Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" -- and how it led mathematicians to conclude that math itself contains unanswerable questions.

Documentary that reveals the secret story behind one of the greatest intellectual feats of World War II, a feat that gave birth to the digital age. In 1943 a 24-year-old maths student and a GPO engineer combined to hack into Hitler's personal super code machine - not Enigma but an even tougher system, which he called his 'secrets writer'. Their break turned the Battle of Kursk, powered the D-day landings and orchestrated the end of the conflict in Europe. But it was also to be used during the Cold War - which meant both men's achievements were hushed up and never officially recognised.

59m • 2011

An algorithm is a method of solving problems both big and small. Though computers run algorithms constantly, humans can also solve problems with algorithms. David J. Malan explains how algorithms can be used in seemingly simple situations and also complex ones.

4m • TED-Ed

John Hendricks, founder of the Discovery Channel and CuriosityStream, explores the largest numbers in the Universe and describes how the average person might be able to comprehend their scale. How can a normal person understand "quadrillion" in real terms?

48m • 2014 • Curiosity Retreats: 2014 Lectures

Pascal’s triangle, which at first may just look like a neatly arranged stack of numbers, is actually a mathematical treasure trove. But what about it has so intrigued mathematicians the world over?

4m • 2015 • TED-Ed

The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.

11m • 2017

Marcus du Sautoy uncovers the patterns that explain the shape of the world around us. Starting at the hexagonal columns of Northern Ireland's Giant's Causeway, he discovers the code underpinning the extraordinary order found in nature - from rock formations to honeycomb and from salt crystals to soap bubbles.

58m • The Code