Dutch artist Piet Mondrian's abstract, rectangular paintings inspired mathematicians to create a two-fold challenge. Can you solve the puzzle and get to the lowest score possible? Gordon Hamilton shows how. [TED-Ed Animation by Anton Trofimov]

The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it's completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people? Jeff Dekofsky solves these heady lodging issues using Hilbert's...

You've stealthily descended into the darkness of a vampire cave, setting a sequence of mirrors as you go. When the sun reaches the right angle in the sky, a beam of light will ricochet along the mirrors, strike a diffuser, and illuminate the great chamber where the vampires sleep. Can you place the diffuser correctly and flood the lair with sunl...

The ratio of a circle's circumference to its diameter is always the same: 3.14159... and on and on (literally!) forever. This irrational number, pi, has an infinite number of digits, so we'll never figure out its exact value no matter how close we seem to get. Reynaldo Lopes explains pi's vast applications to the study of music, financial models...

You and your team have crash-landed on an ancient planet. Can you appease the three alien overlords who rule it and get your team safely home? Created by logician Raymond Smullyan, and popularized by his colleague George Boolos, this riddle has been called the hardest logic puzzle ever. Alex Gendler shows how to solve it. [Directed by Artrake St...

After years of experiments, you've finally created the pets of the future – nano-rabbits! They're tiny, they're fuzzy ... and they multiply faster than the eye can see. But a rival lab has sabotaged you, threatening the survival of your new friends. Can you figure out how to avert this hare-raising catastrophe? Alex Gendler shows how. [Directed ...

You've found Leonardo da Vinci's secret vault, secured by a series of combination locks. Fortunately, your treasure map has three codes: 1210, 3211000, and... hmm. The last one appears to be missing. Can you figure out the last number and open the vault? Tanya Khovanova shows how. [TED-Ed Animation by Artrake Studio].

The villainous Dr. Schrödinger has developed a growth ray and intends to create an army of giant cats to terrorize the city. Your team of secret agents has tracked him to his underground lab. You burst in to find ... that it's a trap! Can you escape from Dr. Schrödinger's lair and save the day? Dan Finkel shows how. [TED-Ed Animation by Artrake ...

One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standa...

As your country's top spy, you must infiltrate the headquarters of the evil syndicate, find the secret control panel, and deactivate their death ray. But your reconnaissance team is spotty, and you have only limited information about the control panel's whereabouts. Can you solve the control room riddle and deactivate their weapon in time? Denni...

The family of giants you work for is throwing a fancy dinner party, but there's a problem — the elder giant's favorite shirt is wrinkled! To fix it, you'll need to power up the giant iron. It needs two batteries to work, but the baby giant mixed the working battery pile with the dead pile. Can you test the batteries so that you get a working pai...

Your team has developed a probe to study an alien monolith. It needs protective coatings — in red, purple and green — to cope with the environments it passes through. Can you figure out how to apply the colors so the probe survives the trip? Dan Finkel shows how. [TED-Ed Animation by Anton Trofimov].

Finding the right mate is no cakewalk -- but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.

Best known as the voice of Roger Rabbit, Charles Fleischer's multi-decade career includes work on stage and on screen, and an online emporium of unusual observations called MonkeyDog.

Your professor has accidentally stepped through a time portal in his physics lab. You've got just a minute to jump through before it closes and leaves him stranded in history. Your only way back is to grab enough colored nodules to create a new portal to open a doorway through time. Can you take the right amount of nodules to get back to the pre...

You and your brother have discovered another realm and set off exploring the new wonderful world. Along the way, you see a troll catching creatures in an enormous net. The troll agrees to release the creatures if you can come up with a statement that is both truth and false. Can you come up with the correct sentence and force the troll to releas...

Townspeople are demanding that a corrupt merchant's collection of 30 rubies be confiscated to reimburse the victims of his schemes. The king announces that the fine will be determined through a game of wits between the merchant and the king's most clever advisor – you. Can you outfox the merchant and win back the greatest amount of rubies to hel...

A consultant to the CIA and the Department of Defense, Bruce Bueno de Mesquita has built an intricate computer model that can predict the outcomes of international conflicts with bewildering accuracy.

Stephen Hawking's scientific investigations have shed light on the origins of the cosmos, the nature of time and the ultimate fate of the universe. His bestselling books for a general audience have given an appreciation of physics to millions.

Want a different perspective of the world? Get a better, more friendly grasp of statistics -- one of the most understood and misused tools in modern society.

After astonishing success as a mathematician, code breaker and billionaire hedge fund manager, Jim Simons is mastering yet another field: philanthropy.

Filmmaker David Hoffman shares footage from his feature-length documentary Sputnik Mania, which shows how the Soviet Union's launch of Sputnik in 1957 led to both the space race and the arms race -- and jump-started science and math education around the world.

By masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses.

"Where do great ideas come from?" Starting with this question in mind, Vittorio Loreto takes us on a journey to explore a possible mathematical scheme that explains the birth of the new. Learn more about the "adjacent possible" -- the crossroads of what's actual and what's possible -- and how studying the math that drives it could explain how we...

Comic author Rob Reid unveils Copyright Math (TM), a remarkable new field of study based on actual numbers from entertainment industry lawyers and lobbyists.

Greg Lynn is the head of Greg Lynn FORM, an architecture firm known for its boundary-breaking, biomorphic shapes and its embrace of digital tools for design and fabrication.

Have you ever sat in a doctor's office for hours, despite having an appointment? Has a hotel turned down your reservation because it's full? Have you been bumped off a flight that you paid for? These are all symptoms of overbooking, a practice where businesses sell or book more than their capacity. So why do they do it? Nina Klietsch explains th...

As an information theorist and computer scientist, David MacKay uses hard math to assess our renewable energy options.

Alex Wissner-Gross applies science and engineering principles to big (and diverse) questions, like: "What is the equation for intelligence?" and "What's the best way to raise awareness about climate change?"

Neil Turok is working on a model of the universe that explains the big bang -- while, closer to home, he's founded a network of math and science academies across Africa.