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. (more…)

]]>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. (more…)

]]>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. (more…)

]]>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. (more…)

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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. (more…)

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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. (more…)

]]>https://www.youtube.com/watch?v=Fn9-3nG-omA

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." (more…)

]]>https://www.youtube.com/watch?v=Fn9-3nG-omA

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." (more…)

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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. (more…)

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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. (more…)

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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. (more…)

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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. (more…)

]]>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.]]>

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.]]>

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. (more…)

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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. (more…)

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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. https://youtu.be/wsOXvQn3JuE

There's some interesting discussion about it at TYWKIWDBI.
]]>

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. https://youtu.be/wsOXvQn3JuE

There's some interesting discussion about it at TYWKIWDBI.
]]>

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:

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.

"Mystery of how sperm swim revealed in mathematical formula"

*(Animated GIF by Michelle Davis)*]]>

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:

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.

"Mystery of how sperm swim revealed in mathematical formula"

*(Animated GIF by Michelle Davis)*]]>

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? (more…)

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? (more…)

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

]]>Many 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.

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

]]>Many 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.

Ever try to move a sofa down a hallway that has a corner? The underlying math behind it inspired a math problem that's been a puzzler since 1966. Gerver's Sofa above shows the parameters: a U-shaped sofa moving around a 90-degree corner in an even-width hallway. Gerver's got the record so far, and it is likely the optimal sofa. (more…)

]]>Ever try to move a sofa down a hallway that has a corner? The underlying math behind it inspired a math problem that's been a puzzler since 1966. Gerver's Sofa above shows the parameters: a U-shaped sofa moving around a 90-degree corner in an even-width hallway. Gerver's got the record so far, and it is likely the optimal sofa. (more…)

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Mathematician Gordon Hamilton presents a curious puzzle inspired by the art of Piet Mondrian: within a square canvas filled with rectangles that all have different dimensions, what's the lowest possible score when subtracting the smallest rectangle's area from the largest? (more…)

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Mathematician Gordon Hamilton presents a curious puzzle inspired by the art of Piet Mondrian: within a square canvas filled with rectangles that all have different dimensions, what's the lowest possible score when subtracting the smallest rectangle's area from the largest? (more…)

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Fast-talking national-treasure math vlogger Vi Hart (previously) takes a statistical look at the polling data from the 2016 presidential election and concludes that the most significant divide in the country is "old vs young," which drives things like rural/urban (because young people leave failing rural areas for cities) and even racial divides. (more…)

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Fast-talking national-treasure math vlogger Vi Hart (previously) takes a statistical look at the polling data from the 2016 presidential election and concludes that the most significant divide in the country is "old vs young," which drives things like rural/urban (because young people leave failing rural areas for cities) and even racial divides. (more…)

]]>"Donald in Mathmagic Land" was released in 1959. As Walt Disney said, "The cartoon is a good medium to stimulate interest."

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"Donald in Mathmagic Land" was released in 1959. As Walt Disney said, "The cartoon is a good medium to stimulate interest."

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Math problems are more interesting when they are posed as horror stories.

The Josephus Problem gets its name from Titus Flavius Josephus, a first-century Jewish scholar.]]>The story goes that he was with 40 other soldiers when they were surrounded by conquering Romans - imagine that scene in Games of Thrones, where Ramsay Bolton's men trap Jon Snow's army in a tight circle and start moving in. Rather than give themselves up, the soldiers decided to commit suicide en mass, but by killing each other rather than themselves, to avoid any last-minute changes of heart. Sitting in a circle, the first soldier would kill the man to the left of him, the next living soldier would kill the man to his left, and so on around the circle. When the circle of slaughter got back to the start, the process would repeat with the smaller group of people. Finally, the last man alive would fall on his sword. Josephus' problem was that he was much keener on living than dying - but he didn't want to let his fellow soldiers in on that secret. So, where should he position himself in the circle to be the last man standing?

Math problems are more interesting when they are posed as horror stories.

