Numberpile looks at an interesting phenomenon using a common Japanese toy: a small paper balloon that can be crushed and re-inflated. What's the science behind it? Read the rest

Numberpile looks at an interesting phenomenon using a common Japanese toy: a small paper balloon that can be crushed and re-inflated. What's the science behind it? Read the rest

The white circles in this gif travel in a straight line across the diameter of the black circle. In the process, they accelerate toward the center and decelerate away with the velocity of a swinging pendulum. Read the rest

In A Hundred Billion Trillion Stars, Seth Fishman and illustrator Isabel Greenberg (previously) present a the astounding, nearly incomprehensible size of the universe in a picture book that even the very youngest readers will delight in; when I blurbed it, I wrote "Dazzling: the astounding, mind-boggling scale of the magnificent universe and our humbling and miraculous place in it, rendered in pictures and words that the youngest readers will understand."

Romanian artist HyperGlu creates programs and algorithms that generate fascinating images and animations with a geometric and mathematical beauty. Read the rest

Zero-knowledge proofs are one of the most important concepts in cryptography: they're a way to "validate a computation on private data by allowing a prover to generate a cryptographic proof that asserts to the correctness of the computed output" -- in other words, a way to prove that something is true without learning the details. Read the rest

The hexidecimal color #C0FFEE (192 Red, 255 Green, 238 Blue, on a scale of 0-255) is a pleasing greenish color, while #BEADED is a kind of mauve. Read the rest

The average person probably assumes that mathematics is a complete system in which all mathematical statements can be proved or disproved. The fine folks at Numberphile are ready to disabuse folks of this notion with a nice overview of Gödel's Incompleteness Theorem. Read the rest

Maria writes, "Funville Adventures is a creative, joyful, and gentle new project that introduces young children to advanced math. Children as young as 5 will enjoy the story and math-rich play; older children and adults can also investigate the deeper mathematical concepts such as inverse function, composition, and functional." Read the rest

Depths of Antiquity is Julius Horsthuis' hypnotic slow-motion dive into fractals generated from images of churches, castles and other imposing edifices of yesteryear. It's perfectly complemented by Beethoven. Read the rest

Generation Tech has done a few fun videos estimating the costs of items in the Star Wars universe. In the latest installment, they calculate the cost of a star destroyer. Spoilers below. Read the rest

theydidthemath is a fun subreddit. In this post a fellow named Nym figured out how many lentils a recording artist can can buy each time someone plays one of their songs. The assumption is that one Spotify play is worth a half cent, and lentils cost $1.50 a pound. Read the rest

The deceptively simple Collatz Conjecture is one of mathematics' most difficult puzzles. Alex Bellos shows off a cool rendering by Edmund Harris that looks like a beautiful life form from the sea. Read the rest

The Museum of Mathematics recently hosted James Grime's talk "Star Trek: The Math of Khan." He debunked a common stereotype about the show's security detail: redshirts are not the most likely crew to die. Read the rest

In 2012, Vi Hart made this video giving "9.999... reasons that .999... = 1" She also made a video of bad proofs why .999... does not equal 1.

There's some interesting discussion about it at TYWKIWDBI. Read the rest

A better understanding how a sperm swims its way toward an egg could help inform new treatments for male infertility. Researchers from the University of York have now come up with a mathematical formula to model how large numbers of moving sperm interact with fluid they're swimming through. From the University:

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By analysing the head and tail movements of the sperm, researchers have now shown that the sperm moves the fluid in a coordinated rhythmic way, which can be captured to form a relatively simple mathematical formula. This means complex and expensive computer simulations are no longer needed to understand how the fluid moves as the sperm swim.

The research demonstrated that the sperm has to make multiple contradictory movements, such as moving backwards, in order to propel it forward towards the egg.

The whip-like tail of the sperm has a particular rhythm that pulls the head backwards and sideways to create a jerky fluid flow, countering some of the intense friction that is created due to their diminutive sizes.

“It is true when scientists say how miraculous it is that a sperm ever reaches an egg, but the human body has a very sophisticated system of making sure the right cells come together," (says University of York mathematician Hermes Gadêlha.)

“You would assume that the jerky movements of the sperm would have a very random impact on the fluid flow around it, making it even more difficult for competing sperm cells to navigate through it, but in fact you see well defined patterns forming in the fluid around the sperm.

One of the most interesting series ever is *Closer To Truth*, which "presents the world’s greatest thinkers exploring humanity’s deepest questions." For instance: is mathematics invented or discovered? Read the rest

High school teacher Joe Howard (the guy who made the "How loud would it be if all of the cats in the world meowed at the same time?" video I posted a couple of weeks ago, is back. This time, he shows how to come up with a formula to determine how long would it take a pay-it-forward chain to reach 7.4 billion people

Read the restMany people are familiar with the concept of paying forward, but how quickly can it actually spread if we commit to it? This video calculates how many layers of pay it forward would need to happen successfully for the chain to reach everyone on the planet.