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Mathematics gets down to work in these talks, breathing life and logic into everyday problems. Prepare for math puzzlers both solved and unsolvable, and even some still waiting for solutions.

Ron Eglash: The fractals at the heart of African designs

When Ron Eglash first saw an aerial photo of an African village, he couldn’t rest until he knew — were the fractals in the layout of the village a coincidence, or were the forces of mathematics and culture colliding in unexpected ways? Here, he tells of his travels around the continent in search of an answer.

How big is infinity?

There are more whole numbers than there are even numbers … right? Actually, there aren’t. This TED-Ed talk makes it crystal clear why not, in a lesson on the infinite infinities and math’s unanswerable questions.

Arthur Benjamin does “Mathemagic”

A whole team of calculators is no match for Arthur Benjamin, as he does astounding mental math in the blink of an eye. But he’s not too worried you’ll steal his show, he says, and so he’s willing to share his secret in this mesmerizing talk.

Scott Rickard: The beautiful math behind the ugliest music

What makes a piece of music beautiful? Pattern and repetition, says Scott Rickard, as he sets out to create just the opposite – a piece mathematically calculated to be totally devoid of repetition. Listen if you dare.

Margaret Wertheim: The beautiful math of coral

The intricate forms of a coral reef can only be expressed through hyperbolic geometry — and the only way humans can model it is by crocheting! Margaret Wertheim and her crew of crotcheters engage the abstract and turn this traditional feminine handicraft into a large-scale environmental statement.

Benoit Mandelbrot: Fractals and the art of roughness

The world is based on roughness, explains legendary mathematician Benoit Mandelbrot. From cauliflower to the human lungs, he shows us objects that defy traditional measurements and consistently inspire curiosity and wonder.

Michael Mitchell: A clever way to estimate enormous numbers

Have you ever tried to guess how many pieces of candy there are in a jar? Physicist Enrico Fermi was very good at problems like these. A guide on how to make reasonable guesses on huge numbers by using the power of 10.

Geoffrey West: The surprising math of cities and corporations

Physicist Geoffrey West sees an urgent need for a scientific theory of cities, and he proposes we look to biology. Using the scaling principles that govern living things, he plots the way that everything – the good, the bad and the ugly – increases as cities grow.