## Numberphile looks at mathematics' undecidable statements

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

## Mathematical conjecture generates beautiful lifelike form

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

## Is mathematics invented or discovered?

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

## The moving sofa math problem: still unsolved 50 years later

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

## This Mondrian math puzzle yields puzzling scores

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

## How a child math prodigy sees numbers as shapes

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

## Mind-blowing explainer on fixed points

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

## Sierra Leone is the roundest country

Gonzalo Ciruelos set out to discover which country was the roundest in shape.

We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem to be.

For that reason, we have to define roundness some other way. We represent countries as a plane region, i.e., a compact set C⊂R2C⊂R2. I will define its roundness as

That's about where I tune out! Turns out the answer is Sierra Leone. Click through to see lots of mathy thingies on the screen, the runners-up, the least round countries, and the source code. Read the rest

## The geometry of fireworks

“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.”

## Pi fleece provides warmth, irrationality

Thinkgeek's Pi Fleece keeps you warm and irrational with the first 413 digits of Pi in machine-washable fleece, measuring 45"x64". Read the rest

## Kickstarting another season of the outstanding Relatively Prime math podcast

Samuel Hansen's fantastic math podcast is everything a technical program should be deep but accessible, thoughtful but funny, and free for all; the new season is on Kickstarter for a few more hours! I put in \$35. Read the rest

## Deep math of the folded pizza slice

Why does a flat pizza slice flop over unless you bend it into a curve? Thank Gaussian curvature, the 19th century mathematical principle that underpins everything from corrugated cardboard to eggshells to Pringles chips. Read the rest

## Rational numbers are impossible!

Brilliant, high-speed math vlogger Vi Hart has revisited the topic of the sizes of infinities. Read the rest

## Online Isaac Newton manuscripts workshop

India's Zetatrek citizen science initiative is online workshop starting on 19th July, where science and math hobbyists from all over the world are invited to study the original manuscripts of Sir Isaac Newton. Read the rest

## Vi Hart on the relative sizes of infinities

Just in time for you to get the most out of "The Fault in Our Stars," the incomparable, fast-talking mathblogger Vi Hart's latest video is a sparkling-clear explanation of one of my favorite math-ideas: the relative size of different infinities. If that's not enough for you, have a listen to this episode of the Math for Primates podcast.

## Mathematics as the basis for leftist reasoning

Chris Mooney of the Inquiring Minds podcast interviewed Jordan Ellenberg about his book How Not to Be Wrong: The Power of Mathematical Thinking, and in a fascinating accompanying post, Mooney investigates whether mathematics are "liberal." His argument is that liberal thought is characterized by "wishy washy" uncertainty and that math professors tend to vote left: Read the rest