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

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.

Professor Jim Al-Khalili investigates one of the most important concepts in the world today - information. He discovers how we harnessed the power of symbols, everything from the first alphabet to the electric telegraph through to the modern digital age. But on this journey he learns that information isn't just about human communication, it's woven very profoundly into the fabric of reality.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.