Henry Segerman takes a brisk stroll through the world of four-dimensional objects with some really cool 3D-printed sculptures, like this sphere that projects a square grid when lit: Read the rest

Henry Segerman takes a brisk stroll through the world of four-dimensional objects with some really cool 3D-printed sculptures, like this sphere that projects a square grid when lit: 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

It's been 15 years since the publication of Steven Wolfram's A New Kind of Science, a mindblowing, back-breaking 1,200-page book that (sort of) says the whole universe is made up of recursive fractals, also noteworthy for the frequent repetition of the phrase "A new kind of science" in its early chapters. Read the rest

FJ Anscome's classic, oft-cited 1973 paper "Graphs in Statistical Analysis" showed that very different datasets could produce "the same summary statistics (mean, standard deviation, and correlation) while producing vastly different plots" -- Anscome's point being that you can miss important differences if you just look at tables of data, and these leap out when you use graphs to represent the same data. 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

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:

Read the restBy 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.

Vi Hart (previously) is the fast-talking, doodling, hyper-charming mathematical vlogger whose Pi Day videos are consistently the best of the season, even when she's pooping on Pi, she always manages to fascinate and delight. Read the rest

MNTNT's Albert Clock is a clock that presents the hours and minutes as simple math problems. Is it annoying or engaging? Or.... both!

In standard mode, the queries change every minute. They are completely random, so even the query for the hours change, even if the result stays the same.

You can speed up this challenge so the queries change in the fastest mode every 10 seconds.

You can also download the Albert Clock as a free mobile app.

*(via Uncrate)* Read the rest

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

"Before a finger leaves a key, the next key is already being pressed. She is making 9 keystrokes per second."

*(From the Japanese TV series Begin Japanology)*

This is indeed an up-to-the-minute text [PDF], dated Mar 7, 2017. It's written by Googler/MIT prof Eric Lehman, MIT/Akamai scientist F Thomson Leighton and MIT AI researcher Albert R Meyer, as a companion to their Mathematics for Computer Science open course. (*via 4 Short Links*)
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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. Read the rest

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? Read the rest

In 1959 Disney released a 30-minute educational featurette called "Donald in Mathmagic Land." Everything about it is superb - the design, the animation, the music, the narration, and the presentation of the material. I remember watching this in school and realizing how interesting math could be.

From Wikipedia:

Read the restDonald in Mathmagic Land is a 27-minute Donald Duck educational featurette released on June 26, 1959.It was directed by Hamilton Luske. Contributors included Disney artists John Hench and Art Riley, voice talent Paul Frees, and scientific expert Heinz Haber, who had worked on the Disney space shows. It was released on a bill with Darby O'Gill and the Little People. In 1959, it was nominated for an Academy Award (Best Documentary - Short Subjects). In 1961, two years after its release, it was shown as part of the first program of Walt Disney's Wonderful World of Color with an introduction by Ludwig Von Drake. The film was made available to schools and became one of the most popular educational films ever made by Disney. As Walt Disney explained, "The cartoon is a good medium to stimulate interest. We have recently explained mathematics in a film and in that way excited public interest in this very important subject."

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:

Read the restWhen 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. Read the rest

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. Read the rest