The Josephus Problem gets its name from Titus Flavius Josephus, a first-century Jewish scholar.]]>The story goes that he was with 40 other soldiers when they were surrounded by conquering Romans - imagine that scene in Games of Thrones, where Ramsay Bolton's men trap Jon Snow's army in a tight circle and start moving in. Rather than give themselves up, the soldiers decided to commit suicide en mass, but by killing each other rather than themselves, to avoid any last-minute changes of heart. Sitting in a circle, the first soldier would kill the man to the left of him, the next living soldier would kill the man to his left, and so on around the circle. When the circle of slaughter got back to the start, the process would repeat with the smaller group of people. Finally, the last man alive would fall on his sword. Josephus' problem was that he was much keener on living than dying - but he didn't want to let his fellow soldiers in on that secret. So, where should he position himself in the circle to be the last man standing?

In this Scientific American video, Rubik's Cube master Ian Scheffler, author of the new book Cracking the Cube, explains some of the math behind "speedcubing." Scheduler's book sounds fascinating even though the only way I could get my Rubik's Cube solved is to hand it to my 10-year-old son's friend Luc who was the first to dazzle me with the fine art of speedcubery.

From the description of Cracking the Cube:

When Hungarian professor Ernő Rubik invented the Rubik’s Cube (or, rather, his Cube) in the 1970s out of wooden blocks, rubber bands, and paper clips, he didn’t even know if it could be solved, let alone that it would become the world’s most popular puzzle. Since its creation, the Cube has become many things to many people: one of the bestselling children’s toys of all time, a symbol of intellectual prowess, a frustrating puzzle with 43.2 quintillion possible permutations, and now a worldwide sporting phenomenon that is introducing the classic brainteaser to a new generation.

In Cracking the Cube, Ian Scheffler reveals that cubing isn’t just fun and games. Along with participating in speedcubing competitions—from the World Championship to local tournaments—and interviewing key figures from the Cube’s history, he journeys to Budapest to seek a meeting with the legendary and notoriously reclusive Rubik, who is still tinkering away with puzzles in his seventies.

Getting sucked into the competitive circuit himself, Scheffler becomes engrossed in solving Rubik’s Cube in under twenty seconds, the quasi-mystical barrier known as “sub-20,” which is to cubing what four minutes is to the mile: the difference between the best and everyone else.

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In this Scientific American video, Rubik's Cube master Ian Scheffler, author of the new book Cracking the Cube, explains some of the math behind "speedcubing." Scheduler's book sounds fascinating even though the only way I could get my Rubik's Cube solved is to hand it to my 10-year-old son's friend Luc who was the first to dazzle me with the fine art of speedcubery.

From the description of Cracking the Cube:

When Hungarian professor Ernő Rubik invented the Rubik’s Cube (or, rather, his Cube) in the 1970s out of wooden blocks, rubber bands, and paper clips, he didn’t even know if it could be solved, let alone that it would become the world’s most popular puzzle. Since its creation, the Cube has become many things to many people: one of the bestselling children’s toys of all time, a symbol of intellectual prowess, a frustrating puzzle with 43.2 quintillion possible permutations, and now a worldwide sporting phenomenon that is introducing the classic brainteaser to a new generation.

In Cracking the Cube, Ian Scheffler reveals that cubing isn’t just fun and games. Along with participating in speedcubing competitions—from the World Championship to local tournaments—and interviewing key figures from the Cube’s history, he journeys to Budapest to seek a meeting with the legendary and notoriously reclusive Rubik, who is still tinkering away with puzzles in his seventies.

Getting sucked into the competitive circuit himself, Scheffler becomes engrossed in solving Rubik’s Cube in under twenty seconds, the quasi-mystical barrier known as “sub-20,” which is to cubing what four minutes is to the mile: the difference between the best and everyone else.

