At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.

Margaret Wertheim leads a project to re-create the creatures of the coral reefs using a crochet technique invented by a mathematician -- celebrating the amazements of the reef, and deep-diving into the hyperbolic geometry underlying...

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

How counting in Ternary can solve a variant of the Tower's of Hanoi puzzle, and how this gives rise to a beautiful connection to Sierpinski's triangle.

Robert Lang is a pioneer of the newest kind of origami -- using math and engineering principles to fold mind-blowingly intricate designs that are beautiful and, sometimes, very useful.

Is there more than one universe? In this visually rich, action-packed talk, Brian Greene shows how the unanswered questions of physics (starting with a big one: What caused the Big Bang?) have led to the theory that our own universe is...

What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak.

It's moments after the Big Bang and you're still reeling. You're a particle of matter, amidst a chaotic stew of forces, fusion, and annihilation. If you're lucky and avoid being destroyed by antimatter, you'll be the seed of a future...

Moser's circle problem. What is this pattern: 1, 2, 4, 8, 16, 31,...

How a famous theorem in topology, the Borsuk-Ulam theorem, can be used to solve a counting puzzle that seems completely distinct from topology.

This is episode 6 of our animated series "Think Like A Coder." This 10-episode narrative follows a girl, Ethic, and her robot companion, Hedge, as they attempt to save the world. The two embark on a quest to collect three artifacts and...

At the 2008 EG conference, famed puzzle designer Scott Kim takes us inside the puzzle-maker's frame of mind. Sampling his career's work, he introduces a few of the most popular types, and shares the fascinations that inspired some of his...

Knots are everywhere in our daily lives, but a new branch of mathematics is taking things to the next level.

Neuroscientist Daniel Wolpert starts from a surprising premise: the brain evolved, not to think or feel, but to control movement. In this entertaining, data-rich talk he gives us a glimpse into how the brain creates the grace and agility...

Mohamad Jebara loves mathematics -- but he's concerned that too many students grow up thinking that this beautiful, rewarding subject is difficult and boring. His company is experimenting with a bold idea: paying students for completing...

If our sun turned into a black hole, you might think our solar system would be doomed, but in reality that's just not how black holes work.

Mathematician Mark Kac asked the question "Can we hear the shape of a drum?" It was a question that took over 20 years to answer. Sine waves, fundamental frequencies, eigenvalues, this episode has got it all!

How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?