bitter, lifelong war between two absolute geniuses. Let’s dive into the calculus clash that divided the scientific world. 2. The Secretive Genius: Sir Isaac Newton The year is 1665. The bubonic plague is ravaging London, and a young Isaac Newton is isolating at his family farm. During this "year of wonders," he invents a new mathematical system to describe the motion of planets and falling apples. He calls it the "method of fluxions." But Newton, terrified of criticism, locks his notes away. 3. The Brilliant Diplomat: Gottfried Wilhelm Leibniz Fast forward to Paris, 1674. Enter Leibniz: a German philosopher, diplomat, and master networker. Working completely independently, Leibniz developed his own version of this math. Unlike Newton, Leibniz realised that good math needs a good language. He designs an elegant, intuitive notation. And crucially? In 1684, he actually published his work. 4. The Spark When Newton's allies see Leibniz's paper, they lose their minds. "He stole it!" they cry. Newton had shared a few letters with Leibniz years earlier. They contained cryptic anagrams hinting at his discoveries, but no actual proofs. Newton became convinced Leibniz had cracked his codes and stolen his life's work. 5. The War of the Minds The scientific community splits into two: the British backing Newton, the Europeans backing Leibniz. Leibniz appeals to the Royal Society in London to settle the dispute fairly. The problem? The President of the Royal Society is... Isaac Newton. 6. The Verdict Surprise, surprise! The Royal Society "investigates" and releases a report declaring Newton the sole inventor and branding Leibniz a plagiarist. We now know Newton secretly wrote the "impartial" report himself. Leibniz’s reputation is destroyed. He dies a few years later, dishonoured and impoverished. 7. The Ultimate Irony Today, historians agree it was a massive coincidence. Both men independently invented calculus, approaching it from different angles. Newton was the first to invent it. But Leibniz was first to publish.

The Dynamics of a Pendulum.

Sir Isaac Newton didn’t actually invent Newton's Cradle. While the toy perfectly demonstrates Newton's laws of motion (specifically the third law: for every action, there is an equal and opposite reaction), the cradle as we know it was invented in 1967 by an English actor named Simon Prebble. He named it after Newton as a tribute to the physics genius, and it quickly became a massive hit.

@joel_ndlovu Yes, this is absolutely what the meme Is about.

@TheMathFlow Ironically 2, the only even prime number amongst infinitely many odd primes, is the the odd one out.

Two is the only even prime number.

@slimsesan Exactly, you said it all.

@TheMathFlow Truly unique, 2 is the only prime number!

The Architecture of Dimensions. A single dot is just a solitary piece of information. Pull a string from it, and it suddenly has direction. Cross it with a second string, and it weaves a flat grid. Add a third, and it blossoms into a solid cube you can hold in your mind. But what happens when you add a fourth? Our human eyes cannot picture a four-dimensional shape, but visual node notation makes the unimaginable beautifully simple. Instead of getting lost in endless, expanding brackets, you simply draw another branch on the circle. From the physics of the universe to the deep learning models shaping our future, this is how complexity is built one simple connection at a time. Sometimes, the most elegant way to grasp the infinite is just to draw a picture.

@voidal_ubiety Somewhat kind of that.

@TheMathFlow It reminds me of black hole lensing effects

The Rössler Attractor.

@Justin511buddy How does that work?

@TheMathFlow Golden spiral stuff..

@techartist_ @WizardAlien This is even more beautiful.💫

@TheMathFlow @WizardAlien Beautiful, I coded the Rossler Attractor with Three.js some time back

Was math discovered or invented?

@Musingsonmath @PhysInHistory This is a great reply. I have had such teachers too.

@PhysInHistory My high school physics teacher. Brilliant guy who will only ever be famous in the minds of his students.

Who do you think is the best Physics explainer of all time? ✍️

The Mind-Bending Anatomy of π:

@pmddomingos Mathematicians already possess the Gabriel horn.

Everyone can fall down a rabbit hole, but only a mathematician can fall down an infinite one.

@ebarschkis A must require feature especially for me.😋

X should add Latex rendering for posts.

Ever wonder how your favorite video games calculate a perfect barrel roll? Or how engineers orient satellites in deep space? It all comes down to the magic of 3D Rotation Matrices! This cheat sheet breaks down the exact linear algebra required to rotate any point or object in 3D space along the primary axes. Here is the mathematical breakdown of how to spin the world: 🔴 Roll (X-axis): To rotate around the x-axis by angle Φ, we keep the x-coordinate the same and mix the y and z coordinates. 🟢 Pitch (Y-axis): To rotate around the y-axis by angle θ, the y-coordinate stays fixed. 🔵 Yaw (Z-axis): To rotate around the z-axis by angle ψ, the z-coordinate locks in while x and y shift.