In a paper published by the International Association for Cryptologic Research, a group of Harvard and MIT cryptographers demonstrate that even if the government were to backdoor encryption and lock up anyone who used non-backdoored systems, people could still hide undetectable, secure, private messages within the messages sent over the compromised systems.
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Multiplying large numbers before calculators led to a number of ingenious inventions to make things easier, like these Genaille-Lucas rulers demonstrated by the fine folks at DONG.

Via manufacturer Creative Crafthouse:

In the days before calculators, methods of simplifying calculations were of much interest. In 1617 Napier also published a book describing a method to multiply, divide and extract square roots using a set of bars or rods. These became known as Napier's Bones. (avail on our website)

In the late 1800s, Henri Genaille, a French civil engineer, invented an improvement to Napier's Bones that eliminates the need to handle carries from one digit position to the next. The problem was posed by Edouard Lucas and thus the alternate name of Genaille-Lucas Rulers (or Rods).

There are also sets for division. You can get your own set online or print your own from these free files.

• Genaille-Lucas Rulers (YouTube / DONG) Read the rest

YouTuber Dani Ochoa says she's a "girl with too much time on her hands," but I disagree. I think figuring out the math formula to play the *Star Wars* "Cantina Band" song with just a paper and pencil is *exactly* what she should be doing with her time.

Listen to this and compare:

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Mathematician Hannah Fry explains the "Ham Sandwich Theorem," a mathematical concept that says that even the most poorly constructed sandwich can be cut exactly in half with only one straight cut of a knife. Read the rest

Mathematician Henry Sagerman and colleagues developed a cool way to observe non-euclidian geometry from a new vantage point: inside the geometry itself via virtual reality. 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