Mathematics

By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems. Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

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. Marcus also reveals the mysterious code that governs the apparent randomness of mountains, clouds and trees and explores how this not only could be the key to Jackson Pollock's success, but has also helped breathe life into hugely successful movie animations.

brilliant mathematicians, whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide. Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity. Ludwig Boltzmann's struggle to prove the existence of atoms and probability eventually drove him to suicide.

The Pythagorean Theorem is simple: x2 + y2 = z2. In this form, the equation can be solved. But what if the 2 is replaced with any positive integer greater than 2? Would the equation still be solvable? More than 300 years ago, amateur mathematician Pierre de Fermat said no, and claimed he could prove it. Unfortunately, the book margin in which he left this prophecy was too small to contain his thinking. Fermat's Last Theorem has since baffled mathematicians armed with the most advanced calculators and computers. Andrew Wiles methodically worked in near isolation to determine the proof for this seemingly simple equation.

Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

The ultimate adventure in scientific inquiry, this fascinating program follows the exploits of a small group of pioneering mathematicians who discovered a whole area of study that is revolutionizing all branches of understanding in the world: fractal geometry. Fractals are most recognized as a series of circular shapes with a border surrounded by jagged "tail-like" objects. The program, aimed at the average viewer does a fine job of explaining the background of fractals, first by beginning with the story of Pixar co-founder, Loren Carpenter's work at Boeing, developing 3D terrain from scratch using fractals. From there the program starts at the beginning with an introduction to Benoit Mandelbrot and his revolutionary work. The explanations are full of solid factual information but never talk above the level of a viewer who has some understanding of basic mathematical principles. Once the concept is presented the program spends the rest of the time showing how prevalent the fractal is in life. For a program about a mathematical concept, "Fractals" is very engaging, showing how the process was applied to special effects as far back as the Genesis planet from "Star Trek II" all the way to the spectacular finale on Mustafar in "Star Wars: Episode III." I found myself astonished at how fractals were the source of the lava in constant motion and action during the Obi-Wan/Anakin fight. What is more amazing is when the program delves into practical applications such as cell phone antennas, and eventually the human body. For the average person who enjoys watching science related programs, even on a sporadic basis, "Fractals" will prove to be a very worthwhile experience. The program is well produced, integrating talking head interviews (including some with Mandelbrot himself) with standard "in the field" footage. The structure of the program is very logical and never finds itself jumping around without direction. In simplest terms, this is a program as elegant as the designs it focuses on.