]]>

When *60 Minutes* profiled child math whiz Jacob Barnett, he demonstrated how he imagined numbers as shapes. Numberphile's Simon Pampena analyzed Jacob's thought process. (more…)

When *60 Minutes* profiled child math whiz Jacob Barnett, he demonstrated how he imagined numbers as shapes. Numberphile's Simon Pampena analyzed Jacob's thought process. (more…)

Understanding advanced mathematics can change how you see the world, so prepare for an eye-opening journey into the world of fixed points, courtesy of Michael at Vsauce. (more…)

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Understanding advanced mathematics can change how you see the world, so prepare for an eye-opening journey into the world of fixed points, courtesy of Michael at Vsauce. (more…)

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The Scottish sketch comedy series *Limmy’s Show!* explores that classic riddle in the best way possible. As someone wrote on Tumblr, “This is me during every moment of math class.”

The Scottish sketch comedy series *Limmy’s Show!* explores that classic riddle in the best way possible. As someone wrote on Tumblr, “This is me during every moment of math class.”

Swirling a ball in a cup gets it spinning in the direction of the swirl, but adding six more starts them swirling in the opposite direction.

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Swirling a ball in a cup gets it spinning in the direction of the swirl, but adding six more starts them swirling in the opposite direction.

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It turns out that folding a pizza slice lengthwise to improve its rigidity is a great example of the "Remarkable Theorem" by Gauss. Cliff Stoll explains. (more…)

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It turns out that folding a pizza slice lengthwise to improve its rigidity is a great example of the "Remarkable Theorem" by Gauss. Cliff Stoll explains. (more…)

]]>Data-scientist Kevin H Wilson argues that computers are tools for manipulating data -- from companies' sales data to the input from games controllers -- but we teach computer programming as either a way to make cool stuff (like games) or as a gateway to "rigorous implementation details of complicated language," while we should be focusing on fusing computer and math curriciula to produce a new generation of people who understand how to use computers to plumb numbers to find deep, nuanced truths we can act upon. (more…)

]]>Data-scientist Kevin H Wilson argues that computers are tools for manipulating data -- from companies' sales data to the input from games controllers -- but we teach computer programming as either a way to make cool stuff (like games) or as a gateway to "rigorous implementation details of complicated language," while we should be focusing on fusing computer and math curriciula to produce a new generation of people who understand how to use computers to plumb numbers to find deep, nuanced truths we can act upon. (more…)

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Meet Danica McKellar who as an undergraduate in college co-published a paper titled "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on Z2," research that resulted in the Chayes–McKellar–Winn theorem. Oh yeah, before that, McKellar was Winnie on The Wonder Years.

(And just to confirm, Josh Saviano who played Paul Pfeiffer did not grow up to become Marilyn Manson.)

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Meet Danica McKellar who as an undergraduate in college co-published a paper titled "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on Z2," research that resulted in the Chayes–McKellar–Winn theorem. Oh yeah, before that, McKellar was Winnie on The Wonder Years.

(And just to confirm, Josh Saviano who played Paul Pfeiffer did not grow up to become Marilyn Manson.)

]]>

Math teacher at Dana Hills High School in southern California, late 1970s. Pitted. So pitted.

Posted by the engaged educator's son on r/OldSchoolCool and making the rounds again. ]]>

Math teacher at Dana Hills High School in southern California, late 1970s. Pitted. So pitted.

Posted by the engaged educator's son on r/OldSchoolCool and making the rounds again. ]]>

https://www.youtube.com/watch?v=arOkGC9lCAk

Love Hulten writes, "The Echo Observatory is a handcrafted tribute to fractals and self-similar patterns. It's a mysterious artifact that both generates and visualizes complex mathematical formations, in real-time." (more…)

]]>https://www.youtube.com/watch?v=arOkGC9lCAk

Love Hulten writes, "The Echo Observatory is a handcrafted tribute to fractals and self-similar patterns. It's a mysterious artifact that both generates and visualizes complex mathematical formations, in real-time." (more…)

]]>To celebrate Pi Day (3/14), have fun with MyPiDay, developed last year by Stephen Wolfram and company. Enter your birthday or any other number and see where it first appears in pi.

Background in Wolfram's post here.]]>

To celebrate Pi Day (3/14), have fun with MyPiDay, developed last year by Stephen Wolfram and company. Enter your birthday or any other number and see where it first appears in pi.

Background in Wolfram's post here.]]>